MTH 174, Summer 2018, Test 1 Practice Questions 1. What is the area between y- a

Question

MTH 174, Summer 2018, Test 1 Practice Questions 1. What is the area between y- and y2 for x 0 to 1? 2. Find the volume using the plate method of y = 5v/25-r2 with 0 x 2 if the curve is rotated around the x axis, f 3. Find the volume using the shell method of y= 102(x 2 2 with 0S1 2 if the curve is rotated around the y axis. 4. A piano weighing 450 lbs is supported by a 10 ft cable weighing 2 lbs/ft. What is the work required to lift the piano to the top? 5. The function T(t) 30+2t -12 approximates the temperature at t hours past noon. s)Find the average temperature betwen noon and 6 pm (b) Find the time when the average temperature occurs. Integrate JIn(r)dz using integration by parts. Integrate the function below using a trigonometric identity. coS () dx sin(r

Explanation / Answer

Answer :

The weight of piano is 450 lbs

The center of mass of cable is 5 ft from the top.

The center of mass of the piano is 10 ft.

Therefore, the work required to lift the piano to the top is

W = 450*10 + 5*20

= 4500 + 100

= 4600

The required work is 4600 ft-lbs

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