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Vera_Pavlovna [14]
2 years ago
11

An artist creates a right prism whose base are regular pentagons. He wants to paints the lateral surfaces of the prism. One can

of paint can cover 30 ft2. How many cans of paints must he buy if buy if the height of the prism is 15 ft and the length of the pentagon is 5 ft?
Mathematics
1 answer:
Usimov [2.4K]2 years ago
6 0
He needs 13 cans of paint.

The lateral area is given by the area of 5 rectangles, whose dimensions are 15 by 5:
5(15)(5) = 375

Divide this by 30:
375/30 = 12.5 ≈ 13
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Answer:

Maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

Step-by-step explanation:

We are given the following information:P(x) = 6400x - 18x^2 - \frac{x^3}{3} - 40000, where P(x) is the profit function.

We will use double derivative test to find maximum profit.

Differentiating P(x) with respect to x and equating to zero, we get,

\displaystyle\frac{d(P(x))}{dx} = 6400 - 36x - x^2

Equating it to zero we get,

x^2 + 36x - 6400 = 0

We use the quadratic formula to find the values of x:

x = \displaystyle\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}, where a, b and c are coefficients of x^2, x^1 , x^0 respectively.

Putting these value we get x = -100, 64

Now, again differentiating

\displaystyle\frac{d^2(P(x))}{dx^2} = -36 - 2x

At x = 64,  \displaystyle\frac{d^2(P(x))}{dx^2} < 0

Hence, maxima occurs at x = 64.

Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

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