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aev [14]
3 years ago
14

Find two positive real numbers whose product is a maximum. the sum of the first and three times the second is 60.

Mathematics
1 answer:
maksim [4K]3 years ago
4 0
P = f*s
f +3s = 60

p = (60 -3s)*s = 3(20 -s)*s

This equation describes a parabola that opens downward. The roots of the equation are s=0 and s=20, so the axis of symmetry is s=(0+20)/2 = 10. That is, the vertex (maximum) will be found at s=10.

The second number is 10. The first number is 60-3*10 = 30.

The product is maximized when the first number is 30 and the second is 10.
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Answer:

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Step-by-step explanation:

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Step 1 of 3

Here we need to find the cost of 30  gallons.

Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.

The cost of 24  gallons is $59.76  to him.

Let, x  be the number of gallons and y  be the cost or price for gas.

Use the formula for direct variation which is given by y=kx.

Step 2 of 3

Now substitute the value y=$59.76 and x=24.

Put value in y=kx, we get

$$\begin{aligned}&59.76=k \times 24 \\&k=2.49\end{aligned}$$

Substitute value of k is y=kx, we get y=2.49x

Step 3 of 3

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Again use direct variation formula y=kx and value of k and x, we get $y=2.49 \times 30$

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