Author Topic: help with question (Read 709 times) Tweet Share

m2121 · « **on:** April 21, 2018, 07:51:35 pm »

I need help with question 8b part i. How do i find y in terms of x?? not sure why the answer is y=100-pi x (how do they even get that answer)?

Opengangs · « **Reply #1 on:** April 21, 2018, 08:16:42 pm »

Hey, m2121.

Sure thing!
So, we are given that the length of the fence is governed by the outer layer, $ AB + BC + CD $ as per the question. And we are given that it is equal to 100.

$\text{So } AB + BC + CD = 100 \Rightarrow AB + y + CD = 100 \\ \Rightarrow y = 100 - AB - CD$
$\text{Now, the cool thing is that we are given that } AB \text{ and } CD \text{ are } \textbf{ arcs}.\\ \text{So, to find the length of an arc, we use the arc-length formula.} \\ l = r\theta. \\ \text{Given that } \theta \text{ is } \frac{\pi}{2} \\ \text{ we see that } AB \textbf{ and } CD = x\cdot \frac{\pi}{2} \\ \text{So, we find that } y = 100 - x\cdot \frac{\pi}{2} - x\cdot \frac{\pi}{2} = 100 - x\cdot \pi$

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Author Topic: help with question (Read 709 times) Tweet Share

m2121

help with question

Opengangs

Re: help with question

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