Answer:
Q2) 29 degree as unrounded to nearest degree is 28.95 degree
Q3) 69 degree as unrounded to nearest degree is 68.56 degree
Step-by-step explanation:
QU 2)
When they speak of plane we see ABCD and also see ABC
So we need the length of AB and BC to find the diagonal CA
AB^2 + BC^2 = CA^2
16.4^2 + 9.1^2 = sqrt 351.77
CA^2 = sqrt 351.77 = 18.8 cm
We know CG = 10.4cm
We identify the hypotenuse for ACG triangle
We do trig tan x = opp/adj for CGA angle
Tan x = tan-1 10.4/18.8 = 28.95099521 degree
Tan x = tan-1 18.8/10.4 = 61.04900479 degree
so we know one is much smaller than the other
We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.
Answer therefore must be 28.95 degree = or 29 degree
QU 3)
we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.
= 7.6/2 = 3.8 cm
Then Pythagoras
BV^2 - 1/2 BC = height
10.4^2 - 3.8^2 = height
Height = sq rt 93.72 =9.68090905 = 9.7cm
Which means V to midpoint VC = V to midpoint AB
They are the same and the midpoints are 90 degree angles.
To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.
We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp
Because if it was the midpoint angle then it would be opp/adj like the question 1 so this time its cos of x.
cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455
Answer is 68.56 degree
The reason we show the height is so we can check by doing opp/hyp
= sin of x = sin-1 (9.68090905/3.8) = 23.11171135
and 90 -23.11171135 = 66.8882887
= 67 degree
So we go with the first one and assume 9.68 was already simplified to 9.7cm
= sin-1 (3.8/9.7) = 23 degree 90-23 = 67 degree
but when rounded to 10.4cm for slant we get the same
= sin-1 (3.8/10.4)
So we realise here trig functions -1 doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.
We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree
and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.
This proves that cos line 1/line2 = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di
and smallest side acts as denominator for both trig functions.
Solve similar triangles (advanced)
Solve for x
Answer:
4
Step-by-step explanation:
AD=4+8=12=DE thus angle EAD= angle AED=90÷2=45
angle ACB=90-45=45 thus CB=AB=4
Answer:
incorrect answer above
A medicine bottle contains 8 grams of medicine. One dose is 400 milligrams. How many doses does the bottle contain?
Answer:
20 doses
Step-by-step explanation:
400 milli. = 0.4 grams
8/0.4 = 20 doses
A box of apples weighing 3 pounds was divided into 6 equal shares. What was the weight of each share in pounds?
Answer:
1/2 pounds or 0.5 pounds, 3/6 = 1/2 :)
hope i helped
Step-by-step explanation:
Answer:
0.5 pound/share
Step-by-step explanation:
Divide 3 pounds by 6 shares, obtaining 0.5 pound/share
Let W be the solution set to the homogeneous system x + 2y + 3z = 0 2x + 4y + 6z = 0 Then W is a subspace of R3. Compute The Distance Between Y =[1 1 1] And W.
Answer:
Step-by-step explanation:
From the given information:
We can see that:
[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]
From equation (1), if we multiply it by 2, we will get what we have in equation (2).
It implies that,
x + 2y + 3z = 0 ⇔ 2x + 4y + 6z = 0
And, W satisfies the equation x + 2y + 3z = 0
i.e.
W = {(x,y,z) ∈ R³║x+2y+3z = 0}
Now, to determine the distance through the plane W and point is;
[tex]y = [1 \ 1 \ 1]^T[/tex]
Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0
Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:
[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]
[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]
[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]
[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]
[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]
H(0)=_______________
Answer:
5
Step-by-step explanation:
the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.
and that is automatically the result. there is not anything else to it.
Name different types of triangles. Illustrate how you can introduce each triangle to the foundation phase learner during the lesson presentation. Mention the resources that you will use.
Answer:
Following are the complete solution to the given question:
Step-by-step explanation:
The two main elements are geometry. One of them is analyzing the form of something. The second element is distance thinking. Four dominant sides are united into the triangle. Its sides can be of any height, however, the biggest side can be even more than and equal to a sum of the other two sides. Also, there are two concentric angles in a triangular, with the overall amount of three angles being 180 °.
Triangle Equilateral. It is a triangle with much the same length on all edges and 60 ° throughout all angles.Right triangle. Right pyramid. It is triangular with one correct angle and two acute angles, with only an oblique of less than 90º.Triangle of Isosceles It is a triangle with the same length along two sides.Acute triangle, three acute angles triangle.Triangle shabby. It is a three-way corner with three different elevations and a shallow angle, with a shallow angle which measures and over 90 °.Triangle scalene. The triangle has distinct lengths on any and all three sides.Assume that Publication is the root class of an inheritance tree. You want to form a linked list of different publications in the inheritance tree, including Book, Report, Newspaper, etc. What is the best way to create a linked list using PublListNode and Publication classes? a. The Publication class is derived from the PublListNode class. b. The PublListNode class is derived from the Publication class. c. The Publication class contains the PublListNode class. d. The PublListNode class contains the Publication class.
Answer:
The best way to create a linked list using PublListNode and Publication classes is ensuring that:
d. The PublListNode class contains the Publication class.
Step-by-step explanation:
A linked list contains a set of address-connected nodes (elements). The first node is called a header address, while the last node is called a null address. A linked list can be a single list (linear list), double list, multiple linked list, or circular linked list. The PublListNode is a type of multiple linked list. It forms a linked list of different publications using an inheritance tree.
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
3. Solve the initial value problem. a. 2yy^ prime =e^ x-y^ 2 , given y(4) = - 2 .
It looks like the equation reads
2yy' = exp(x - y ²)
(where exp(blah) = e ^(blah))
This DE is separable:
2y dy/dx = exp(x) exp(-y ²)
==> 2y exp(y ²) dy = exp(x) dx
Integrating both sides gives
exp(y ²) = exp(x) + C
The initial condition tells you that y = -2 when x = 4, so that
exp((-2)²) = exp(4) + C
exp(4) = exp(4) + C
==> C = 0
Then the particular solution to this DE is
exp(y ²) = exp(x)
Solving for y as a function of x gives
y ² = x
y = ±√x
But bearing in mind that y = -2 < 0 when x = 4, only the negative square root solution satisfies the DE. So
y(x) = -√x
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, T for turkey, I for Italian, and F for French. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: Italian, French
Answer: He can make 36 different salds
Step-by-step explanation:
( 7 x 10 ^-5) x (5 x 10 ^-8)
[tex]\huge{\colorbox{pink}{Solution}}[/tex]
Step 1 : Equation at the end of step 1
(((7•(x^10 ))-5)•x)•(5x^10-8)
Step 2 : Equation at the end of step 2 :
((7x^10 - 5) • x) • (5x^10 - 8)
Step 3 :
Trying to factor as a Difference of Squares:
3.1 Factoring: 7x^10-5
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B² =
[tex] \: \: \: \: \: \blue {A² - B²}[/tex]
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 7 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares.
Equation at the end of step 3 :
x • (7x10 - 5) • (5x10 - 8)
Step 4 :
4.1 Factoring: 5x^10-8
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares.
Final result : ☞ x • (7x10 - 5) • (5x10 - 8)
→ 3.5 × 10^-12
____________________________
Hope It Helps You ✌️
Find the slope of the line which passes through the points A (-4, 2) and B (1,5).
Answer:
3/5 so A.
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)
m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 7 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is [larger, smaller] for New York because the sample size is [larger, smaller] than for California.
Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
Learn more about Arithmetic operations here:
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Consider a set of data in which the sample mean is 26.826.8 and the sample standard deviation is 7.97.9. Calculate the z-score given that x.
Answer:
The answer is "0.59".
Step-by-step explanation:
Please find the whole question in the attached file.
Given:
[tex]\mu=26.8\\\\\sigma=6.4\\\\X=30.6[/tex]
Using formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]=\frac{30.6-26.8}{6.4}\\\\=\frac{3.8}{6.4}\\\\=\frac{380}{640}\\\\=\frac{38}{64}\\\\=\frac{19}{32}\\\\=0.59375\approx 0.59[/tex]
In order for the parallelogram to be a
rectangle, x = [?]
Diagonal AC = 7x - 35
Diagonal BD = 3x + 45
A
B.
D
C С
Explanation:
For any rectangle, the diagonals are the same length.
AC = BD
7x-35 = 3x+45
7x-3x = 45+35
4x = 80
x = 80/4
x = 20
Nick buys a bag of cookies that contains 9 chocolate chip cookies, 8 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies. What is the probability that Nick reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie
Answer:
7/26
Step-by-step explanation:
Add all of it up.
9 + 8 + 4 +5 = 26
26 cookies, but done twice so,
26 × 2 = 52
14/52 = 7/26
SAQ 5.1
1. Find the first four terms of the sequence whose general term is given by
i.
ii.
7 x 3"
n-2 5 x
2. Say what the pattern of is for each of the following sequences and give the next three
terms
i.
ii.
2, 6, 12, 20
8, 0.8, 0.08, 0.008
1 1 1 '2'3'4
Answer:
1. (i) 7, 21, 63, 189
(ii) 20, 10, 5, 2.5
2. (i) n²+n (where n = 1, 2, 3, ..)
(ii) 8/(10^n) (where n = 1, 2, 3, ..)
(iii) 1/(n+1) (where n = 1, 2, 3, ..)
PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
Which expression is equivalent to the area of square A, in square inches?
1. 1/2(10)(24)
2. 10(24)
3. (10+24)^2
4. 10^2 + 24^2
Answer:
4.) 10^2 + 24^2
Step-by-step explanation:
From the attached diagram, the area of a square A is given by the measure of the square of its hypotenus :
The hypotenus is given by :
Hypotenus² = opposite² + Adjacent²
Hypotenus² = 10² + 24²
The square of hypotenus = 10^2 + 24^2
Find z such that 6% of the standard normal curve lies to the right of z.
P(Z ≥ z) = 1 - P(Z ≤ z) = 0.06
==> P(Z ≤ z) = 0.94
==> z ≈ 1.7507
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
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Sam is making a table of values and a graph for the equation 16x + y = −48. He says that when x = 3, y = 0. Is Sam correct?
Answer:
No
Step-by-step explanation:
16x + y = −48
Substitute the point into the equation and see if it is true
16(3) +0 = -48
48 = -48
This is not true so the point is not a solution
Help plz help needed i need the answer
Answer:
x = ±sqrt(26)
Step-by-step explanation:
ln ( x^2 -25) = 0
Raise each side to base e
e^ln ( x^2 -25) = e^0
x^2 -25 = 1
Add 25 to each side
x^2 -25 +25 = 1+25
x^2 = 26
Take the square root of each side
sqrt(x^2) = ±sqrt(26)
x = ±sqrt(26)
Answer:
The third option
Step-by-step explanation:
If we rewrite this in log form, we get
[tex]e {}^{0} = {x}^{2} - 25[/tex]
Remeber anything to the 0 power is 1, so simplifying the equation first
[tex]1 = {x}^{2} - 25[/tex]
Add 25 to both sides
[tex]26 = {x}^{2} [/tex]
Take the square root of both sides
[tex]x = \sqrt{26} [/tex]
Square root are both so
[tex]x = - \sqrt{26} [/tex]
Is also a answer.
The third option is the answer
The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation
p = −0.00051x + 5 (0 ≤ x ≤ 12,000)
where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by
C(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000).
Hint: The revenue is
R(x) = px,
and the profit is
P(x) = R(x) − C(x).
Find the revenue function,
R(x) = px.
R(x) =
Answer:
[tex]R(x) = -0.00051x^2 + 5x[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
Step-by-step explanation:
Given
[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]
[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]
Solving (a): The revenue function
We have:
[tex]R(x) = x * p[/tex]
Substitute [tex]p = -0.00051x + 5[/tex]
[tex]R(x) = x * (-0.00051x + 5)[/tex]
Open bracket
[tex]R(x) = -0.00051x^2 + 5x[/tex]
Solving (b): The profit function
This is calculated as:
We have:
[tex]P(x) = R(x) - C(x)[/tex]
So, we have:
[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]
Open bracket
[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]
Collect like terms
[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Which is an x-intercept of the graph of the function?
Answer:
D
Step-by-step explanation:
X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
