The volume,Vm³, of liquid in a container is given byV = (3h² + 4) ³ - 8,where h m is the depth of the liquid. Which of the following is/are true?Liquid is leaking from the container. It is observed that, when the depth of the liquid is 1 m, the depthis decreasing at a rate of 0.5 m per hour. The rate at which the volume of liquid in the containeris decreasing at the instant when the depth is 1 m is 4.5√7.dV6h√3h² +4.dhdVThe value of at h = 1 mis 9√7.Non of the above is true.d²v9h√3h² +4.dh2=2

Given, V=(3h2+4)34-8 Where V m2 is the volume at any depth h m.

Answered: The volume, Vm³, of liquid in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A water tank, in the shape of a cone, has water draining out, where its volume is changing at a rate of -0.25 ft³/sec. Find the rate at which the level of the water is changing when the level (h) is 10 feet. 12 V = 14 ↓ r²h Hint: If = then r = 3h; 14 Get V in terms of h only. -0.25 ft³/sec dh = [?] ft/sec dt Round your answer to the nearest thousandth. Enter
Ohm’s law says that the current, I, (in amps) obeys the formulaI =V/Rwhere V represents the voltage (in volts) and R represents the resistance (in ohms). In this problem, V , I, and R are all functions of time. If the current is increasing at a rate of 2 amps/secand the voltage is decreasing at a rate of 3 volts/sec,then how fast is the resistance changing when I = 1, V = 3, and R = 3?
4.1: 10) A circle is inside a square.The radius of the circle is decreasing at a rate of 1 meter per minute and the sides of the square are decreasing at a rate of 3 meters per minute. When the radius is 6 meters, and the sides are 20 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is ? square meters per minute.
Q2: In the two-tank mixing process shown in Fig.(2), x varies from 0 lb salt/ft³ to 1 lb salt/ft³ according to a step function. At what time does the salt concentration in tank 2 reach 0.6 lb salt/ft³? The volume of each tank is 6 ft³. 3ft/min 777 Tank 1 Fig.(2) Tank 2
Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in hours and Ct is the concentration of caffeine. If C0 = 1000, estimate the time needed for 80% of the caffeine to be eliminated from the body (i.e. 20% left). What if C0 = 500?
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.
Suppose that the production Q (in gallons of paint) of a paint manufacturer can be modeled by Q = 140K/2L/2, where K is the company's capital expenditures in thousands of dollars and L is the size of the labor force (in hours worked). Find aQ/ƏK when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/ək = Interpret aQ/ƏK. If labor hours remain at 900 and K increases by $1000, will increase about gallons of paint. Find aQ/ƏL when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/Ək = Interpret aQ/aL. If capital expenditures remain at $230,000 and L increases by one hour, Q will increase about gallons of paint. Need Help? Read It Watch It
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is V = {mr?h.)
A conical container, with its axis vertical and vertex downwards, is full of water. The water is emptying through a small hole at the vertex. If the depth of water after 1 minutes is h cm, and the rate at which the volume of water flows out is proportional to √h, show that -kh-3/2, where k is a positive constant. dh di
Assign variables and restate the following problem in terms of known and unknown derivatives (but do not solve it): How fast is the volume of a cube increasing if its side increases at a rate of 0.5 cm/s?

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS