MATH 22

A bucket weighing 10 Newton when empty is loaded with 90 Newton of sand and lifted at 10 cm at a constant speed. Sand leaks out of a hole in a bucket at a uniform rate and one third of sand is lost by the end of the lifting process in Joules.

• 30 Joules

• 850 Joules

• 24 Joules

• 100 Joules

A conical vessel is 12 m across the top and 15 m deep. If it contains water to a depth of 10m find the work done in pumping the liquid to a height 3 m above the top of the vessel.

• 560 pi w N.m

• 660 pi w N.m

• 342 pi w N.m

• 150 pi w N.m

A small in the sack of rice cause some rice to be wasted while the sack is being lifted vertically to a height of 30 m. The weight lost is proportional to the cube root of distance traversed. If the total loss was 16 kg, find the work done in lifting the said sack of rice which weighs 110 kg.

• 2409 kg.m

• 1245 kg.m

• 2940 kg.m

• 3108 kg.m

A full tank consists of a hemisphere of radius 4 m surmounted by a circular cylinder of the same radius of altitude 8 m. Find the work done in pumping the water to an outlet of the top of the tank.

• (2332/3) pi w

• (2125/3) pi w

• (2752/3) pi w

• (20002/3) pi w

Determine the differential equation of a family of lines passing thru (h, k).

• (x + h) dx – (y – k) dy = 0

• (x – h) dx – (y – k) dy = 0

• (x – h) + (y – k) = dy/dx

• (y – k) dx – (x – h) dy = 0

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis

• 2x dy – y dx = 0

• x dy + y dx = 0

• 4x dy – y dx = 0

• -2x dy – y dx = 0

Find the differential equations of the family of lines passing through the origin.

• ydx – xdy = 0

• xdy – ydx = 0

• xdx + ydy = 0

• ydx + xdy = 0

The radius of the moon is 1080 miles. The gravitation acceleration of the moons surface is 0.165 miles the gravitational acceleration at the earth’s surface. What is the velocity of escape from the moon in miles per second?

• 0.5

• 1.47

• 23.27

• 56

Find the equation of the curve at every point of which the tangent line has a slope of 2x

• -y2 + C

• -x2 + C

• y2 + C

• x2 + C

The radius of the earth is 3960 miles. If the gravitational acceleration of earth surface is 31.16 ft/sec2, what is the velocity of escape from the earth in miles/sec?

• 76,553

• 23.557

• 6.9455

• 0.1235