<h3>165 degrees :) your welcome</h3>
Answer:
you need a photo
Step-by-step explanation:
Answer:
![r=\dfrac{p}{4+\pi}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bp%7D%7B4%2B%5Cpi%7D)
Step-by-step explanation:
Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then
![p=2y+2r+\pi r.](https://tex.z-dn.net/?f=p%3D2y%2B2r%2B%5Cpi%20r.)
Express y:
![y=\dfrac{p-2r-\pi r}{2}.](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bp-2r-%5Cpi%20r%7D%7B2%7D.)
The area of the window is
![A=y\cdot 2r+\dfrac{1}{2}\pi r^2.](https://tex.z-dn.net/?f=A%3Dy%5Ccdot%202r%2B%5Cdfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2.)
Substitute y into the area expression:
![A=\dfrac{p-2r-\pi r}{2}\cdot 2r+\dfrac{1}{2}\pi r^2=pr-2r^2-\pi r^2+\dfrac{1}{2}\pi r^2=pr-2r^2-\dfrac{1}{2}\pi r^2.](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7Bp-2r-%5Cpi%20r%7D%7B2%7D%5Ccdot%202r%2B%5Cdfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2%3Dpr-2r%5E2-%5Cpi%20r%5E2%2B%5Cdfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2%3Dpr-2r%5E2-%5Cdfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2.)
Find the derivative A':
![A'=p-4r-\pi r.](https://tex.z-dn.net/?f=A%27%3Dp-4r-%5Cpi%20r.)
Equate A' to 0:
![p-4r-\pi r=0\Rightarrow r=\dfrac{p}{4+\pi}.](https://tex.z-dn.net/?f=p-4r-%5Cpi%20r%3D0%5CRightarrow%20r%3D%5Cdfrac%7Bp%7D%7B4%2B%5Cpi%7D.)
When
then
and the function A is increasing, when
then
and the function A is decreasing. This means that at point
the function A takes it maximal value (the area is maximal).
The polynomial function is P(x) = x^3(x + 1)^3(x -1)
<h3>How to determine the polynomial function?</h3>
The zeros of the polynomial and the multiplicities are given as:
- -1 as a zero of multiplicity 3,
- 0 as a zero of multiplicity 3,
- 1 as a zero of multiplicity 1
The degree is given as
Degree = 7
The polynomial is represented as:
P(x) = (x - zero)^multiplicity
Using the above format, we have
P(x) = (x + 1)^3(x - 0)^3(x -1)
This gives
P(x) = x^3(x + 1)^3(x -1)
Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)
Read more about polynomial function at
brainly.com/question/2833285
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The total amount he would have at 69 is $343,347.81.
<h3>What is the total amount saved?</h3>
The formula that can be used to determine the future value of the deferred annuity is:
Future value = annuity factor x monthly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = interest rate = 5.5 /2 = 2.75%
- n = number of payments = 2 x (69 - 24) = 90
Amount he would save every 6 months:
- amount saved per day = $2.50 x 2 = $5
- Amount saved per month : $5 x 30 = $150
- Amount saved every 6 months = $150 x 6 = $900
Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81
To learn more about annuities, please check: brainly.com/question/24108530
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