Shelly is trying to improve her running time for a track race. She ran the first race in 43.13 seconds. Her time was 43.1 seconds in the second race and 43.07 seconds in the third race. If this pattern continues what will shellys time be in the fourth race?

Solution:

Given that,

Shelly is trying to improve her running time for a track race

She ran the first race in 43.13 seconds

Her time was 43.1 seconds in the second race and 43.07 seconds in the third race

Therefore, pattern is:

43.13, 43.1, 43.07 , ..

Find the difference between each terms

d = 43.13 - 43.1 = 0.03

d = 43.1 - 43.07 = 0.03

Thus the difference is same

If this pattern continues what will shellys time be in the fourth race?

Fourth race = third race - 0.03

Fourth race = 43.07 - 0.03 = 43.04

Thus the time in fourth race is 43.04 seconds

step-by-step explanation:

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.