The yoga company yoga for life offers 45-minute classes at $12 per class. if the number of minutes randolf
spent doing yoga this month was 132 greater than the number of dollars he paid, how many classes did he attend?
(a) 3
(b) 4
(c) 5
(d) 6
(e) 8

This is a classic example of where you would need to use the process of elimination. Let's start with answer A, 3 classes.
If A were to be correct, 3 classes of 45 minutes each would be 132 greater than the amount he paid, 3 classes worth $12. We could easily express this as a math equation:

45 * 3 = 132 + (12 * 3)               Then, all you would have to do is simplify:
135 = 132 + 36
135 = 168

Obviously this equation isn't true, and you can continue with answer choice B.
But wait... there's a better way. Using this starting equation, we can come up with a formula to solve for c, the number of classes. Let's take our starting equation:

45 * 3 = 132 + (12 * 3)         Now, let's turn all the 3s into cs.
45c = 132 + 12c                   Then, using algebra, we can solve this equation.
-12c           - 12c
33c = 132
33c/33 = 132/33
c = 4

And finally, we have our answer, B! I hope both methods help you in your further studies.

Answer

1 number

explanation

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.