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efcd013e3fbe079e7680d581/1185304.pdf Suppose "% .. Aye" . Answer the following 1 / 3 - 100% HO 1) Separate the differential equation, then integrate both sides. 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second. If the mattress is completely inflated after 1 minute, how much air can the mattress hold? Include units in your answer. 2) Write the general solution as a function y(x). 2) The same mattress in Problem 1 is later deflated by opening its release valve. Air escapes at a rate of (f) = 0.25e , where r is in cubic feet per second. Assuming the mattress is still completely inflated when the valve is opened, how much air is released in the first 30 seconds? Suppose of - ( and P(1) = 4. Answer the following. 3) Separate the differential equation, then integrate both sides 3) Refer to the information in Problems 1 and 2. How much air remains in the mattress after 45 seconds from opening the release valve? 4) Find the constant of integration. 4) A projectile travels at a velocity of v(() = 45 - 32t, where v(f) is measured in feet per second. Find the change in position (displacement) of the projectile on the time interval [0, 3]. Include units in your answer. I 5) Refer to the scenario in Problem 4. If the projectile started with an initial position at s(0) = 25 feet, find its position at t = 3. 5) Write the particular solution as a function Pr Suppose Ox - y' cosmin' 8. Answer the following. 6) The graph of g'(f) on the interval [0, 10] is shown below. If g(0) = 3, find g(10). g'(t ) 6) Separate the differential equation, then integrate both sides. () Write the general solution as a function y(0). 10 3 / 3 - 50% + Suppose of . . and of " ton and rx(1) . -2. Answer the following. 6) Separate the differential equation, then integrate both sides ) Find the constant of integration. ()A tumor is found with an initial mass of 3.5 grams. Its growth rate is measured and recorded in the le below, where R(1) is the rate of growth in grams permonth. Use a trapezoidal approximation with four subintervals to determine the increase in mass of the tumor over the 4-month period. 10) Write the particular solution as a function n(). o 1 2 3 4 R(1 0.2 0.3 0.5 0.7 0.8 ) Refer to the information in Problem 7. Find the mass of the tumor when t = 4. Find the general solution to the following differential equations. 9) A skydiver jumps from a plane from 4000 meters and begins to fall at a velocity of v(!) - 40 -60, (21 + 1 ) 11) 3-12 -8 here v(0) is mea ters per cond. What is the skydiver's altitude after 15 seconds? 12) Ju _ X' .x tanu 3) -6-21 +3K -KI 14) oh _ z(1+ n') 1+2 10) The rate of change in the volume of a tank is known to be - 0.6t . cos(0.08:* -1). where V(Q is in minutes? gallons per minute and 0 s t s 10. if the tank has a volume of 14 gallons initially, what is its volume at 10 15 ) 1 -165-5-0
