Using a midpoint Riemann sum with 3 subintervals of equal length to approximate is 2020 and means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
From the given question,
An initial height of 0 feet at time t=0 seconds.
The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.
(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate .
A midpoint Riemann sum with 3 sub intervals so, n=3
∆t= (70-10)/3
∆t = 60/3
∆t = 20
Intervals: (10, 30), (30,50), (50,70)
Midpoint: 20 40 60
Midpoint Riemann Sum
= ∆t[v(20+v(40)+v(60)]
From the table
= 20[22+35+44]
= 20*101
= 2020
(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight .
It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
To learn more about a midpoint Riemann sum link is here
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I think the answer is 2 my friend :)
Answer:
Step-by-step explanation:
The a line that is perpendicular to the reference line will have a slope that is the negative inverse of the slope of the reference line. We'll look for a line that has the form y=mx+b, where m is the slope and b is the y-intercept. The reference line y=(4/3)x has a slope of (4/3) and a y-intercept of 0 (it crosses the y axis at x = 0).
The negative inverse the the slope (4/3) would be -(3/4).
The new line will be y = -(3/4)x + b.
To find point, use the given point and solve for b:
y = -(3/4)x + b
y = -(3/4)x + b for point (4,2)
2= -(3/4)(4) + b
2= -3 + b
b = 5
The equation of the perpendicualr line is y = -(3/4)x + 5
See attached graph.
Answer:
(0, 4), (4, 2)
Step-by-step explanation:
Locate each point on the graph. If it is on the blue line, then it is a solution to the equation.
The solutions are:
(0, 4), (4, 2)