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various algebra questions

Please help with attached algebra problems.

? Write an equation to describe each variation. Use k for the constant of proportionality.(1-3)
? If y varies directly as x, find the constant of variation K and the direct variation equation for each situation (4-6)
? If y varies inversely as x, find the constant of variation k and the inverse variation equation for each situation (7- 9)
? Write each statement as an equation (10)

1) P varies directly as q
2) Y varies jointly as q,r, and t
3) Y varies directly as a^5 and inversely as b
4) Y = 12 when x = 8
5) Y = 11 when x = 1/3
6) At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see. Round answer to one decimal place.
7) Y = 20 when x = 9
8) Y = 1/10 when x = 40
9) The weight of an object on or above the surface of Earth varies inversely as the square of the distance between the object and Earth's center. If a person weighs 160 pounds on Earth's surface, find the individual's weight if he moves 200 miles above Earth. Round the answer to the nearest pound.(assume that earths radius is 4000 miles)
10) P varies jointly as R and the square of S.

I need help with number 2, 6, 10, 14, 18
If a number is subtracted from the numerator of 13/8 and added to the denominator of 13/8, the resulting fraction is equivalent to 2/5. Find the number.

In 2000, 43 out of every 50 Navy personnel were men. If there are 375,618 total Navy personnel on active duty, estimate the number of men. Round to the nearest whole.

A new printing press can print newspaper twice as fast as the old once can. The old one can print the afternoon edition in 4 hours. Find how long it takes to print the afternoon edition if both printers are operating.

The speed of a boat in still water is 24 mph. if the boat travels 54 miles upstream in the same time that it takes to travel 90 miles downstream, find the speed of the current.

3 cube root of x^15
3 cube root of 27/64
5 cube root of -243
5 cube root of -1
5 cube root of -32x^15
3 cube root 64a/b^9

Write a positive exponents : 2/3y^-5/7


Solution Summary

The solution works with a variety of algebra problems, which includes evaluating exponential expression, direct and inverse variation and proportions, and fractions.