Problem

In the following exercises, solve the given maxim…

Problem 47 Easy Difficulty

In the following exercises, solve the given maximum and minimum problems.
A race track $400 \mathrm{m}$ long is to be built around an area that is a rectangle with a semicircle at each end. Find the length of the side of the rectangle adjacent to the track if the area of the rectangle is to be a maximum. See Fig. 24.66.

Answer

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

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Video Transcript

The question is given that track and fill playing area in shape of a single but semi circles at each end. The perimeter off the trick is 1500 meters and I should do the diamonds and off the record angle. So that area off the angle is maximized. So the area off a tangle bilby two x in a way, because the sides off the rectangular has to accent by no the perimeter believing to why Plus the perimeter off Semi circle is Dubai are and artists X So we have to find the perimeter offside musicals to this movie by our right to this will be my are so this will become buy into eggs on there are two semi circles So this will be by express by X which is given Nicole returned from here. Do I plus two pi X quite to 1500 now area Quito To ex divi. You have to maximize the area so far, you have to sew substitute the really off by in terms off X. So this led to X multiplied by 1500 minus two x divided by so so too is conserved like to so here we will get 1500 ECs minus group by excess Got. Now we find that very well to do Realtor by D X, which is a call to 1500 menace foot by eggs. Now we find up Critical point. We have to find out where you off area balloon. That's not very much so. This will be 1500 called toe by Ex from here. The value off X equal to 1500 direct right foot. Now you find out the value off X now the most suitable off X in experts are Do I plus by X to 1500 from here we will care if I called to 1500 us to buy prepared by 500 right? Right foot by disability, the right like toe. Here they will care 1500 minus 7 50 which will be called 7 15 Now we have to find out the secondary body off area so the secondary but off area will be described it right, the access card. So this will be the defendants are off 200 will be Jill on defense isn't off foot by extra new sort by now, if you see the value off secondary were too off area is less than general. So we can say that X equal to 1500 for my invite. Little 7 50 107 7 complete. We will get the maximum area. So this is over Answer.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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