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Alborosie
3 years ago
13

A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function o

f the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?
Mathematics
2 answers:
ivann1987 [24]3 years ago
3 0
A quadratic function models the profit of the company and the maximum/minimum value of the quadratic function occurs on its vertex. 

The given function is:

P(x)=-3(x-5)^{2}+12

The equation is already in standard form, the vertex of the parabola as seen from the equation is (5,12)

This mean if the company sets the price of socks to $5 they will earn a maximum profit which is $ 12 million
Vilka [71]3 years ago
3 0

Answer:

5

Step-by-step explanation:

i took the quiz

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Write the slope-intercept form of the equation of the line through the given point with the given slope.
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Slope itnercept is y=mx+b

ok, let's start with point slope form
y-y1=m(x-x1)
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5 0
3 years ago
A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t
Vlad1618 [11]

Answer:

 185553.7\text{ feet}^3

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is 84\text{ feet}, and the total height of the building up to the top of the dome is 91\text{ feet}.

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be h\text{ feet}

As the dome hemispherical.

circumference of a hemisphere =\frac{1}{2}\times2\pi\times radius

                                                    =\pi\times radius

                                                    \frac{22}{7}\times radius=84

                                                    radius=26.75\text{ feet}

total height of the building up to the top of the dome =\text{radius of hemisphere}+\text{height of mountaintop}

=26.75+h=91

h=64.25\text{ feet}

Volume of building =\text{volume of cylindrical mountaintop}+\text{volume of dome}

                                =\pi(radius)^2h+\frac{2}{3}\pi(radius)^3

as radius of mountain top is same as dome

putting values

                                =3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3      

                               =145484.6+40069.1

                               185553.7\text{ feet}^3

Hence the total volume of the building is 185553.7\text{ feet}^3                                      

5 0
3 years ago
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