The volume of water in a cylindrical tank is given by: V = лr²hwhere V is the volume of water in m³,r is the radius of the tank in metres, andh is the height of the water in metres.For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is aconstant. Water is filling the tank, so the height and volume are constantly changinghence h and V are variables.At a certain point in time, the height of the tank is increasing by 0.21 metres/hourand the height is 29 metres. Determine the rate of change of volume (in units ofm³/h) at this point in time. Give your answer to three decimal places.Hint 1: You are being asked to find dv/dt.Hint 2: dh/dt = 0.21 m/h

Let V be the volume of water in the tank Let r be the radius of the tank Let h be the height of the…

Answered: The volume of water in a cylindrical…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Evalúe usando cambio de variable: Sobre la región R Y=4x2 y=x XY=1 X XY=5 2 foxy dA R
A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x from x = -1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 and the density of water is 1000 kg m³ m s²
(d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is 1000 kg/m3. - y =L-h y=0 L. h y=-h
The density of air changes with height. Under some conditions density p, depends on height z, and temperature T according to the following equation where Po and A are both constants. A meteorological balloon ascends (i.e., starts at z = 1 and gains height) over the course of several hours. Complete parts (a) and (b) below. Az P(z,T) = Po e ..... dz v) and that the temperature changes over time (i.e., that T is given by a function T(t)), derive, using the chain rule, an expression for the rate of change of air density, (a) Assuming that the balloon ascends at a speed v (i.e., dt as measured by the weather balloon. Choose the correct answer below. dp Az dT O A. dt T2 dt dp %3D dt Az dT dp С. dt %3D + T dt dp Az) dT O D. dt T2) dt (b) Assume that v = 1, Po = 1, and A = 1 and that when t= 0, T= 1. Are there any conditions under which the density, as measured by the balloon will not change in time? That is, find a differential equation that T must satisfy, if dp = 0, and solve this…
A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = Tr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S = 2πrh.) (A) B C (D The surface area is increasing by 28 square millimeters per second. The surface area is decreasing by 287 square millimeters per second. The surface area is increasing by 32π square millimeters per second. The surface area is decreasing by 32π square millimeters per second.
The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules when y = 18 m/sec, what is K when y = 10 m/sec.
The cross-section of a hill with a steep cliff face is modelled by the equation: where y is the height of the ground above sea level, measured in decametres (dam), and is the horizontal distance from the sea, also measured in decametres. The model applies for values of in the range 0.01 ≤ x ≤ 3. a) Find the formula that describes the gradient of the hill at any given horizontal distance from the sea. b) What is the gradient of the hill at a horizontal distance of: 10 metres (1 dam) from the sea? . dam y=-e +5ln (z) +6 • 1 metre (0.1 dam) from the sea? dam Give your answers to 2 decimal places when necessary.
5. A ball is launched vertically into the air from a height of h meters and with an initial upward velocity of u meters/second. The ball's height above ground is given by the equation H(t) = -4.9t2 + vt + h, where H is in meters and t is in seconds. (This is the metric version of the gravity model.)
A tire company has found that the quantity demanded x, in thousands of units per week, of their best-selling tire is related to the unit price p by the equation (see image). A.) Use differentials to find an approximate change in the quantity of tires demanded per week if the unit price of the tires is increased from $119 to $122 per tire. B.) Use your calculator to find the actual demand for tires when the price is set at $119 and $122 per tire. Then find the difference in demand. C.) Explain why the answers to parts A and B are not the same.
the water level in a cylindrical container is increasing at a rate of 3cm/s. initially, at a level of 5cm, after t seconds the water level is l cm. a)write a rule of formula connecting the variables b) state the rate of change of gradient c) draw a graph that shows the relationship between the variables
A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 200 kilograms of a 57% fat-content chocolate. How many kilograms of each kind of chocolate must they use? Answer: They must mix Kilograms of the 40% chocolate and Kilograms of the 60% chocolate. Question Help: D Post to forum Submit Question esc Search or type UF @ 23 2$ % 1 2 3 4 Q W R < CO

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