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proportional to the area Aof the surface of the ater and that the constant of proportionality k0.01. Output: water evaporates at rate proportional to area A of surface R Input: water pumped in at rate 'min (a) hemispherical tank (b) cross-section of tank ca) The rata of change at the voluma el the vater at time tia a net rata. Use tha net rate to detrmina a ditfrertal equation for the haght hel the vater at time . The valume of the vater shan in the fque ia ve na -a, where e = s0. Bpres the area el the surtace of the vater a- neme of h. () Selve the dferential aten in pat (a). Graph the solution. 20 20 15 15 13 15 10 10 10 10 so00 1000 2000 10000o 6000 so00 10000 o 10000 2000 4000 6000 4000 6000 so00 2000 4000 2000 4000 6000 S000 () there vere ne evaporation, hew leng weuldt taie the tank te fa (Reund your anver te be decimal places.) min

proportional to the area Aof the surface of the ater and that the constant of proportionality k0.01. Output: water evaporates at rate proportional to area A of surface R Input: water pumped in at rate 'min (a) hemispherical tank (b) cross-section of tank ca) The rata of change at the voluma el the vater at time tia a net rata. Use tha net rate to detrmina a ditfrertal equation for the haght hel the vater at time . The valume of the vater shan in the fque ia ve na -a, where e = s0. Bpres the area el the surtace of the vater a- neme of h. () Selve the dferential aten in pat (a). Graph the solution. 20 20 15 15 13 15 10 10 10 10 so00 1000 2000 10000o 6000 so00 10000 o 10000 2000 4000 6000 4000 6000 so00 2000 4000 2000 4000 6000 S000 () there vere ne evaporation, hew leng weuldt taie the tank te fa (Reund your anver te be decimal places.) min

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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f Facebook Content MATLAB CODING - OneDrive * Design Problem - MATH156_202 x Answered: A 4-pound weight stre X + A webassign.net/web/Student/Assignment-Responses/last?dep=28859853 An outdoor decorative pond in the shape of a hemispherical tank is to be filled with water pumped into the tank through an inlet in its bottom. Suppose that the radius of the tank is R = 10 ft, that water is pumped in at a rate of a ft/min, and that the tank is initially empty. As the tank fills, it loses water through evaporation. Assume that the rate of evaporation is proportional to the area A of the surface of the water and that the constant of proportionality is k = 0.01. Output: water evaporates at rate proportional to area A of surface Fr- Input: water pumped in at rate 7 ft/min (a) hemispherical tank (b) cross-section of tank 갓⒤뀐갓 (a) The rate of change of the volume of the water at time t is a net rate. Use this net rate to determine a differential equation for the height h of the water at time t. The volume of the water shown in the figure is V = TRH2 - nh, where R = 10. Express the area of the surface of the water A = in terms of h. dt (b) Solve the differential equation in part (a). h(t) = Graph the solution. h h h h 20 20 20- 20- 15 15 15 15 10 10 10 10 5 5 10000 O 6000 800 10000 O 10000 O 2000 4000 6000 8000 2000 4000 2000 4000 6000 8000 2000 4000 6000 8000 10000 (c) If there were no evaporation, how long would take the tank to fill? (Round your answer to two decimal places.) min (d) With evaporation, what is the depth of the water at the time found in part (c)? (Round your answer to three decimal places.) ft Will the tank ever be filled? Prove your assertion. 5:54 pm O Type here to search 32°C Mostly sunny A 9 4) ENG 09/02/2022
Transcribed Image Text:f Facebook Content MATLAB CODING - OneDrive * Design Problem - MATH156_202 x Answered: A 4-pound weight stre X + A webassign.net/web/Student/Assignment-Responses/last?dep=28859853 An outdoor decorative pond in the shape of a hemispherical tank is to be filled with water pumped into the tank through an inlet in its bottom. Suppose that the radius of the tank is R = 10 ft, that water is pumped in at a rate of a ft/min, and that the tank is initially empty. As the tank fills, it loses water through evaporation. Assume that the rate of evaporation is proportional to the area A of the surface of the water and that the constant of proportionality is k = 0.01. Output: water evaporates at rate proportional to area A of surface Fr- Input: water pumped in at rate 7 ft/min (a) hemispherical tank (b) cross-section of tank 갓⒤뀐갓 (a) The rate of change of the volume of the water at time t is a net rate. Use this net rate to determine a differential equation for the height h of the water at time t. The volume of the water shown in the figure is V = TRH2 - nh, where R = 10. Express the area of the surface of the water A = in terms of h. dt (b) Solve the differential equation in part (a). h(t) = Graph the solution. h h h h 20 20 20- 20- 15 15 15 15 10 10 10 10 5 5 10000 O 6000 800 10000 O 10000 O 2000 4000 6000 8000 2000 4000 2000 4000 6000 8000 2000 4000 6000 8000 10000 (c) If there were no evaporation, how long would take the tank to fill? (Round your answer to two decimal places.) min (d) With evaporation, what is the depth of the water at the time found in part (c)? (Round your answer to three decimal places.) ft Will the tank ever be filled? Prove your assertion. 5:54 pm O Type here to search 32°C Mostly sunny A 9 4) ENG 09/02/2022
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