19. If f(x) = 6x + 3, find f-1(x).

Mathematics

1 answer:

KengaRu [80]3 years ago

4 0

Answer:

$f^{-1}$ (x) = $\frac{x-3}{6}$

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 6x + 3 ( subtract 3 from both sides )

y - 3 = 6x ( divide both sides by 6 )

$\frac{y-3}{6}$ = x

change y back into terms of x, thus

$f^{-1}$ (x) = $\frac{x-3}{6}$

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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.

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