Just took the test, the answer is;
Answer:
h = 5(tane)
Step-by-step explanation:
The diagrammatic representation of the question given is attached below ;
The height of the light pole, h = opposite side
Adjacent side = 5 feets
Angle of elevation = e
Using trigonometry ;
Tan e = opposite / Adjacent
Tan e = h / 5
Making h the subject ;
h = 5(tane)
First note the intersections of each pair of lines.
x = 3 ⇒ y = 2•3 + 1 = 7 ⇒ (3, 7)
y = -3 ⇒ -3 = 2x + 1 ⇒ x = -2 ⇒ (-2, -3)
y = -3 and x = 3 ⇒ (3, -3)
Using the disk method, we consider disks with thickness ∆y and radius equal to the horizontal distance between the line y = 2x + 1 (or x = (y - 1)/2) and the axis of revolution, x = 3. Each disk will then contribute a volume of
∆V = π (radius)² (thickness) = π/4 (y - 1)² ∆y
As we let ∆y go to zero and let the number of disks go to infinity, the total volume of the resulting cone will be given by the integral
![\displaystyle \frac\pi4 \int_{-3}^7 (y-1)^2 \, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%5Cpi4%20%5Cint_%7B-3%7D%5E7%20%28y-1%29%5E2%20%5C%2C%20dy)
Answer:
-4
Step-by-step explanation: