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Yuki888 [10]
3 years ago
7

Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 500 meters long

.
Mathematics
1 answer:
rewona [7]3 years ago
7 0
Let x and y be the sides of the rectangle. The perimeter is given to be 500m, so we are maximizing the area function A(x,y)=xy subject to the constraint 2x+2y=500.

From the constraint, we find

2x+2y=500\implies x+y=250\implies y=250-x

so we can write the area function independently of y:

A(x,y)=\hat A(x)=x(250-x)=250x-x^2

Differentiating and setting equal to zero, we find one critical point:

\dfrac{\mathrm d\hat A(x)}{\mathrm dx}=250-2x=0\implies x=125

which means y=250-125=125, so in fact the largest area is achieved with a square fence that surrounds an area of A(125,125)=125^2=15625\text{ m}^2.
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Answer:

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Given as :

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<u>Now, According to question</u>

Total slices of cake required for 60 people when each people eat 2 slices = total number of people × number of slices each person will eat

i.e Total slices of cake required for 60 people when each people eat 2 slices = x × A

Or, Total slices of cake required for 60 people when each people eat 2 slices = 60 × 2 slices

Or,Total slices of cake required for 60 people when each people eat 2 slices = 120 slices

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∴ The number of cake for order = \dfrac{\textrm Total slices of cake required for 60 people when each people eat 2 slices}{\textrm number of slices per cake }

Or, z = \frac{x\times A}{y}

i.e z = \frac{120}{8}

∴   z = 15 cakes

So,The number of cake for order = z = 15 cakes

Hence,The number of cake for order is 15 cakes . Answer

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