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
No.
When you are distributing, you are multiplying to each monomial
4(4a) = 16a
4(20b) = 80b
16a + 80b is your actual answer
hope this helps
Answer:
27 and 23
Step-by-step explanation:
x + y = 50
x - y = 4
2x = 54
x = 27
y = 23
Answer:
5.83 units
Step-by-step explanation:
See attached picture. You can use the Pythagorean Theorem. I added some lines to show the legs of a right triangle. AB is the hypotenuse.

A(4,5) and B(-2,3)
AB (-6,-2)
And let's make M point from this line
M(x,y)
AB (-6,-2) and AM (x-4,y-5)
so , -6*(y-5)-(x-4)*-2=0
-6y+30+2x-8=0
The equation is :-6y+2x+22=0