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Derivatives Word Problems
- A ball is thrown vertically upwards with an initial velocity (#1613)
A ball is thrown vertically upwards with an initial velocity of 60m/s. After time t seconds, its height above the ground is given as s=60t-16t2. Find its instantaneous velocity after t seconds. Discuss the specialty about time t=15/8
derivatives
- A one-product firm estimates (#1154)
(cost and profit) a one-product firm estimates that its daily total cost function (in suitable units) is
C(x)=x3-6x2+13x+15
and its total revenue function is
R(x) = 28...
derivatives
- A water trough is 10 meter long (#3488)
A water trough is 10 meter long and a cross-section has the shape of an isosceles trapezoid that is 30 centimeter wide at the bottom, 80 centimeter at the top, and has height 50 centimeter. If the trough is being filled with water the rate of 0.2 meter cube per ...
derivatives
- Let f(t) be the weight (in grams) of a solid (#434)
Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the wieght of the solid at any time t can be be determined from the weight using the formula:
f'(t)=-5(t)(2+f(t))
If there is 3 grams of solid at time t=2...
derivatives
- On her way down from Mount Everest (#1418)
On her way down from Mount Everest, Kim notices for every three meters she travels northwest she climbs a 1/2 meter, and that for every two meters she travels northeast she descends 1/4 meter. In what direction should she start for fastest ...
derivatives
- The north-east section of a municipality (#2762)
The north-east section of a municipality is a rectangle whose 17 km west boundary is Highway 7 and whose 20 km south boundary is Highway 15. A by-pass road is planned to alleviate traffic ...
derivatives
- To estimate a height of a building, a stone is dropped (#3237)
Use the position function s(t)= -4.9t2 + v0t + s0 for free-falling object.
To estimate a height of a building, a stone is dropped from the top a building into a pool of water at ground level. How high is the building if the splash is seen 6...
derivatives
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