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 > sign and the answer on the other.

-4c - 4 > \( \frac{c}{8} \)
8 x (-4c - 4) > c
(8 x -4c) + (8 x -4) > c
-32c - 32 > c
-32c - 32 - c > 0
-32c - c > 32
-33c > 32
c > \( \frac{32}{-33} \)
c > -\(\frac{32}{33}\)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

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

sa = 2πr² + 2πrh
sa = 2π(7²) + 2π(7 x 8)
sa = 2π(49) + 2π(56)
sa = (2 x 49)π + (2 x 56)π
sa = 98π + 112π
sa = 210π

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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

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 = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.