The volume of a cylinder is πr²h:

v = πr²h
v = π(1² x 7)
v = 7π

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 51° - 63° = 66°

So, d° = 63° + 66° = 129°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 51° = 129°

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

z² + 13z + 36 = 0
(z + 4)(z + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 4) or (z + 9) must equal zero:

If (z + 4) = 0, z must equal -4
If (z + 9) = 0, z must equal -9

So the solution is that z = -4 or -9

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 = \( \sqrt{2} \)