A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.2 in. The slant height of the pyramid is 88.2 in. What is the height of the pyramid?

Step-by-step explanation:

We can solve the height of a square pyramid using the Pythagoras theorem, this is because the slant height the height and the section of the base form a right triangle

the slant height is equivalent to the hypotenuse

the height is equivalent to the opposite

while the base(half) is the adjacent

Given

the base of the pyramid=

the adjacent is =

the slant height (hypotenuse)=

we know that Pythagoras theorem states that "The sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle) is equal to the square of the length of the hypotenuse ('c').

substituting we have

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.