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3 years ago

Help me please I need a answer

Mathematics

1 answer:

Stels [109]3 years ago

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The profit P (in thousands of dollars) for an educational publisher can be modeled by P 52b31 5b21b where b is the number of wor

Anna007 [38]

Answer:

The lesser number of workbooks are 1,000

Step-by-step explanation:

The correct question is

The profit P (in thousands of dollars) for an educational publisher can be modeled by P=-b³+5b²+b where b is the number of workbooks printed (in thousands). Currently, the publisher prints 5000 workbooks and makes a profit of $5000. What lesser number of workbooks could the publisher print and still yield the same profit?

we have

$P=-b^3+5b^2+b$

For $P=\$5,000$

substitute in the equation and solve for b

Remember that the profit and the number of workbooks is in thousands

P=5

$5=-b^3+5b^2+b$

Using a graphing tool

Solve the cubic function

The solutions are

x=-1

x=1

x=5

therefore

The lesser number of workbooks are 1,000

<u><em>Verify</em></u>

For b=1

$P=-(1)^3+5(1)^2+1$

$P=5$ -----> is in thousands

$P=\$5,000$ ----> is ok

7 0

3 years ago

One gallon of paint covers 400 square feet of surface area. A typical spherical water tower holds 66,840.28 cubic feet of water.

enot [183]

Answer: There will enough to paint the outside of a typical spherical water tower.

Step-by-step explanation:

1. Solve for the radius r from the formula for calculate the volume of a sphere. as following:

$V=\frac{4}{3}r^{3}\pi\\\frac{3V}{4\pi}=r^{3}\\r=\sqrt[3]{\frac{3V}{4\pi}}$

2. Substitute values:

$r=\sqrt[3]{\frac{3(66,840.28ft^{3})}{4\pi}}=25.17ft$

3. Substitute the value of the radius into the equation fo calculate the surface area of a sphere, then you obtain that the surface area of a typical spherical water tower is:

$SA=4r^{2}\pi\\SA=4(25.17ft)^{2} \pi\\SA=7,964.95ft^{2}$

3. If a city has 25 gallons of paint available and one gallon of paint covers 400 square feet of surface area, you must multiply 25 by 400 square feet to know if there will be enough to paint the outside of a typical spherical water tower.

$25*400ft^{2}=10,000ft^{2}$