SOLUTION: i need detailed answers for these solutions to two problems 1. F = KmM/r^2 for r 2. A right triangle has legs a and b with hypotenuse c. Find the length of the missing side.

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Question 480235: i need detailed answers for these solutions to two problems
1. F = KmM/r^2 for r
2. A right triangle has legs a and b with hypotenuse c. Find the length of the missing side. b= 10, c = 26
I do appreciate the help need asap
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Problem 1:
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Multiply both sides by to eliminate the denominator on the right side and also for the purpose of getting the unknown term containing r on the left side of the equation.
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On the right side the in the denominator cancels the multiplier and you are left with the equation:
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Next, divide both sides by F to eliminate the F on the left side. The result is:
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and as the final step, solve for r by taking the square root of both sides to get:
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That's the answer for your first problem.
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Problem 2:
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A property of right triangles is covered by the Pythagorean theorem which says that the square of the hypotenuse (longest side) is equal to the sum of the squares of the two short sides which are called the legs. In equation form this is:
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For this problem you are told that b = 10 (one of the legs) and c = 26 (the hypotenuse). Substitute these values into the above equation and you have:
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Square the two known numbers to get:
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Subtract 100 from both sides to isolate the on the right side:
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transpose the equation to get it into a more standard form with the unknown on the left side:
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Take the square root of both sides to solve for a:
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and simplify by finding the square root of 576 to get:
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Hope the solution to these two problems help you to understand how you can work with equations involving squares by simplifying them and taking the square roots of both sides.