8.1
Calculator active problem.
Jordan's driveway temperature (in F) t hours after 4pm is represented by the function T(t)=60-sin(t). Find the average temperature of the driveway during the time period 12pm to 4pm
Answer:
59.587*F(rounded)
John drops a pen from a 1000-ft building. The velocity of the pen is v(t)=-28ft per second. Find both the position function and acceleration function
Answer:
Acceleration Function: a(t)=-28
Position Function: h(t)=-14t^2+1000
Jordan is cleaning the floor at a rate of (150-3t) square feet per hour, where t is the number of hours since he started painting. If the floor is 600 square feet, how long would it take him to finish cleaning the floor? Round your answer to the nearest minute.
Answer:
250 Minutes
Find the area of the region bounded by the following graph. y= (2/x^2) , y=0, y=3
Answer:
9.798
Find the area of the region bounded by the following graph in respect to y. y= 3 x= square root of Y
Answer:
9
Find the average value of each function on the given interval.
F(x)=x^2 on [5,9]
Answer:
151/3
Alexis throws a ball down a building to Jordan with a velocity of v(t)=-38t-6 where t is time in seconds and v is ft/sec. The ball is 15 feet in the air at t=1. What is the initial height of the ball?
Answer:
40ft
Water in a shower is leaking at a rate modeled by V(t) measured in inches per hour and t is measured in hours since the morning. By the morning, there has been 5 inches of water that has already leaked. Write, but do not solve, an equation involving an integral to find the time A when the amount of leaked water that has fallen for the day has reached a total of 6 inches.
Answer:
5+ Integral 0 to A of V(t)dt=6
Find the area of the region bounded by the following graph. y= x+3, y=0, x=0 x=3
Answer:
13.5
Find the area of the region bounded by the following graph in respect to y. x= y+4 x= square root of Y
Answer:
4/3
Find the average value of each function on the given interval.
f(x) x^1/2 on [0,2]
Answer:
0.943
Calculator Active: A particle moves along the x-axis. The velocity of the particle at time t is given by v(t)=4/t^2+7. If the position of the particle is x=5 when t=2, what is the position of the particle when t=2?
Answer:
3.660
Calculator Active: The ocean depth near the shore is changing at a rate modeled by v(t)= 2.5459cos(pie/2t), measured in feet per hour t hours after 7 A.M. If the depth is 7 feet at 7 A.M., how deep is the water at 11 A.M. ?
Answer:
11.2109 feet
Find the area of the region bounded by the following graph. y=x^2, y=x
Answer:
1/6
Find the area of the region bounded by the following graph in respect to y. x= y^2 x= 3y
Answer:
9/2
Find the average value of each function on the given interval.
f(x)=x^1/2 on [-14,-7]
Answer:
1/98
John leaves for a jazz tour at 6:00p.m. (time t=0) and drives with velocity v(t)= (-1/3)t-40 miles per hour, where t is measured in hours. Find out how much John has traveled from 6:00p.m. to 9:00p.m.
Answer:
118.5 Miles
Rain is falling at a rate modeled by R(t) measured in inches per hour and (t) is measured in hours since noon. By noon, there has been 0.5 inches of rain that has already fallen that day. Write, but do not solve, an equation involving an integral to find the time (A) when the amount of rain that has fallen for the day has reached a total of 5 inches.
Answer:
0.5+integral 0 to A of R(t)dt=5
Find the area of the region bounded by the following graph. y=2x^2-x, y=1,
Answer:
9/8
Find the area of the region bounded by the following graph in respect to y. y=x y=1-square root of x y=0
Answer:
(5 square root of 5)/6
qFind the instantaneous rate of change is equivalent to the average rate of change MVT
y=x^2-5x+1 on [3,7]
Answer:
x=5
A particles velocity is given by v(t)=t^2+3t-7, where t is measured in minutes, v is measured in meters per minute, and s(t) represents the particle's position. What is the net change in distance in the first 7 minutes?
Answer:
833/6 meters
Alexis is pouring paint at a rate modeled by P(t) measured in cubic feet per minute and (t) is measured in minutes since the start. When the day begins, there was already 78.5 cubic feet of paint that has been poured from the day before. Write, but do not solve, an equation involving an integral to find the time x when the amount of paint poured has reached a total of 200 cubic feet.
Answer:
78.5+ integral 0 to x of P(t)dt=200
Calculator Active: Find the area of the region bounded by the following graph. y=e^(x)^(2) - 1) and y= square root of 2-x
Answer:
4.506
Find the area of the region bounded by the following graph in respect to y. y=x^2,x= 1/2
Answer:
1/24