QUESTION 1 REMARKS Only simple geometriesrectangles and trianglescan be solved e

Question

QUESTION 1

REMARKS Only simple geometriesrectangles and trianglescan be solved exactly with this method. More complex shapes require calculus or the square-counting technique in the next worked example.

QUESTION 1: When stretching springs, does half the displacement require half as much work? (Select all that apply.)

a. Yes, because the work is equal to the force times the distance.

b. Yes, because the spring exerts a constant force.

c. Yes, because half the displacement means the force from the spring is half as large.

d. No, because the spring does not exert a constant force.

e. No, because the force of the spring is proportional to x.

f. No, because the force exerted by the spring is proportional to x2.

QUESTION 2:

REMARKS Mathematically, there are a number of other methods for creating such estimates, all involving adding up regions approximating the area. To get a better estimate, make smaller boxes.

QUESTION 2: In developing such an estimate, is it necessary for all boxes to have the same length and width? (Select all that apply.)

a. Yes, because otherwise the number of boxes is not proportional to the area.

b. No, because we are just counting boxes, not estimating area.

c. Yes, because we need square boxes to count accurately.

d. No, because counting boxes would work in exactly the same way if the boxes are rectangles but not squares.

e. No, if we have some idea what area the average box has and use the average area as an estimate.

Explanation / Answer

for question 1

d. No, because the spring does not exert a constant force.

e. No, because the force of the spring is proportional to x.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.