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larisa [96]
2 years ago
15

Find the volume of a rectangular pyramid

Mathematics
1 answer:
Nesterboy [21]2 years ago
8 0

Answer:

192 yd³

Step-by-step explanation:

The volume of a rectangular pyramid is given by the formula:

V=\frac{1}{3} lwh\text{ where } l \text{ is the base length, }w \text{ is the base width, and }h \text{ is the pyramid height}

In this case: l = 9, w=8, h = 8

\therefore V=\frac{1}{3}(9\text{ yd})(8\text{ yd})(8\text{ yd})=192\text{ yd}^3

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il63 [147K]

Answer:

a)  P(x)=-0.042x^2+530x-18000

b)  P'(x)=-0.084x+530

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Step-by-step explanation:

a)

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000

This is the profit function.

b)

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

\frac{d}{dx}(x^n)=nx^{n-1}

Now, we differentiate the profit function to get the marginal profit function (P'):

P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530

This is the marginal profit function , P'.

c)

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194

and

P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268

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