How do I simplify(i)237?
1 answer:
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Answer:
The matrix equation is
Step-by-step explanation:
* Lets change the story problem to equations
- The distance between the starting point and checkpoint 1 is x
- The distance between checkpoint 1 to checkpoint 2 is y
- The distance between checkpoint and the finish line is z
- The total distance for the race is 120 miles
∴ x + y + z = 120 ⇒ (1)
-The distance from the starting point to checkpoint 1 is 35 miles
more than half the distance from checkpoint 1 to checkpoint 2
∵ The distance from the starting point to checkpoint 1 is x
∵ The distance from checkpoint 1 to checkpoint 2 is y
- x is more than half y by 35
∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides
∴ x - (1/2) y = 35 ⇒ (2)
- The distance from checkpoint 2 to the finish line is 20 miles less
than twice the distance from checkpoint 1 to checkpoint 2
∵ The distance from checkpoint 2 to the finish line is z
∵ the distance from checkpoint 1 to checkpoint 2 is y
- z is less than twice y by 20
∴ z = 2y - 20 ⇒ add 20 to both sides
∴ z + 20 = 2y ⇒ subtract z from both sides
∴ 2y - z = 20 ⇒ (3)
* Now lets write the three equations
# x + y + z = 120 ⇒ (1)
# x - (1/2) y = 35 ⇒ (2)
# 2y - z = 20 ⇒ (3)
- Now lets write the matrix equation that models this situation
∴
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