Questions in Section Algebra I

If `P` varies inversely as the cube of `Q` and `Q` varies directly as the square of `R`, what is the relationship between `P` and `R`?

A large drain and a small drain are opened to drain a pool. The large drain can empty the pool in 7 hours. After both drains have been open for 1 hour, the large drain becomes clogged and is closed. The small drain remains open and requires 11 more hours to empty the pool. How long would it have taken the small drain, working alone, to empty the pool?

Find the equation of the line that passes through point `(-3,5)` and is perpendicular to the line `4x+3y=6`.

Simplify `3sqrt(10)+4sqrt(40)-5sqrt(40)`.

Given the equation `y=x^2-6x+8`. For what value of `x` is `y = -10`?

Write out the partial fraction decomposition, but do not solve for the unknown constants: `3/(x^2(x-1)(x^2+1))`.

Suppose that a given road has a maximum load of 20 tons per axle on a given vehicle. Suppose a truck has 16 wheels, with four wheels per axle, and weighs 14 tons. What is the maximum weight in kilograms that this truck can carry on a given road?

Given the linear equation `y=-3/2x+1`.Find the y-coordinates of the points (-4, ), (-2, ) and (6, ).