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m_a_m_a [10]
3 years ago
8

A boundary stripe 6 in. wide is painted around a rectangle whose dimensions are 120 ft by 230 ft. Use differentials to approxima

te the number of square feet of paint in the stripe.
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
7 0

Answer:

350 square feet

Step-by-step explanation:

We are given that

Width of strip=6 in

Dimension of rectangle=20 ft\times 230 ft

We know that

Area  of rectangle ,A=xy

Differentiate

dA=\frac{\partial A}{\partial x}x+\frac{\partial A}{\partial y}y

We have \frac{\partial A}{\partial x}=y=230 ft

\frac{\partial A}{\partial y}=x=120

dx=\frac{12}{12}=1 ft

1 ft=12 in

Because 6 in added in both side of breadth

dy=\frac{12}{12}=1 ft

Because 6 in added on both sides of length of rectangle

Substitute the values

dA=230\times 1+120\times 1=350 ft^2

Hence, the number of square feet of paint in the strip=350 square feet

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