1. [-I4Points] ETAILS l MYNOTES ll ASKYOURTEACHER l The height of an object launched straight up is h(t) = 100 + 64t 16t2 where t is measured in seconds and his measured in feet. Answer the following questions. All answers must have correct units and must be accurate to two decimal places. How high is the object when t = 5 seconds? How fast is it moving when t = 5 seconds? [: When is the height exactly 5 feet? (Assume t > 0.) :3 When is the velocity exactly 5 ftfsec? Submit Answer 2. [5 Points] ETAILS MY NOTES ASK YOUR TEACHER The electric potential in a circuit is given by m) = 32091\" where t is measured in seconds and V is measured in volts. Answer the following, with correct units. When is the potential equal to 150 volts? Be accurate to 4 decimal places. H How fast is Vchanging at that instant in time? Be accurate to one decimal place. H When is the voltage changing at 50 volts per second? Be accurate to 4 decimal places. IH Submit Answer 3. [l2 Points] DETAILS MY NOTES ASK YOUR TEACHER The height of a Falling object is given by h(t) = 400 39r 157e-0-25r where t is measured in seconds and h is measured in feet. Answer the following questions, with correct units. To 2 decimal places, when is its velocity 730 ftfs? [: How high is the object at that instant? Round to the nearest foot. . Submit Answer 4. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER Water is draining out of a tank. The volume of water remaining in the tank is m) = 10 7 a with Vin liters and t in minutes. Answer the following questions. All answers must have correct units and must be accurate to two decimal places. At the instant when the ow rate is 7 2 l/min, how much water is left in the tank? H Find the flow rate at the instant when there is exactly 1 liter of water left in the tank. It Submit Answer 5. [I1Points] l DETAILS I I MYNOTES ll ASKYOURTEACHER I An object is launched straight upward from a platform. Its height above ground is h(t) : 3 + vot 7 4.9m2 where h is in meters and t is in seconds. The symbol v0 is an unknown constant. The velocity of the object is 0 at the instant when t = 2 seconds. Compute V0. V0:[ I Your answer should be accurate to 1 decimal place. If you are not sure how to determine the units, click here. Submit Answer 6. [11 Points] DETAILS MY NOTES ASK YOUR TEACHER An object is launched straight upward from a platform. Its height above ground is h(t) = no + 23: 7 4.9:2 where n is in meters and t is in seconds. The symbol ho is an unknown constant. The object hits the ground when t : 5 seconds. Compute ho. Your answer should be accurate to 1 decimal place. If you are not sure how to determine the units, click here. Submit Answer 7. [-11 Points] DETAILS | MY NOTES ll ASKYOURTEACHER I An object is launched straight upward from a platform 10 feet above ground. Its height above ground as a function of time is h(t) = 10 + 50: + %at2 where h is in feet and t is in seconds. The symbol a is an unknown constant. Suppose you know that h'(1.25) = 9.75 ftfs. Find a, accurate to 1 decimal place. a: U Submit Answer 8. [12 Points] DETAILS MY NOTES ASK YOUR TEACHER An object is launched straight upward from a platform. Its height is h(t) = no + th 7 15.1:2 where n is in feet and t is in seconds. Both no and V0 are unknown constants. At the instant I = 1.5 seconds you know that the height is 50 feet and the velocity is 0. Find both unknown constants, accurate to 1 decimal place. Submit Answer 9. [-11 Points] DETAILS MY NOTES ASK YOUR TEACHER The pressure in a cylinder is given by P(t) = 101 + where P is in kilopascals (WebAssigh abbreviation kPa) and t is in minutes. Assume that t 2 1 and k is constant. At time t = 7.5 minutes the pressure is changing at 1.35 kPaimin. Find k. Your answer should be accurate to 1 decimal place and must include units. If you are not sure how to enter unusual combinations of units, click here. Submit Answer 10. [-11 Points] DETAILS I MY NOTES ll ASKYOURTEACHER I The electrical potential in a circuit is given by 'l/(t) = vou era-1f) where V is in volts, t is in seconds, and V0 is constant. Potential is changing at 2.75 volts/sec at the instant t = 1 second. Find V0, accurate to 1 decimal place. If you use this method to think about units, you may nd it useful to know the following FACT: The output of an exponential function must be dimensionless. I.e., it has no units. Su bmil Answer 11. [-12 Points] D TAILS MY NOTES ASK YOUR TEACHER The electrical potential in a circuit is given by V(t) = 15 7 15e-kt where V is in volts, t is in seconds, and k is constant. When t = O the rate of change of potential is 6.9 volts/sec. Find the rate of change 3 seconds later, accurate to 2 decimal places. l; Find k, accurate to 2 decimal places, with correct units. You may find it useful to know... FACT: The input to an exponential function must be dimensionless. ].e., it has no units. Submil Answer 12. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER An object is launched straight upward from a platform above ground. Its height is nu) = 10 + v0: 4.9:2 where h is in meters and t is in seconds. It hits the ground with a velocity of 25.0 m/s. Find v0, accurate to 1 decimal place. Von ] When did it hit the ground? Be accurate to 2 decimal places. l: 13. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER An object is launched straight upward from a platform. Its height above ground is h(t) = n0+ vnt 7 16.1t2 where h is in feet and t is in seconds. The graph of h is shown below. h (ft) 126 2.5 t (3) Find both unknown constants, accurate to 1 decimal place. Submil Answer 5U bn'llt An swer 14. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER The pressure in a cylinder is given by Pm = 101 + i t where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes. Assume that t 2 1 and k is constant. At the instant when pressure is 114 kPa, it is changing at 70.85 kPa/min. When does this happen? Be accurate to 1 decimal place. i: What is the pressure when t = 1 minute? Round to the nearest kilepascal. Submit Answer 1- [0/3Points] I DETAILS II PREVIOUSANSWERS I I MYNOTES II ASKYOURTEACHER I An object is thrown straight up. Its height is given by y(f) = 100: 16t2 with yin feet and t in seconds. Compute the derivative of y at the location t. Find the velocity of the object at the instant t = 1.3 seconds. Give an exact decimal answer with units. At what instant in time is the velocity exactly zero? Give an exact decimal answer with units. Viewing Saved Work Revert to Last Response Submit Answer 2. [113 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER Water is draining out of a tank. The volume of water remaining in the tank is a function of time: v0) = 10 , 3'5 with V in liters tin minutes. Compute the derivative of V at the location t. 3 Vi\" = ' m J Find the flow rate at the Instant when t = 3 minutes. Use correct units and be accurate to three decimal places. At what instant in time is the ow rate exactly 1 I/min? Give an exact decimal answer with units. _ Viewing Saved Work Revert to Last Response Submit Answer 3. [-3 Points] DETAILS MY NOTES ASK YOUR TEACHER The pressure in a cylinder is a function of time: P(r)=1oo+%;t21 with P in kilopascals (kPa) and tin seconds. Find the rate of change of P at the instant t. How fast is pressure changing at the instant when t = 4 seconds? Use correct units and be accurate to three decimal places. At what instant in time is the pressure changing at a rate of 70 kPa/s? Be accurate to two decimal places and include correct units. [:1 4. [I3 Points] The number of bacteria cells in a petri dish grows according to the function with N How fast is number of cells changing at 2 days? Be accurate to one decimal place and include units. N(t) = 30st; t 2 0 is number of cells and t in days. Find the rate of change of N at the instant t. [:l ASK YOUR TEACHER At what instant in time is the number of cells changing at a rate of 500 cells per day? Be accurate to three decimal places and include correct units. Submit An SWEI' :l 5. [-I1 Poin ts] An object is thrown straight up. Its height is given by in which y is in meters, tis in seconds, and k is an unknown constant. Find the velocity of y(t) = 10: ktz the object at the instant t = 1.5 seconds. Your answer will be an expression that includes k. Do not include units. l: Submit Answer 6. [I1 Points] The height of a moving object is given by h(t) = 4.295in(2.16t + 7.9) where h is in feet and t is in seconds. Find the velocity at the Instant t = 2 seconds. Be accurate to 3 decimal places and include correct units. [:1 Submit Answer 7. [-l7 Points] The population of sh in a lake is observed to fluctuate during a six month period according to the formula P\") = 50000 + ZOOOOSint where t is time in months. Answer the questions below. Note that the units are provided Outside the answer boxes. You don't have to include them in your You ma answers. y find it useful to graph this function on the domain 0 s t S 6 months. HOW fast iS the population changing at the instant I = 4 months? What is when d Shortly sh/month, rounded to the nearest whole number. the smallest number of sh during the six month period? sh oes the population low ponnt occur? Be accurate to 2 decimal places. months before the low point, the population was 70,000 sh. How fast was the population changing at that instant? Shortly sh/mo Li'lSl'i/IT'IOI'Ith, rounded to the nearest whole number. \\ after the low point there is an instant when the population is changing at 10,000 nth. when is it? Be accurate to 2 decimal places. months If the population is changing at 11,000 fish/month, how many fish are there? NOTE: There are two possible correct answers. ASK YOUR TEACHER ASK YOUR TEACHER ASK YOUR TEACHER 8. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER The velocity of an object is given by Q = 40 _ 32t ftIsec dt' Where it is the height of the object in feet and t is time in seconds. The initial height, at t = 0, of this object is 80 feet. at Find the formula for the height of this object. hit) = ' b. Find the velocity of this object the instant it hits the ground. Round your answer to two decimal digits. :1 Submit Answer 9. [-12 Points] DETAILS MY NOTES ASK YOUR TEACHER The velocity of an object is given by Q = 205in(t) cm/sec dt Where it is the height of the object in centimeters and t is time in seconds. The initial height, at t = 0, of this object is 30 centimeters. a. Find the formula for the height of this object. mt) = ' b. Find the maximum height of this obiect. Round your answer to one decimal digit. :i Submit