A cylindrical container has initially 400 cm3 of water and is being filled at the constant rate of 100 cm3 per second. The radius of the container is 40 cm. a) Write a formula for the quantity Q of water in the container after t seconds. b) Write a formula for the height H of water in the container in terms of Q. c) Find an expression for the composition (H o Q)(t) and its meaning.  d) How long does it take the height H of the water in the container to reach 50cm?

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Q: (b) If its' owner uses 3 pipes of radius 4cm, with water flowing at a rate of 30cm/s, how long will…

A: (a) Area of circuler face= pi*r2  =pi*102 = 314 cm2.                    (pi=3.14)

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Q: If the work required to stretch a spring 5 feet beyond its natural length is 15 foot-pounds, how…

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Q: A boat with its load weighs 1,435 N. If the force exerted upon the boat by the motor in the…

A: F=72- 2vma = 72- 2v14359.81 dvdt=72-2v∫(146.3) dv72-2v=∫ dtt=-146.32ln(72-2v)+Cv=0 at…

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A: Given :Length of the vibrating portion = 32.8 cmMass= 0.343 gLength= 32.8 cm

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Q: (6) An aluminum tube is 30000m long at 200C. What is its length at (a) 1000C and (b) OoC?

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Q: t requires 4 ft-lb of work to stretch a certain spring from its natural length of 1 ft to a length…

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Q: 2. The height of a cone shaped tank for liquid storage in a chemical factory is 9 ft with a diameter…

A: Topic:- volume of cone

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Q: A water reservoir is shaped like a rectangular solid with a base that is 50 yards by 40 yards, and a…

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Q: Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A…

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Q: A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft…

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Q: If. the.work.required to stretch a spring 3 ft beyond its natural length is 9 ft-lb, how much work…

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Q: A spring has a natural length of 10 cm. It takes 4 J to stretch the spring to 17 cm. How much work…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.