Miscellaneous Algebra Questions

1. Rationalize the denominator.
√13 - √14 / √13 + √14

2. The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/4 foot wide, 1/2 foot high, and 16 feet long can support 30 tons, find how much a similar beam can support if the beam is 2/3 foot wide,1/3 foot high, and 12 feet long.

3. If y varies directly as x, find the constant of variation k and the direct variation equation for the situation. Y=2 when x=8.
Find the constant of variation k: k=?
Write the direct variation equation. y=?

4. A plane flies 470 miles with the wind and 310 miles against the wind in the same length of time. If the speed of the wind is 40 mph, find the speed of the plane in still air.

5. Jill can paint a room in 7 hours while it takes Patty 4 hours to paint the same room. How long would it take them to paint the room if they worked together?

6. Find the LCD of the rational expressions. Answer in factored form.

7m/m2-n2 , 3/m2-2mn+n2

7. Find the function value.
If f(x) = x+6 / 2x-1 please find f(4), f(0) and f(-3).

8. Write an equation to describe the variation. Use k for the constant of proportionality.
u varies inversely as c.