To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

8c - 2 = \( \frac{c}{9} \)
9 x (8c - 2) = c
(9 x 8c) + (9 x -2) = c
72c - 18 = c
72c - 18 - c = 0
72c - c = 18
71c = 18
c = \( \frac{18}{71} \)
c = \(\frac{18}{71}\)

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

The volume of a cylinder is πr²h:

v = πr²h
v = π(2² x 1)
v = 4π

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(9²) + 2π(9 x 8)
sa = 2π(81) + 2π(72)
sa = (2 x 81)π + (2 x 72)π
sa = 162π + 144π
sa = 306π

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 1² + 1²
c² = 2
c = \( \sqrt{2} \)