Solve a set of various maths problems. Detailed solutions with explanations to these problems are provided.
Problem 1:
The circumference of a circle is equal to 72 pi. Find the radius of this circle.
Problem 2:
The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the width and the length of the garden.
Problem 3:
A rectangular field has a length 10 feet more than it is width. If the area of the field is 264, what are the dimensions of the rectangular field?
Problem 4:
A company has found that when x units of a product are manufactured and sold, its revenue is given by x^{ 2} + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars? (HINT: profit = revenue  costs)
Problem 5:
A square has a side 5 centimeters shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.
Problem 6:
Find two numbers whose sum is 26 and whose product is 165.
Problem 7:
The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
Problem 8:
The sum of two numbers is 20. The larger number is four less than twice the smaller number. What rae the two numbers?
Problem 9:
The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.

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