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Calculus
A circular swimming pool has a diameter of 14 m, the sides are 3 m high, and the depth of the water is 2.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3.)
Calculus
The spring-flex exercise system consists of a spring with one end fixed and a handle on the other end. The idea is that you exercise your muscles by stretching the spring from its natural length, which is 31 cm. If a 200 Newton force is required to keep the spring stretched to a length of 47 cm, how much work is required to stretch it from 46 cm to 70 cm?
Calculus
A carpet which is 6 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is
f(x)= 900/((x+2)^2)
How much work is done unrolling the entire carpet?
f(x)= 900/((x+2)^2)
How much work is done unrolling the entire carpet?
Calculus
Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 45 cm to a length of 66 cm. How much work is needed to stretch it from 60 cm to 74 cm? Your answer must include the correct units.
Calculus
for each of the following function sketch three level curves in xy-plane labeling each one with its Z-value
(1) f(x,y) = x - 2y
(2) g(x, y) = 3x^2 + 3y^2
(3) h(x,y) = intergral of (2t)dt, from y to x.
(1) f(x,y) = x - 2y
(2) g(x, y) = 3x^2 + 3y^2
(3) h(x,y) = intergral of (2t)dt, from y to x.
Calculus
Robin is running around on the inside of a bowl-like surface, z = x^2 + y^2 , with distance measured in meters. It is noon, the sun is directly overhead, and the birds are silent. All of a sudden, much to her horror, she realizes someone has chopped off the bowl at a height of 3 meters. But she is too close to the edge and running too fast, so she flies up off the edge of the bowl at a speed of 5 meters per second. As she flies up off the edge, she looks down at the ground below (the xy-plane) and sees her shadow. She observes that it is in the first quadrant, has x-coordinate 1, and it is heading directly towards a house with coordinates (2,4). Realizing she has no parachute, she wonders (of course) how long it will be before she hits the ground and where she will land. Set her mind at ease by answering these two questions for her. Ignore air resistance.
Calculus
Use the first differentiation principle to get f(x)=x^2 -2x -15
Calculus
james has 8 rocks CDs and 6 country CDs, he will pick one cd at random, replace it, then pick another cd at random. what is the probability that james will pick one rock cd and then a country cd?
Calculus
My dear Expert please solve the following question.
what is fundamental law of trigonometry
what is fundamental law of trigonometry
Calculus
Expert sir expalain the difference between function and operator.best wishes.
Finding a professional expert in "partial differential equations" in the advanced level is difficult.
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#340153 on Dec 2023
#340153 on Dec 2023