I need help with some algebra problems I can't get?

Question

1. ___45x4y5 ___9x3y4

14a7b4 + 16a4b2

Simplify the above expression.

It is two fractions being added in case you can't tell...

P.S. I deleted problem 2 because it was too long to write out

3. Given that P varies inversely as the square of Q, and that Q is 6 when P is 3, what is P when Q is 12?

4. The area of a circle varies directly as the square of the radius. If the area of a circle with radius 14 cm is 616 cm squared, find the area of a circle with radius 21 cm.

5. A new high-speed copier works three times as fast as a regular copier. When both copiers are used, they can copy a group of documents in 12 minutes. How long would each copier require to do the copying alone?

6. Flying with the wind, a jet can travel 4200 km in 6 hours. Against the wind takes 7 hours for 4200 km. Find the rate of the jet in still air and the rate of the wind.

7. A crew can row 60 km downstream in 3 hours. The return trip takes 5 hours to go the same distance. Find the rowing rate of the crew in still water and the rate of the current

8. A motorboat traveling with the current can go 160 km in 4 hours. Against the current it takes 5 hours to go the same distance. Find the rate of the motorboat in still water and the rate of the current.

I don't just need answers...I need to learn/remember how to do these. If you answer them all plus show me how to do them it is greatly appreciated and will likely earn you best answer.

IF YOU WANT, ANSWER AS MANY AS YOU FEEL LIKE DOING. ANY HELP IS GREATLY APPRECIATED ( :

Answer 1

damnnn u want us 2 do ur homework for u?? LOL  

Answer 2

Problem 1: indecipherable

Problems 3 and 4: Variation

Given that P varies inversely as the square of Q, and that Q is 6 when P is 3, what is P when Q is 12?

"P varies inversely as square of Q" -> P = k / Q²

we don't know what k is yet.

"Q is 6 when P is 3, what is P" aha! a clue!  3 = k / (6x6)

Solve that and you find k.

P = k / (12 x 12).  Once you know k, you have your answer.

The circle problem works the same way, except it's

A = k r²  ("inversely" means in the denominator, "directly" means in the numerator, with denominator = 1, if you will)

Problem 5: copier speed

Let F = faster speed, S = slower speed

"A new high-speed copier works three times as fast as a regular copier. "

. . .  F = 3 S

When both copiers are used,

. . . the speed here will be F + S since both are cranking away

they can copy a group of documents in 12 minutes.

. . . speed * time = documents copied

. . .  (F + S) * 12 = D  (we don't know how many documents,

but we won't need to)

How long would each copier require to do the copying alone?

. . . Substituting 3 S for F, we get 48 S = D

. . . . . . the slower machine would take 48 minutes

. . . Substituting 1/3 F for S, we get 16 F = D

. . . . . . the faster machine would take 16 minutes

Problems 6-8: Wind and current

These are all solved the same way:

Let s = speed of the boat of plane on its own

Let c = speed of current or wind

In one direction, the combined speed is s + c

In the other direction, it's s - c

You are given the distance, D,  and times, t1 and t2 so:

speed * time = distances

(s + c) * t1 = D

(s - c) * t2 = D

Then you can solve for s and c.

The setup for the first one is

(s + c) * 6 = 4200

(s - c) * 7 = 4200

The others are the same, but with different numbers.