In quadratic functiοn -
g(x) h(x) d(x)
vertical shift dοwn 3 reflectiοn acrοss the x-axis vertical shift dοwn 3
hοrizοntal shift left 3 vertical strecht οf 3 hοrizοntal shift right 3
What is the οperatiοn οf a quadratic functiοn?The expressiοn f(x) = ax² + bx + c, where a, b, and c are all integers with a nοt equal tο zerο, denοtes a quadratic functiοn. The shape that a quadratic functiοn's graph takes οn is called a parabοla.
In spite οf the fact that parabοlas might have οpenings that are upward οr dοwnward, varying "widths" οr "steepnesses," they all have the same basic "U" shape.
Quadratic parent: f(x)=x²
The graph is a parabοla with vertex V=(0,0) at the οrigin and οpens up.
When x=1→f(1)=1²→f(1)=1
1) g(x)
The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.
The vertex is at the pοint (-3,-3): 3 units tο the left and 3 units dοwn οf the vertex οf the parent funtiοn.
When x is 1 unit tο the right frοm the vertex g(x)=1
Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:
1.1) vertical shift dοwn 3.
1.2) hοrizοntal shift left 3.
2) h(x)
The graph οpens dοwn, then there is a reflectiοn acrοss the x-axis.
The vertex is at the οrigin (0,0).
When x is 1 unit tο the right frοm the vertex h(x)=-3
Then the transfοrmatiοns were applied tο the quadratic parent functiοn are:
2.1) reflectiοn acrοss the x-axis.
2.2) vertical strecht οf 3.
3) d(x)
The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.
The vertex is at the pοint (3,-3): 3 units tο the right and 3 units dοwn οf the vertex οf the parent funtiοn.
When x is 1 unit tο the right frοm the vertex d(x)=1
Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:
3.1) vertical shift dοwn 3.
3.2) hοrizοntal shift right 3.
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The complete question is -
The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. Determine which transformations were applied to the quadratic parent function to result in each graph.
Transcranial magnetic stimulation (TMS) is a noninvasive method for studying brain function, and possibly for treatment as well. In this technique, a conducting loop is held near a person's head. When the current in the loop is changed rapidly, the magnetic field it creates can change at a rate of 3.00 104 T/s. This rapidly changing magnetic field induces an electric current in a restricted region of the brain that can cause a finger to twitch, a bright spot to appear in the visual field, or a feeling of complete happiness to overwhelm a person. If the magnetic field changes at the previously mentioned rate over an area of 1.75 10-2 m2, what is the induced emf?
The induced emf in a region of the brain when a conducting loop is held near a person's head and the current in the loop is changed rapidly, is equal to -525 V.
The induced emf can be calculated using Faraday's law of electromagnetic induction, which states that the emf induced in a loop of wire is equal to the rate of change of magnetic flux through the loop.
The magnetic flux (Φ) is equal to the product of the magnetic field (B) and the area (A) through which it passes. Therefore, the induced emf (ε) is given by:
ε = -dΦ/dt ⇒ -B dA/dt.
Where the negative sign indicates that the emf is induced in a direction that opposes the change in magnetic flux.
In this problem, the magnetic field changes at a rate of 3.00 × 10^4 T/s over an area of 1.75 × 10^-2 m^2. Therefore, the induced emf is:
Plugging in our values, we get:
E = (-3.00 10^4 T/s)(1.75 10^(-2) m^2)/(1 s)
E = -525 V
Therefore, the induced emf, in this case, is -525 V. Here, the negative sign shows that the emf is induced in a direction that opposes the change in magnetic flux
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Can someone help me? I’m not sure what to do.
Step-by-step explanation:
A. To find f(x+h), we substitute (x+h) for x in the equation f(x) = 4x + 7:
f(x+h) = 4(x+h) + 7
Expanding the brackets:
f(x+h) = 4x + 4h + 7
Simplifying, we get:
f(x+h) = 4x + 7 + 4h
Therefore, f(x+h) = 4x + 7 + 4h.
B. To find f(x+h)-f(x)/h, we use the formula for the difference quotient:
[f(x+h) - f(x)] / h
Substituting the expressions we derived earlier:
[f(x+h) - f(x)] / h = [(4x + 7 + 4h) - (4x + 7)] / h
Simplifying, we get:
[f(x+h) - f(x)] / h = (4x + 4h - 4x) / h
Canceling out the 4x terms, we get:
[f(x+h) - f(x)] / h = 4h / h
Simplifying further, we get:
[f(x+h) - f(x)] / h = 4
Therefore, f(x+h)-f(x)/h = 4.
What is the next fraction in this sequence? Simplify your answer. 13/ 21 , 9/ 14 , 2/ 3 , 29 /42 ,
Answer:
5/7
Step-by-step explanation:
Make all the denominators 42.
26/42, 27/42, 28/42, 29/42
The pattern is the numerator increases by one each time.
30/42 = 5/7
Hope this helps!
b) The nearest-known exoplanet from earth is 4.25 light-years away.
About how many miles is this?
Give your answer in standard form.
The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
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The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5
The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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what is the percentage of 28% of n is 196
Answer:
700
Step-by-step explanation:
28 % of n = 28/100 x n = 0.28n
If 28% of n = 196 that means
0.28n = 196
Divide both sides by 0.28
0.28n/0.28 = 196/0.28
n = 700
which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.
The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.
What is Stratified random sampling?Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.
Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.
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Which of the following subsets of M3(R) are subspaces of M3(R)? (Note: M3(R) is the vector space of all real 3 x 3 matrices)
A. The 3×3 matrices in reduced row-echelon form
B. The 3×3 matrices with all zeros in the third row
C. The diagonal 3×3 matrices
D. The invertible 3×3 matrices
E. The non-invertible 3×3 matrices
F. The symmetric 3×3 matrices
The subsets B. The 3×3 matrices with all zeros in the third row. C. The diagonal 3×3 matrices, and F. The symmetric 3×3 matrices are subspaces of M3(R).
What is a subspace?A subspace of a vector space is a portion of that space that meets the three criteria of closure under addition, closure under scalar multiplication, and the presence of the zero vector. If two vectors from the subspace are added, the resultant vector will still be in the subspace because of closure under addition. If a vector from the subspace is multiplied by any scalar, the resultant vector will still be in the subspace, according to the concept of closure under scalar multiplication.
The conditions of a subspace are: closure under addition, closure under scalar multiplication, and contains the zero vector.
For all the options we have:
A: The 3 x 3 matrices in reduced row-echelon form (A): As this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
B. The 3 x 3 matrices with all zeros in the third row: Due to its closure under addition and scalar multiplication as well as the presence of the zero vector, this subset is a subspace of M3(R).
C. The diagonal 3 x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
D. The invertible 33 matrices: Because this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
E. The 3 x 3 matrices that are not invertible Due to the fact that it is not closed under scalar multiplication, this subset is not a subspace of M3(R).
F. The symmetric 3x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
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In the coordinate plane, the points X9, 5, Y−−3, 6, and Z−8, 4 are reflected over the x-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
Answer:
When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is multiplied by -1.
So, the coordinates of X' are (9, -5) since the x-coordinate remains the same and the y-coordinate is multiplied by -1.
Similarly, the coordinates of Y' are (-3, -6) and the coordinates of Z' are (-8, -4).
Therefore, X′ is (9,−5), Y′ is (−3,−6), and Z′ is (−8,−4).
The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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There are two coins in a bin. When one of them is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3. One of these coins is to be chosen at random and then flipped. a) What is the probability that the coin lands on heads? b) The coin lands on heads. What is the probability that the chosen coin was the one that lands on heads with probability 0.6?
When one of the coin is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3, then the probability that the coin lands on heads is 0.45 and the coin lands on heads but the probability that the chosen coin was the one that lands on heads with probability 0.6 is 0.67.
a) The probability of getting heads, we can use the law of total probability.
There are two coins, and each has a probability of landing on heads. So we can calculate the probability of getting heads by weighting each coin's probability by its probability of being chosen.
Therefore,
P(heads) = P(heads from coin 1) * P(choose coin 1) + P(heads from coin 2) * P(choose coin 2)
Plugging in the values, we have:
P(heads) = 0.6 * 0.5 + 0.3 * 0.5 = 0.45
Therefore, the probability of getting heads is 0.45.
b) The probability that the chosen coin was the one that lands on heads with probability 0.6, given that the coin lands on heads, we need to use Bayes' theorem. Specifically, we have:
P(choose coin 1 | heads) = P(heads from coin 1 | choose coin 1) * P(choose coin 1) / P(heads)
Plugging in the values, we have:
P(choose coin 1 | heads) = 0.6 * 0.5 / 0.45 = 0.67
Therefore, the probability that the chosen coin was the one that lands on heads with probability 0.6, given that the coin lands on heads, is 0.67.
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Given that a=14 and b=25, work out the height of the triangle
The height of the triangle is 1.12 units (rounded to two decimal places).
The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.
We can use the formula for the area of a triangle:
Area = (1/2) * base * height
And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):
h = (2a) / b
Plugging in the values of a and b:
h = (2 * 14) / 25
h = 28 / 25
Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).
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A 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5 gram tennis ball is dropped from the same 3 meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9, determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls. (Balls meet at 0.5073 m above ground, final height of tennis ball = 12.6 m above the ground)
Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,
determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.
The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.
Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9
The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.
When a ball falls from height, it gains potential energy.
Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height
PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules
Initial kinetic energy (KE) = PE of Basketball
KE of Basketball = 18.4 J
Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.
Using the coefficient of restitution (e) we can find the velocity of the balls after collision
v1 - v2 = -e(u1 - u2)
Initial momentum (P) = Final momentum (P)
before the collision P = m1u1 + m2u2
after collision P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P
= (0.625 kg * v1) + (0.0585 kg * v2)
Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)
Here, m1 = mass of basketball
= 0.625 kg,
m2 = mass of tennis ball
= 0.0585 kg,
u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)
Also given that the time taken by the balls to meet is 0.15 seconds
Let h be the height to which the tennis ball bounces after the collision.
When the tennis ball bounces to height h, it gains potential energy.
KE + PE = Total energy
= Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h
= (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²
= (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²
= (1/2) * u2² - g * h
Substituting the values of u1, u2, m1, m2, e, t and g, we get:
v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1
= 1.96 m/sv2
= (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2
= 5.5 m/s
Here, u1 = u2 = 0.
Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J
= -0.286 J - 0.572 h0.572 h
= -12.83 J / 2h
= -12.83 J / (2 * 0.572)
= 11.2 m
Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.
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Which graph represents this equation? [tex]y=\frac{3}{2}x^{2}-6x[/tex]
I know the answer is C. What I want to know is WHY.
The x-intercepts are (0, 0) and (4, 0), and the y-intercept is (0, 0).
Why are equatiοns graphed?By graphing linear equatiοns, yοu can explain the relatiοnship between twο variables visually. We can easily see what happens tο οne variable as the οther grοws by using a graph. The value οf the x variable rises as we mοve tο the right οn a graph.
[tex]y = (3/2)x^2 - 6x[/tex] is the given equatiοn.
We can use the fοrmula tο find the x-cοοrdinate(s) οf the vertex οf this parabοla:
x = -b/2a
where a and b are the cοefficients οf the equatiοn's x² and x terms, respectively.
In this case, a = 3/2 and b = -6, resulting in:
x = -(-6)/(2*3/2) = 4
As a result, the vertex's x-cοοrdinate is 4.
Tο find the y-cοοrdinate οf the vertex, enter this value οf x intο the fοllοwing equatiοn:
[tex]y = (3/2)(4)^2 - 6(4) = -12[/tex]
As a result, the parabοla's vertex is at the pοint (4, -12).
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$2$ white balls and $5$ orange balls together weigh $8$ pounds. $6$ white balls and $3$ orange balls together weigh $20$ pounds.
What is the weight of $4$ white balls and $4$ orange balls together, in pounds?
Let's break this problem down step by step.
First, we can work out the weight of one white ball by subtracting the weight of 6 white and 3 orange balls (20 pounds) from the weight of 2 white and 5 orange balls (8 pounds):
Weight of 1 white ball = 8 - 20 = -12
Next, we can work out the weight of one orange ball by subtracting the weight of 2 white and 5 orange balls (8 pounds) from the weight of 6 white and 3 orange balls (20 pounds):
Weight of 1 orange ball = 20 - 8 = 12
Now that we know how much one white and one orange ball weigh, we can work out the weight of 4 white and 4 orange balls together:
Weight of 4 white and 4 orange balls = (4 x -12) + (4 x 12) = 0
Therefore, the weight of 4 white and 4 orange balls together is 0 pounds.
By solving two given simultaneous equations using algebra, we find that the combined weight of 4 white balls and 4 orange balls is 16 pounds.
Explanation:The subject matter of this question pertains to simultaneous equations. The equations in question are, 2w + 5o = 8 and 6w + 3o = 20, where w stands for the weight of a white ball and o stands for the weight of an orange ball. We can solve these equations to find the individual weights of these balls. After finding these values, we substitute these into a new equation, 4w + 4o, to find the total weight of 4 white and 4 orange balls together. By solving these equations, we find that the weight of 4 white balls and 4 orange balls together is 16 pounds.
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Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent
Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.
To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.
The purchase price for 1,000 shares of stock was:
$35.50 x 1,000 = $35,500
The selling price for 1,000 shares of stock was:
$55.10 x 1,000 = $55,100
The capital gain is the difference between the selling price and the purchase price:
$55,100 - $35,500 = $19,600
To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:
($19,600 / $35,500) x 100 = 55.21%
In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.
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Find m ∠ R . Use the Picture
m∠R is therefore 76 degrees as a triangle's total sides equal 180 degrees.
what is angle ?The degree of rotation between two lines or two planes around a central point is measured by an angle. Typically, it is expressed in radians or degrees. Angles are used in many mathematical and scientific uses, including trigonometry, physics, and engineering, where they are crucial in determining the shape and characteristics of geometric figures. Angles come in four different varieties: acute (less than 90 degrees), right (exactly 90 degrees), oblique (more than 90 degrees), and straight (exactly 180 degrees).
given
Because a triangle's total sides equal 180 degrees, we have:
R, S, and T add up to 180.
Inputting the numbers provided yields:
m∠R + 72 + 32 = 180
Simplifying the equation:
m∠R = 76
m∠R is therefore 76 degrees as a triangle's total sides equal 180 degrees.
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Find a particular solution to the differential equation day dy 8 dt + 20y = 68 – 20t dt2 You do not need to find the general solution. y(t) = symbolic expression
The particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
To solve the given differential equation, we'll need to use the method of undetermined coefficients. In this method, we assume that the particular solution to the differential equation has the same form as the forcing term. Here's how we can solve the given differential equation: Identify the forcing term and its derivatives. The forcing term is given by: f(t) = 68 - 20tWe can find its first derivative as follows: f'(t) = -20We can find its second derivative as follows: f''(t) = Guess the form of the particular solution We assume that the particular solution has the same form as the forcing term.
Since the forcing term is a first-degree polynomial, we assume that the particular solution also has the form of a first-degree polynomial: y_ p(t) = At + B Here, A and B are constants that we need to determine. Find the derivatives of the assumed form of the particular solution. Here are the first and second derivatives of the assumed form of the particular solution: y_ p(t) = At + B ==> y_ p'(t) = A ==> y_ p''(t) = 0. Substitute the assumed form of the particular solution and its derivatives into the differential equation Substituting y_ p(t), y_ p'(t), and y_ p''(t) into the differential equation, we get:8A + 20(At + B) = 68 - 20t Simplifying the above equation, we get: (8A + 20B) + (20A - 20)t = 68Comparing the coefficients of t and the constant terms on both sides,
we get two equations:8A + 20B = 68 (1)20A - 20 = 0 (2)Solving equation (2) for A, we get: A = 1 Substituting A = 1 into equation (1), we get:8 + 20B = 68Solving for B, we get: B = 3. Write the particular solution to the differential equation Substituting A = 1 and B = 3 into the assumed form of the particular solution, we get :y_ p(t) = t + 3Therefore, the particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
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The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?
Answer:
Step-by-step explanation: In the problem, they tell us that
dL / dt = 7 cm/s (the rate at which the length is changing) and
dw / dt = 8 cm/s (the rate at which the width is changing)
Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm
The equation for the area of a rectangle is:
A = L·w, so will need the product rule when taking the derivative.
dA/dt = L (dw/dt) + w (dL/dt)
Now just plug in all of the given numbers:
dA/dt = (7)(7) + (5)(8) = 49+40 = 89 cm²/s
there are 2 coins in a bin. when one of them is flipped it lands on heads with probability 0.6 and when the other is flipped it lands on heads with probability 0.3. one of these coins is to be randomly chosen and then flipped. without knowing which coin is chosen, you can bet any amount up to 10 dollars and you then either win that amount if the coin comes up heads or lose if it comes up tails. suppose, however, that an insider is willing to sell you, for an amount c, the information as to which coin was selected. what is your expected payoff if you buy this information? note that if you buy it and then bet x, then you will end up either winning x - c or -x - c (that is, losing x c in the latter case). also, for what values of c does it pay to purchase the information? reference: https://www.physicsforums/threads/expected-payoff-given-info.200076/
It pays to purchase the information for any value of c less than $13.25 then we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
To calculate it Let C1 be the event that the first coin is selected and C2 be the event that the second coin is selected. Then, we have:
P(C1) = P(C2) = 1/2 (since one of the two coins is randomly chosen)
P(H|C1) = 0.6 (probability of getting heads when the first coin is flipped)
P(H|C2) = 0.3 (probability of getting heads when the second coin is flipped)
Let's consider the case when we do not buy the insider's information. Then, our expected payoff can be calculated as follows:
E(X) = P(C1) * P(H|C1) * (10) + P(C1) * P(T|C1) * (-10) + P(C2) * P(H|C2) * (10) + P(C2) * P(T|C2) * (-10)
= (1/2) * (0.610 - 0.410 + 0.310 - 0.710)
= -1
Therefore, if we do not buy the insider's information, our expected payoff is a loss of $1.
Now, let's consider the case when we buy the insider's information for an amount c.
If we buy the information, we will know which coin was selected and we can bet accordingly to maximize our expected payoff.
If we know that the first coin was selected, we should bet on heads since it has a higher probability of occurring. If we know that the second coin was selected, we should bet on tails since it has a higher probability of occurring.
Therefore, if we buy the insider's information, our expected payoff can be calculated as follows:
E(X|buying information) = P(C1) * P(H|C1) * (10-c) + P(C1) * P(T|C1) * (-c) + P(C2) * P(H|C2) * (-c) + P(C2) * P(T|C2) * (10-c)
= (1/2) * (0.6*(10-c) - 0.4c + 0.3(-c) - 0.7*(10-c))
= -0.2c + 1.5
To find the values of c for which it pays to purchase the information, we need to solve the inequality:
E(X|buying information) > E(X)
-0.2c + 1.5 > -1
Solving for c, we get:
c < 13.25
Therefore, it pays to purchase the information for any value of c less than $13.25. If we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
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If the weight of the package is multipled by 5/7 the result is 40. 5. How much does the package weigh
The weight of the package is 56 using arithmetic operations.
What is multiplication?Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the numbers.
let weight of package be= x
x*5/7=40
x=(40*7)/5
x=56
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Factorise fully - 4x² - 16x
Answer: 4x(x - 4)
Step-by-step explanation:
4x² - 16x = 4x(x - 4)
Now we can see that the expression inside the parentheses can also be factored:
x - 4 = (x - 4)
So the fully factorized expression is:
4x² - 16x = 4x(x - 4) = 4x(x - 4)
Answer:
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- 4x( x + 4 )
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Step-by-step explanation:
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[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]
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[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]
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[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
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[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.
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[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.
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[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.
list the sides of ΔRST in ascending order
m∠R=2x+11°, m∠S=3x+23°, m∠T=x+42°
pls help
Answer:
Step-by-step explanation:
[tex]\angle R+\angle S+ \angle T =180[/tex] (angle sum of a triangle is 180°)
[tex]2x+11+3x+23+x+42=180[/tex]
[tex]6x+76=180[/tex]
[tex]6x=104[/tex]
[tex]x=17.667[/tex]
[tex]\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667[/tex]
In ascending order:
[tex]\angle R= 46.33,\angle T=59.667,\angle S=76[/tex]
Fatima 56 roses, 48 irises and 16 freesia. she wants to create bouquets using all the flowers. calculate the highest number of similar bouquets she can make without having any flowers left over
Answer:
We see that each fraction is in simplest form, and they add up to 1, so this confirms that 168 is the highest number of similar bouquets that Fatima can make without having any flowers left over.
Step-by-step explanation:
Yeah, I guess what that person said ^^ ??
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that of high schoolers in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be x1 = 6 hours, with a standard deviation s1 = 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be x2 = 4 hours, with a standard deviation s2 = 2 hours. Let u1 and u2 represent the mean amount of time spent in extracurricular activities per week by the populations of all high school students in the suburban and city school districts, respectively.
Assume the two-sample t-procedures are safe to use. With a level of 5%, test the hypothesis that the amount of time spent on extracurricular activities is no different in the two groups.
Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis.
What is null hypothesis?In statistical hypothesis testing, the null hypothesis is a statement about a population parameter that is assumed to be true until there is sufficient evidence to suggest otherwise. The null hypothesis is typically denoted by H0 and represents the status quo or default assumption.
The null hypothesis often takes the form of an equality or a statement of "no difference" or "no effect" between two or more groups, variables, or populations. For example, the null hypothesis could be that the mean score of a group of students on a test is equal to a certain value, or that there is no difference in the average height of males and females in a population.
We want to test the hypothesis that the mean amount of time spent in extracurricular activities per week is the same in the suburban and city school districts. Set up the null and alternative hypotheses is as given by:
Null hypothesis: u1 - u2 = 0
Alternative hypothesis: u1 - u2 ≠ 0
To test this hypothesis, we can use a two-sample t-test. We first calculate the test statistic:
t = ((x1 - x2) - (u1 - u2)) / √(s1²/n1 + s2²/n2)
where x1, s1, and n1 are the sample mean, standard deviation, and sample size for the suburban school district, and x2, s2, and n2 are the sample mean, standard deviation, and sample size for the city school district.
Plugging in the values, we get:
t = ((6 - 4) - 0) / √((3²/60) + (2²/40)) ≈ 3.14
This test's degrees of freedom are given by:
df = (s1²/n1 + s2²/n2)² / ( (s1²/n1)² / (n1 - 1) + (s2²/n2)² / (n2 - 1) )
Plugging in the values, we get:
df = ((3²/60) + (2²/40))² / ( (3²/60)² / 59 + (2²/40)² / 39 ) ≈ 93.24
Using a t-distribution table with 93 degrees of freedom and a level of significance of 0.05, we find the critical values to be approximately -1.98 and 1.98.
Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean amount of time spent in extracurricular activities per week is different between the suburban and city school districts.
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the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error
Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
How do we find the error?Given:
Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%
Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%
The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
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FOR 50 POINTS AND BRAINLIEST!! PLEASE HELP ASAP! thank you :)
Answer :
1. We are given with a parallelogram whose opposite sides are :-
PS = (-1 + 4x) RQ = (3x + 3)We know that opposite sides and angles of the parallelogram are equal.
PS = RQ
[tex] \implies \sf \: (-1 + 4x) = (3x + 3) \\ [/tex]
[tex] \implies \sf \: 4x - 3x = 3 + 1\\ [/tex]
[tex] \implies \sf \: x = 4 \\ [/tex]
Length of RQ is (3x + 3)
Substituting value of x = 4 in RQ.
[tex] \implies \sf \: (3x +3) \\ [/tex]
[tex] \implies \sf \: 3(4) + 3 \\ [/tex]
[tex] \implies \sf \: 12 + 3 \\ [/tex]
[tex] \implies \sf \: 15 \\ [/tex]
Therefore, Length of RQ will be 15
2. Find [tex] \sf \angle G [/tex]
We are given with :-
[tex] \sf \angle G [/tex] = 5x - 9 [tex] \sf \angle E [/tex] = 3x + 11Since, Opposite angles of parallelogram are also equal :
[tex]\angle G = \angle E \\ [/tex]
[tex]\implies \sf \: 5x -9 = 3x + 11 \\ [/tex]
[tex]\implies \sf \: 5x - 3x = 11 +9 \\ [/tex]
[tex] \implies \sf \: 2x = 20 \\ [/tex]
[tex] \implies \sf \: x = \dfrac{20}{10} \\ [/tex]
[tex] \implies \sf \: x = 10 \\ [/tex]
Since [tex] \sf \angle G [/tex] is 5x - 9.
Substituting value of (x = 10) in [tex] \sf \angle G [/tex]
[tex] \implies \sf \: 5(10) - 9 \\ [/tex]
[tex] \implies \sf \: 50 -9 \\ [/tex]
[tex] \implies \sf \: 41 \\ [/tex]
Therefore, [tex] \sf \angle G [/tex] is 41.
Answer:
19. QR = 15 units.
20. m ∡G=41°
Step-by-step explanation:
The properties of a parallelogram are:
Opposite sides are parallel: This means that the two sides opposite each other in a parallelogram are parallel, which means they have the same slope and will never intersect.Opposite sides are equal in length: This means that the two sides opposite each other in a parallelogram are the same length.Opposite angles are equal: This means that the two angles opposite each other in a parallelogram are the same measure.Consecutive angles are supplementary: This means that the sum of any two consecutive angles in a parallelogram is 180 degrees.Diagonals bisect each other: This means that the diagonals of a parallelogram intersect at their midpoint.Each diagonal divides the parallelogram into two congruent triangles: This means that the two triangles formed by a diagonal of a parallelogram are the same size and shape.Question No. 19.
We know that the opposite side of parallelogram is equal, So
PS=QR
-1+4x=3x+3
First of all we will find the value of x.
-1 + 4x = 3x + 3
Subtracting 3x from both sides, we get:
x - 1 = 3
Adding 1 to both sides, we get:
x = 4
SO, QR=3*4+3=15
Side QR is 15 units.
Question No. 20.
We know that the opposite angle of parallelogram is equal, So
EF=GD
3x+11=5x-9
Subtracting 3x from both sides:
3x + 11 - 3x = 5x - 9 - 3x
11 = 2x - 9
Next, we can add 9 to both sides to isolate the variable term on one side:
11 + 9 = 2x - 9 + 9
20 = 2x
Finally, we can solve for x by dividing both sides by 2:
20/2 = 2x/2
x=10
Now
m ∡G=5x-9=5*10-9=41°
therefore m ∡G=41°
What is the image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the
origin?
The image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin is given as follows:
(-1, 3).
What is a dilation?A dilation is a transformation that changes the size of a figure, but not its shape. Specifically, a dilation is a type of similarity transformation that involves multiplying the coordinates of each point in a figure by a scale factor. This causes the figure to either enlarge or reduce in size.
The scale factor in the context of this problem is given as follows:
1/2.
The coordinates of the original point are given as follows:
(-2, 6).
Multiplying the coordinates of the original point by the scale factor, the coordinates of the image are given as follows:
(-1,3).
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Solve for x and y 100 points
The solution to the system of equations is x = 16/5 and y = 11/5.
What are the four equation systems?Graphing, substitution, elimination, and matrices are the four methods for solving systems of equations.
Using the substitution method, we can find x and y.
To begin, let us solve the first equation for x:
2x + 3y = 13
2x = 13 - 3y
x = (13 - 3y)/2
This expression for x can now be substituted into the second equation:
x - y = 1
[(13 - 3y)/2] - y = 1
To remove the denominator, multiply both sides by 2:
13 - 3y - 2y = 2
Simplifying:
13 - 5y = 2
Taking 13 off both sides:
-5y = -11
-5 divided by both sides:
y = 11/5
Now that we've discovered y, we can plug it back into either of the original equations to find x. Let's look at the first equation:
2x + 3y = 13
2x + 3(11/5) = 13
To eliminate the fraction, multiply both sides by five:
10x + 33 = 65
Taking 33 away from both sides:
10x = 32
Divide both sides by ten:
x = 16/5
As a result, the system of equations solution is x = 16/5 and y = 11/5.
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David is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, he can work no more than 16 total hours and must earn no less than $160. Also, he must work at most 13 hours landscaping. If
� x represents the number of hours landscaping and �y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer: One possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
Step-by-step explanation:
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
lua
Copy code
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
The vertices of the feasible region are (0, 16), (12.3, 3.7), and (13, 0).
To determine one possible solution, we can evaluate the objective function (total earnings) at each vertex:
(0, 16): 13(0) + 8(16) = $128
(12.3, 3.7): 13(12.3) + 8(3.7) ≈ $167.1
(13, 0): 13(13) + 8(0) = $169
Therefore, one possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
