Hard word problem Solve the following word problems using positive and negative numbers.

Find the difference in height between the top of a hill 973 feet high and a crack caused by an earthquake 79 feet below sea level.

As top of hill means a positive value so, 973 feet.

As crack means below or lower, it has negative value so, -73 feet.

As we know that Difference means the subtraction of two numbers, so,

Therefore, the difference in height between the top of a hill 973 feet high and a crack caused by an earthquake 79 feet below sea level is 1052 feet.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

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.