Answer:
Step-by-step explanation:
Split the polygon into 3 triangles as pictured below
<u>They have base and height:</u>
<u>Find the area of 3 triangles and add up:</u>
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
Number of days Val rented the bicycle is 8
<h3><u>Solution:</u></h3>Given that val paid a flat rental fee of $55.00 plus $8.50 each day
The total cost was $123
To find: number of days she rented the bicycle
Let "a" be the number of days she rented the bicycle
Rental fee = $55.00
Fee for one day = $ 8.50
So total cost is equal to rental fee and fee for "a" days
Total cost = rental fee + (number of days she rented the bicycle x Fee for one day)
123 - 55 = 8.50a
8.50a = 68
Thus number of days she rented the bicycle is 8