To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

6a x 3b = (6 x 3) (a x b) = 18ab

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

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.

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

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 1)
sa = 2π(36) + 2π(6)
sa = (2 x 36)π + (2 x 6)π
sa = 72π + 12π
sa = 84π

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

c² - 44 = -c - 2
c² - 44 + 2 = -c
c² + + c - 42 = 0
c² + c - 42 = 0

Next, factor the quadratic equation:

c² + c - 42 = 0
(c - 6)(c + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 6) or (c + 7) must equal zero:

If (c - 6) = 0, c must equal 6
If (c + 7) = 0, c must equal -7

So the solution is that c = 6 or -7