There are three consecutive even numbers such that twice the first is 20 more than the second. find the number

Step-by-step explanation:

2n is an even number.

Your three even numbers are 2n, 2n + 2, 2n + 4

Twice the first is 20 more than the second.

2n * 2 = 2n + 2 + 20

Simplify:

4n = 2n + 22

Use simultaneous equations to solve n.

4n = 2n + 22 - 2n

2n = 22 ÷ 2

n = 11

Subsitiye n into the three even numbers.

2n, 2n + 2, 2n + 4

2 * 11, 2 * 11 + 2, 2 * 11 + 4

22, 24, 26

Check that the numbers meet the requirements.

22 * 2 = 24 +20

44 = 44

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.