1. A rectangular swimming pool measures 12 cm by 15 cm. What is the area of the pool?
1 answer:
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Answer:
a) The length of the building that should border the dog run to give the maximum area = 25feet
b) The maximum area of the dog run = 1250 s q feet²
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given function </em>
<em> A(x) = x (100-2x)</em>
<em> A (x) = 100x - 2x²...(i)</em>
<em>Differentiating equation (i) with respective to 'x'</em>
<em> </em><em></em>
<em> ⇒ </em> ...(ii)
<em>Equating zero</em>
⇒ 100 - 4x =0
⇒ 100 = 4x
Dividing '4' on both sides , we get
x = 25
<em>Step(ii):</em>-
Again differentiating equation (ii) with respective to 'x' , we get
Therefore The maximum value at x = 25
The length of the building that should border the dog run to give the maximum area = 25
<u>Step(iii)</u>
Given A (x) = x ( 100 -2 x)
substitute 'x' = 25 feet
A(x) = 25 ( 100 - 2(25))
= 25(50)
= 1250
<u><em>Conclusion</em></u>:-
The maximum area of the dog run = 12 50 s q feet²
<em> </em><em> </em>
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