Bob leaves for a trip at 3 pm and drives with a velocity of v(t)= 60 - (1/2)t mph, where t is hours after 3.
Find the distance Bob drove by 5 pm.
119 miles
200
∫(2x^6-8x^3-9x^2+3)dx
(2/7)x^7-2x^4-3x^3+3x+c
200
-10≤x≤10 ∫(x-x^3+6x^5)dx
0
200
A faucet is turned on and water flows at a rate of f(t) = t^3 - (1/2)t^2 + 4 gallons per minute. How much water flowed out of the socket during the first 2 minutes it was on? (Round to the nearest gallon)
11 gallons
300
∫√(7x+9)dx
(2/21)(7x+9)^(3/2)+c
300
0≤x≤ln8 ∫(e^x-e^(-x))dx
49/8
300
Sonya can paint at a rate of p(t) = 150 - 4t square feet per hour, where t is the number of hours since she started.
If Sonya starts up early, approximatly 6 am, how many square feet can she cover by her lunch break at noon?
828 square feet
400
∫4cos(3x)dx
(4/3)sin(3x)+c
400
-1≤x≤1 ∫(2^(x+1))dx
3ln2
400
A ball is thrown at the ground from the top of a building. The speed of the ball in meters per second is v(t) = 9.8t + v Where t is in seconds and v is the initial speed of the ball. If the ball travels 25 meters in the first 2 seconds after it is thrown, what is the initial speed of the ball?
5.4 m/s
500
∫e^(5x+2) dx
(1/5)e^(5x+2)+c
500
1≤x≤2 ∫(1/x^2)dx
1/2
500
The acceleration of a particle can be defined as a(t) sin(2t) + 6t, where t is in seconds. At + t = 0, the velocity of the object is 2 m/s, and the position of the object is 0 meters. Find the position of the ball at t = 2 seconds.