91Ó°ÊÓ

The power \(P\) (measured in horse power, hp) needed to propel a boat is directly proportional to the cube of the speed \(s .\) An 80 -hp engine is needed to propel a certain boat at 10 knots. Find the power needed to drive the boat at 15 knots.

Solve the equation for the indicated variable. $$a-2[b-3(c-x)]=6 ; \text { for } x$$

Which of the points \(P(3,1)\) or \(Q(-1,3)\) is closer to the point \(R(-1,-1) ?\)

Multiply the algebraic expressions using a Special Product Formula and simplify. $$(x+5)(x-5)$$

Solve the equation for the indicated variable. $$a^{2} x+(a-1)=(a+1) x ; \quad \text { for } x$$

The loudness \(L\) of a sound (measured in decibels, \(\mathrm{dB}\) ) is inversely proportional to the square of the distance \(d\) from the source of the sound. A person who is \(10 \mathrm{ft}\) from a lawn mower experiences a sound level of \(70 \mathrm{dB} .\) How loud is the lawn mower when the person is \(100 \mathrm{ft}\) away?

Find an equation of the line that satisfies the given conditions. Through \((-1,-2) ; \quad\) perpendicular to the line \(2 x+5 y+8=0\)

Simplify each expression. (a) \(x^{8} x^{2}\) (b) \(\left(3 y^{2}\right)\left(4 y^{5}\right)\) (c) \(x^{2} x^{-6}\)

Perform the multiplication or division and simplify. $$\frac{\frac{x^{3}}{x+1}}{\frac{x}{x^{2}+2 x+1}}$$

A rectangular garden is 25 ft wide. If its area is \(1125 \mathrm{ft}^{2},\) what is the length of the garden?