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3 years ago

Find the exact length of the curve. Use a graph to determine the parameter interval.. r = (cos(θ/2))^2

1 answer:

8 0

Cos(2θ) = 2cos^2θ - 1,

 cos^2(θ/2) 
Solving 
cos^2θ = [1 + cos(2θ)]/2. 

replacing θ with θ/2 gives. 
cos^2(θ/2) = (1 + cosθ)/2. 

length of a polar curve of the form r = f(θ) on [a, b] is given by: 
L = ∫ √[r^2 + (dr/dθ)^2] dθ (from θ=a to b).
hope this helps

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P + 13x = q p = 7 x = 4 q =

Leviafan [203]

13(4)=52 52+7=59 so q=59

5 0

3 years ago

Over the course of a year, a company goes from 115 employees to 124 employees.

just olya [345]

An equation that could be used to find the percent change, p, in the number of employees is:

$\begin{array}{l}{p=\frac{\text {change in number of employees}}{\text {previous count}} \times 100} \\\\ {\mathrm{p}=\frac{9}{115} \times 100}\end{array}$

<h3>Solution:</h3>

Given that, Over the course of a year, a company goes from 115 employees to 124 employees.

Given that "p" represents the percent change

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by 100.

$\text { Percent change "p" }=\frac{\text { change in number of employees }}{\text { previous count }} \times 100$

Change in number of employees = present count – previous count

So, change in number of employees = 124 – 115 = 9

$\begin{array}{l}{p=\frac{9}{115} \times 100} \\\\ {p=\frac{9}{23} \times 20} \\\\ {p=\frac{180}{23}=7.82}\end{array}$

The equation that is used to find the percent change is:

$\begin{array}{l}{\mathrm{p}=\frac{\text { change in number of employees }}{\text { previous count }} \times 100} \\\\ {\mathrm{p}=\frac{9}{115} \times 100}\end{array}$

7 0

3 years ago

If the marginal propensity to consume is 0.9, what is the maximum amount that the equilibrium gross domestic product could chang

Katen [24]

Answer: There is change of $0.9 billion in government expenditures.

Step-by-step explanation:

Since we know that

Marginal propensity to consume tells that the rate at which there is change in consumption due to change in income.

According to our situation, MPC is the change in amount of gross domestic product due to change in government expenditure.

So, it becomes,

$MPC=\dfrac{\text{Change in gross domestic product}}{\text{Change in government expenditure}}\\\\0.9=\dfrac{x}{1}\\\\x=0.9$

Hence, there is change of $0.9 billion in government expenditures.

7 0

3 years ago

Bob sees a very tall white pine tree. He estimates that the angle of elevation from him to the top of the tree is 77°

vlabodo [156]

Answer:

86.63 ft

Step-by-step explanation:

The tangent relation applies.

Tan = Opposite/Adjacent

tan(77°) = (tree height)/(20 ft)

tree height = (20 ft)·tan(77°) ≈ 86.63 ft

_____

Additional comment

It is somewhat problematic for Bob to see the top of a white pine tree at that angle of elevation. His view would likely be obscured by the branches of the tree.

8 0

2 years ago

The total ages of Sarah, Jake and Matthew add up to 36. Jake is two years younger than Sarah and Matthew is 16 years younger tha

Hatshy [7]

Answer:

Step-by-step explanation:

S+J+M=36

J=S-2 or J=x-2

M=S-16 or M=x-16

6 0

3 years ago

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