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.

Solution Summary

The expert examines rationalization of denominators. The maximum weight that a rectangular beam can support is determined.

1. Allen, Bonita, Chloe and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the new subcommittee are there? There will be _____possible subcommittees.
2. Use induction to predict the next three numbers in the pattern. 25, 5, 1, 1/

Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider X\E = Y. Show that all sets B which can be expressed as A\E, where A belongs to the sigma algebra in X, form a sigma-algebra in Y.
Please justify every step and claim you make in the solution.

1. Very rarely do people use algebra in their jobs or their lives. At most, people use arithmetic. If this is the case then why do you suppose it is that we study algebra in the first place?

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only 'food for thought.' I welcome your constructive ideas and comments on one or several of them.
Whether you agree or do not agree, the study of algebra is good for the brain. The b

Boolean Algebra and Digital Logic
1. Convert the following binary numbers to their decimal equivalents
a. 1101
b. 0011
c. 11100111
d. 10101011
2. Convert the following decimal numbers to their binary, octal, and hexadecimal equivalents
a. 16
b. 32
c. 48
d. 80
3. Do the following work and answer the fol