MAT 132 Midterm: MAT 132 SBU Exam Midterm II132 s10

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turquoisegnu128

31 Jan 2019

School

Stony Brook University

Department

Mathematics

Course

MAT 132

Professor

All

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MAT 132 Full Course Notes

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Document Summary

Print your name, id number and section number on your answer sheet. Show some work or give an explanation when you are asked to do so. It is not necessary to simplify your answers. Please do not use calculators or any other electronic devices, notes or books during the exam time. Show work: find the length of the curve given by y = z x. Express the volume of s1 as a de nite integral. (c) let s2 be the solid obtained by rotating the region r about the line y-axis. Express the volume of s2 as a de nite integral: a spherical tank of radius 3 meters is buried in the ground so that the top of the tank is 4 meters beneath ground level. The tank is lled with liquid which has a density of 1500 kilograms/meter3.

Related Questions

- A variable force of 6x^â2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 17 ft. (Round your answer to two decimal places.)

____ ft-lb

- The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 3 to x = 35.

x	3	7	11	15	19	23	27	31	35
f(x)	5	5.5	7.3	8.8	9.5	8.1	6.5	5.4	4.3

W = _____ J

- Suppose that 5 J of work is needed to stretch a spring from its natural length of 26 cm to a length of 37 cm.

(a) How much work is needed to stretch the spring from 31 cm to 35 cm? (Round your answer to two decimal places.)
____ J

(b) How far beyond its natural length will a force of 50 N keep the spring stretched? (Round your answer one decimal place.)
____ cm

- A spring has natural length 20 cm. Compare the work W₁ done in stretching the spring from 20 cm to 30 cm with the work W₂ done in stretching it from 30 to 40 cm. (Use k for the spring constant)

W₁ = ____ J

W₂ = ____J

- If 12 J of work are needed to stretch a spring from 14 cm to 18 cm and 20 J are needed to stretch it from 18 cm to 22 cm, what is the natural length of the spring?
____ cm

Hooke's Law

In Exercises 9-14, use Hooke’s Law to determine the work done by the variable force in the spring problem.

An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of the pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 8 feet, and the springs are at their natural length when the door is open. Find the work done by the pair of springs.

help please!