<span>Proofs are often over-complicated in math class. They are basically a step by step way of doing an assignment. There can be ones that are done using only math equations, but there are also ones that you write out as you would an essay, and those are my personal favorite. In those, you basically write out moment by moment how you find out the answer to a given problem.</span>
Answer:
(0,3) and (5,0)
Step-by-step explanation:
a. Use the mean value theorem. 16 falls between 12 and 20, so
(Don't forget your units - 5 m/min^2)
b. gives the Johanna's velocity at time . The magnitude of her velocity, or speed, is . Integrating this would tell us the total distance she has traveled whilst jogging.
The Riemann sum approximates the integral as
If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of is determined by the value of at each sample point, 200, 240, |-220| = 220, and 150.
c. Bob's velocity is given by , so his acceleration is given by . We have
and at his acceleration is m/min^2.
d. Bob's average velocity over [0, 10] is given by the difference quotient,
m/min
What is the rest of the bottom pic?