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1 year ago

In a volatile housing market, the overall value of a home can be modeled by V(x) = 415x2 - 4600x + 200000, where V

Mathematics

1 answer:

tensa zangetsu [6.8K]1 year ago

4 0

Answer:

See below

Step-by-step explanation:

This is a bowl shaped parabola ( due to the positive coefficient of x^2)

the minimum value (vertex )

will occur at x value = - b/2a = - -4600/2(415) = 5.54 years

the minimum VALUE will be the quation with this value of x inserted

415 (5.54)^2 - 4600(5.54) + 200 000 = $ 187 253.01

The home will reach a minumum value of 187253.01 in 5.54 years

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The profit per acre from a grove of orange trees is given by x(190 − x) dollars, where x is the number of orange trees per acre.

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Answer:

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In order to maximize the last equation we can derivate the function in term of x and we got:

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And solving for x we got:

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And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$

Step-by-step explanation:

For this case we have the following function for the profit:

$P(x) = x(190-x)$

And we can rewrite this expression like this:

$P(x) = 190 x -x^2$

In order to maximize the last equation we can derivate the function in term of x and we got:

$\frac{dP}{dx} = 190 -2x$

And setting this derivate equal to 0 we got:

$\frac{dP}{dx} = 190 -2x=0$

And solving for x we got:

$x = 95$

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$

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