The largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].
It is given to us that -
The rectangle has the base on x-axis
The rectangle has its upper vertices on the curve [tex]y = 8 -x^{2}[/tex] ----- (1)
We have to find out the largest possible area for the rectangle with given specifications.
We know that the area of a rectangle can be represented as -
[tex]A = xy[/tex] ---- (2)
where,
[tex]x =[/tex] length of the base of the rectangle
[tex]y =[/tex] vertices of the curve = width of the rectangle
Since it is given to us that the rectangle has it base on the x-axis, therefore the length of the base of the rectangle = [tex]2x[/tex] ---- (3)
Substituting equations (1) and (3) in equation (2), we have
[tex]A = xy\\= > A = (2x)(8-x^{2}) \\= > A = 16x-2x^{3}[/tex]----- (4)
For the largest possible area, we know that -
[tex]\frac{dA}{dx}=0[/tex] ---- (5)
Substituting equation (4) in equation (5), we have
[tex]\frac{dA}{dx}=0\\= > \frac{d}{dx}(16x-2x^{3}) =0\\ = > \frac{d}{dx}(16x)-\frac{d}{dx}(2x^{3} )=0\\= > 16-6x^{2} =0\\= > 6x^{2} =16\\= > x^{2} =\frac{16}{6} \\= > x=\frac{4}{\sqrt{6} }[/tex]------ (6)
To find out the largest possible area, we have to put the value of x from equation (6) in the area of the rectangle in equation (4). So, we have
[tex]A = 16x-2x^{3}\\= > A = (16*\frac{4}{\sqrt{6} }) -[2(\frac{4}{\sqrt{6} } )^{3} ]\\= > A = \frac{16*4}{\sqrt{6} } -\frac{2*4*4*4}{\sqrt{6}*\sqrt{6}*\sqrt{6} } \\= > A = \frac{64\sqrt{6} }{9}[/tex]
Therefore, the largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].
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Write an equation in point-slope form of the line that passes through the given point with the given slope.
(-3, -5); m = -2
Answer:
y+5 = -2(x+3)
Step-by-step explanation:
y-(-5) = -2(x-(-3)
y+5 = -2(x+3)
y +5 = -2x - 6
y = -2x - 6 - 5
y = -2x - 11
Consider the discrete probability distribution to the right when answering the following question. Find the probability that x equals 5x2568P (x)0.16?0.30.21
In the discrete distribution the probability that x equals 5 is 0.51
A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum
The summation of the discrete probabilities must be always equal 1,
The probaility of 2 is 0.16
The probaility of 6 is 0.30
The probaility of 8 is 0.21
We need to find The probaility of 5
To find the probaility of 5, we can subtract the probaility of all other numbers from 5.
Probability (X = 5) = 1 - (0.25+0.16+0.08) = 0.51
Therefore, in the discrete probability distribution the probability that x equals 5 is 0.51
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You have at most 7 hours to spend playing soccer and swimming. You
want to spend at least 2 hours playing soccer and more than 2 hours
swimming. Write and graph a system that represents the situation. Give
one example of the amount of time you can spend on each activity.
Answer:
Step-by-step explanation:
an object rolls without slipping onto a surface where the coefficient of friction between object and surface is twice as great as that needed to prevent slipping. part a describe the subsequent motion.
The object continues to roll without slipping, and the actual force of static friction stays constant.
What is static friction?A force that holds an object at rest is called static friction.
The definition of static friction is: The resistance people feel when they attempt to move a stationary object across a surface without actually causing any relative motion between their body and the surface they are moving the object across.
The range of static friction is 0 to the minimum force required to initiate motion.
The following is the formula to determine static friction: Normal Force x Static Friction Coefficient = Static Friction.
So, in the given situation the object keeps rolling without slipping, and the static friction's actual force remains constant.
Therefore, the object continues to roll without slipping, and the actual force of static friction stays constant.
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Which grade is best in school?
A (C)
B (A-)
C (A)
D(B+)
I think its B+ because B stands for Best, and the + equals means advanced best I got it wrong, please help.
Answer:
I didn't know kindergardeners had Brainly.
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
129723
Explanation:
[tex]1800(1+0.13)^{35} \approx 129723[/tex]
The sum of two numbers is 33, and the sum of 7 times the first number and 5 times the second number is 197.
Answer: First number is 16, second number is 17.
Step-by-step explanation
16 + 17 = 33
16 x 7 = 112
17 x 5 = 85
112 + 85 = 197
Please help me out, thanks.
calcule el valor de los materiales consumidos si una empresa al inicio de año tiene una existencia en almacen de 15,000 pesos. Durante el ejercicio realiza unas compras de 25,000 pesos. Al final del ejercicio quedan en el almacen existencias por 8,000 pesos
The final answer to this Problem is 32000 pesos.
What is Company?
A company is an organization that provides goods or services to its customers in exchange for money. Companies are typically formed by entrepreneurs or business owners who have a vision for a product or service they want to offer. The company is responsible for producing the product or service, marketing it, and then distributing and selling it to the public. Companies must also manage their finances and comply with any legal or regulatory requirements. Companies are typically owned by shareholders who reap the profits of the business. Successful companies often have a strong corporate culture that is reflected in their mission and values.
Pesos that initially was available = 15000 pesos
During year Pesos purchased by company = 25000 pesos
Total pesos at end of the year = 15000 + 25000 pesos = 40000 pesos
Total pesos remaining at end of year = 8000 pesos
Hence pesos consumed in the complete year = 40000 - 8000= 32000 pesos
Hence 32000 pesos are left in the company
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PLEASE HELP!!! 50 points!!!!!!
System A:
5x + 3y = 2
4x + 3y = 1
The system has no solution.
The system has a unique solution:
Equation:____________
The system has infinite solutions
System B:
y = 5x + 8
y = 5x + 5
The system has no solution.
The system has a unique solution:
Equation:____________
The system has infinite solutions
System A: (1, -1)
System B: No solution
Answer:
System A
The system has a unique solution: x=1, y=-1
System B
The system has no solution
Step-by-step explanation:
System A
Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:
5x + 3y = 2
-4x - 3y = -1
We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1
If x=1:
5+3y=2
3y=-3
y=-1
Since we have specific answers for x and y, we can say the system has a unique solution.
System B
If y is equal to both 5x+8 and 5x+5, that means
5x+8=5x+5
Subtracting 5x from both sides we get 8=5, which is illogical.
Therefore the system has no solution
Hi, i wa wondering if anyone could explain why -3^2 i -9, but (-3)^2 i 9. Int the anwer found through the ame proce?
Given two calculations are different.
What is a square of a number?
The square of any number can be calculated by multiplying the number by itself twice.
Let 'a' be any number then the square of this number 'a' will be
a² = a × a
Now - 3² = - (3) × (3)
= -9 ----------(I)
and (-3)² = (-3) × (-3)
= 9 ----------(II)
By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.
But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.
Hence, These two calculations are different.
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The function f(x) has a domain of [-5, 2] and a range of [-3, 6]. If f(x) is reflected over the y-axis, horizontally translated 3 units to the right and vertically stretched by a factor of 2, what will the domain and range of the transformed graph be? Group of answer choices
The domain and the range of the transformed graph are given as follows:
Domain: [1,8].Range: [-6,12].What are the domain and the range of a function?The definitions of the domain and of the range of a function are given as follows:
Domain: input values -> values of x.Range: output values -> values of y.After the reflection over the y-axis, the domain of the function is of:
[-2,5].
(as the reflection over the y-axis changes the signal of the x-values of the function).
After the translation of 3 units right, the domain of the function is of:
[1,8].
As the translation adds 3 to each value of x of the function.
After the vertical stretch by a factor of 2, the range of the function is of:
[-6,12].
As the stretch means that all the output values of the function are multiplied by 2.
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Sheila gained 20 pounds in 9 1/2
Months. Find Sheila’s rate of gaining weight in pounds per month
Answer:
About 2.1 pounds a month.
Step-by-step explanation:
In this question, we know the amount of weight gained and the time it took, 20 pounds and 9.5 months.
to find the rate, we can do:
20/9.5
about 2.1
So, the answer will be:
about 2.1 pounds / month
points a (3, 3) and b (3, 6) are two vertices of rectangle abcd. the rectangle is dilated by a scale factor of 1/3. what are the coordinates of a'?
The coordinates of a' after scaling factor of 1/3 is a'(1,1).
Given:
points a (3, 3) and b (3, 6) are two vertices of rectangle abcd. the rectangle is dilated by a scale factor of 1/3.
Rectangle:
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.
Scale factor :
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
scale factor = 1/3
= (3*1/3 , 3*1/3)
= (3/3 , 3/3)
= (1,3/3)
= (1,3)
Therefore the coordinates of a'(1,1).
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8. Divide-2x³-4x² + 3x + 2 by x-3. (1 point)
-2x²10x-27, R-79
-2x²10x-27
-2x²10x - 27, R 83
-2x²10x + 27, R 83
The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28
What does it mean to divide polynomials?A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.
How do you divide polynomials?Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).
Divide the divisor by the outcome you just got (the first term of the eventual quotient).
By following the above rules where
2x3-4x2+3x+2 is divided by the x-3, We get the following equation
where
quotient is 2x2+2x+10
and the remainder is 28
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A line with the slope of 10/17 passes through the point (17,3). Whats is its equation in slope intercept form?
Answer:
y = 10/17x - 7
Step-by-step explanation:
→ Write in standard form
y = 10/17x + c
→ Substitute in (17, 3)
3 = 10 + c
→ Solve for c
c = -7
→ Rewrite
y = 10/17x - 7
2n-15=-5n+4n
Thank You
6n squared -19n+10 can you please help me with factoring
Answer:
(2n -5)(3n -2)
Step-by-step explanation:
You want to factor 6n² -18n +10.
Sum and productYou want to start by finding factors of the product (6)(10), the first and last coefficients, that have a sum equal to -18, the linear term coefficient.
This sum is negative, but the product is positive, so both factors will be negative. Listing the smallest magnitude first, we have ...
60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)
The sums of these pairs are -61, -32, -23, -19, -17, -16. This identifies the pair of interest as (-4)(-15).
Final stepsFrom here, there are a couple of ways you can proceed. One is to write the linear term as a sum using these values:
6n² -4n -15n +10
Now, you can factor by grouping:
= (6n² -4n) -(15n -10)
= 2n(3n -2) -5(3n -2)
= (2n -5)(3n -2) . . . . . . . . the factorization you want
Another way you can do this is to write binomial factors using the leading coefficient for each one. The product of these must be divided by the leading coefficient for it to remain equal to the original trinomial.
= (6n -4)(6n -15)/6
The denominator of 6 is used to reduce each of the binomial factors.
[tex]=\dfrac{(6n-4)(6n-15)}{2\cdot3}=\dfrac{6n-4}{2}\cdot\dfrac{6n-15}{3}[/tex]
= (3n -2)(2n -5) . . . . . . . the factorization you want
Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
The fundamental difference between t-test and z-score is: t-test is used to determine the difference in data sets, the standard deviation and the z-score is used to to draw data from a given population with different means and standard deviation. A) The t statistic uses the sample mean in place of the population mean
How to know the use of t-test and z-score?T-test is a statistic model which is used to find how averages of different data sets differ in case the standard deviation and Z-scores statistic helps to draw data from populations with different means and standard deviations and also place them on a common scale.
The z-core formula is:
Z₁=[tex]\frac{x-m}{s}[/tex]
Therefore the fundamental difference is that the t-test uses the variance in place of the population variance.
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Complete question:
Which of the following is a fundamental difference between the t statistic and a z-score?
A) The t statistic uses the sample mean in place of the population mean
B) All of the choices are differences between t and z.
C) The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.
D) The t statistic uses the sample variance in place of the population variance.
Evaluate a+b+cd if a=78 , b=−716 , c=0.8 , and d=14 . Write your answer as a fraction in simplest form
Answer:
-626.8
Step-by-step explanation:
78 -716 + (0.8)(14)
78 - 716 + 11.2
(78 -716) + 11.2
-638 + 11.2
-626.8
If θ i an angle in tandard poition and it terminal ide pae through the point (-9,-1), find the exact value of tan theta implet radical form
The exact value of tan(θ ) in simplest radical form is 1/9 .
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
(-9,-1), is a point with x= -9 = adjacent side, y= -1 = opposite side
tan(θ ) = opposite side/adjacent side = -1/-9 = 1/9
1/9 can't be simplified further
So, the exact value of tan(θ ) in simplest radical form is 1/9 .
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write a division equation that has a solution of -9/14 .
The Division Equation that has solution of -9/14 will be [tex]\frac{-18x}{28x}[/tex].
What is Division Equation?
Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety.
For given solution i.e. -9/14, we can write division equation as follows,
[tex]\frac{-9* 2x}{14*2x}[/tex]
i.e. [tex]\frac{-18x}{28x}[/tex]
Hence, The division equation that has solution of -9/14 will be [tex]\frac{-18x}{28x}[/tex].
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An 80% confidence interval for a proportion is found to be (0. 27 , 0. 33). What is the sample proportion?
A. 0. 29
B. 0. 30
C. 0. 31
D. 0. 33
If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30
What do you understand by sample proportion?Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.
The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.
How to solve?
For this case the confidence interval is given by:
(0.27; 0.33)
We can find the estimaed proportion in the following way:
p = (0.27 + 0.33)/2 = 0.30
then the sample proportion would be 0.30
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Determine if the ordered triple is a solution to the system of equations.
1. 3x+4y-z=5. a) (-1, 2, 0)
5x-y + 3z=-7. b) (-2, -6, 3)
9x + 5y + 7z=-21
Please show step by step
Ordered triplet (-2, -6, 3) is the solution of the system of equations
3x+4y-z = 5
5x-y + 3z = -7
9x + 5y + 7z = -21
How to determine if an ordered triplet is solution to system of equations?
To determine if an ordered triplet is a solution to a system of three equations, we substitute the values of the variables into each equation. If the ordered triple makes all three equations true, it is a solution to the system.
According to the given question:
System of equations are
3x+4y-z = 5
5x-y + 3z = -7
9x + 5y + 7z = -21
Now, substituting (-1, 2, 0) in every equation to check if LHS = RHS for each.
1. 3x + 4y - z = 5
LHS = 3(-1) + 4(2) - 0 = -3 + 8 = 5 = RHS
2. 5x-y + 3z = -7
LHS = 5(-1) - 2 + 0 = - 5 -2 = -7 = RHS
3. 9x + 5y + 7z = -21
LHS = 9(-1) + 5(2) + 0 = -9 + 10 = 1 ≠ RHS
Therefore (-1, 2, 0) is not the solution for the system of equations.
Similarly substituting (-2, -6, 3) in every equation.
Clearly (-2, -6, 3) satisfies the system of equations.
Hence (-2, -6, 3) is the solution to the system of equations.
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A set of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviation of 101010 centimeters. Ikue is an elementary school student with a height of 90. 490. 490, point, 4 centimeters. What proportion of student heights are lower than ikue's height?.
0.0721 proportion of the students in the class have a height less than Ikue's height.
Here, we are given that a set of elementary school student heights are normally distributed with a mean of 105 cm ⇒ μ = 105 and standard deviation 10 cm ⇒ σ = 10
The z score can be calculated using the formula-
Z = (X - μ) / σ
X is the observed value, here, X = 90.4
Since we need the proportion of student heights are lower than ikue's height, we look at the negative z score only.
Substituting the values in the z score formula we get-
Z = ( 90.4 - 105) / 10
Z = - 1.46
Now, from the z score tables, we see that the value of Z < -1.46 is 0.0721.
Thus, 0.0721 proportion of the students in the class have a height less than Ikue's height.
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Vocabulary Use the terms divisor,
dividend, quotient, and remainder to
describe how to divide.
The divide rule will be;
⇒ Divisor = (Dividend - Remainder) / Quotient
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Vocabulary Use the terms divisor, dividend, quotient, and remainder.
Now,
If we have to find the divisor , then we can use the divide rule as;
⇒ Divisor = (Dividend - Remainder) / Quotient
Thus, The divide rule will be;
⇒ Divisor = (Dividend - Remainder) / Quotient
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PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent. Which statement is used to prove that angle PTR is always equal to angle STQ? (1 point) Lines PQ and RS do not have a fixed length. Angle PTR and angle PTS are supplementary angles. Lines PQ and RS intersect at an angle less than a right angle. Angle PTR and angle PTS are complementary angles.
The statement that is used to prove the congruence of angles PTR and STQ is given by:
Lines PQ and RS intersect at an angle less than a right angle.
What are congruent angles?Congruent angles are angles that have the same measure.
One example of congruent angles is for vertical angles, as these angles are opposite by the same vertex in crossing segments, with an angle less than a right angle of 90º, and then these two angles will be congruent.
The common vertex in the segment given at the end of the answer is of:
T.
The vertical angles are both acute angles, that is, angle measures that are less than 90º, which is the reason for the correct statement.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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A four-sided figure is resized to create a scaled copy. The lengths of its four
sides change as in the table below.
Original Figure Scaled Copy
36
45
54
8
10
12
Find the constant of proportionality from the original
figure to the scaled copy. Express your answer as a
fraction in reduced terms.
The proportionality constant from the original figure to the scaled copy is 2/9.
What is the proportionality constant?The constant of proportionality is the ratio between two given integers in what is known as a proportional relationship. The proportionality constant is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
We have here
To make a scaled duplicate, a four-sided figure is resized.
The proportionality constant from the original figure to the scaled copy is: 8/36 = 10/45 = 12/54 = 2/9.
As a result, the proportionality constant from the original figure to the scaled copy is 2/9.
Hence, the proportionality constant from the original figure to the scaled copy is 2/9.
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use the paste option to paste the content, including formulas, but none of the formatting into a worksheet.
What is this question I don't understand
2. Paola's dog, Rex, dug holes in opposite corners of
Paola's rectangular yard. If the yard is 11 meters long and
4 meters wide, what is the distance between the holes?
17
4. Feng is designing the layout for his rectangular garde
The distance between holes is 11.7m
What is a diagonal?A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.
let x be the distance between opposite holes which is the diagonal of the rectangle.
so that,
x^2 = 11^2 + 4^2
x^2 = 121 + 16
x^2 = 137
x = [tex]\sqrt{137}[/tex]
x = 11.7km
In conclusion the distance between holes is 11.7km
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