MATH 1210 Week 6 Assignment

MATH 1210 Week 6 Assignment | Tulane University

Module 6 Quiz

Solve the problems below and write up a solution to each problem using complete English sentences and well-organized calculations as appropriate. Your solution will be graded based on mathematical accuracy and clarity of presentation.

Late submissions will not be accepted. You must submit your responses as a single .pdf file that includes all pages of your solution. You may resubmit until the deadline but only the most recent submission will be graded. Quiz submissions will not be accepted via e-mail. After submitting you must download your file to ensure that it submitted properly. See technical instructions on Module Quiz submissions.

Problem 1:

According to Newton’s Law of Gravitation we know the force FFFF exerted by a body of mass m1m1mm 1 on a body of mass m2m2mm 2 is given by the formula:
F=Gm1m2r2F=Gm1m2r2FF = G m 1 m 2 r 2,
where GGGG is the gravitational constant, m1m1mm 1and m2m2mm 2 are constant, and rrrr is the distance between the bodies.

a.       Find the derivative of ofFFFF with respect to the distance rrrr.

b.      What does the negative sign in the expression of F′F′FF ′ mean?

c.       Assume planet Mars attracts another body at a rate of 5 N/km when it is 10000 km away. How fast is FFFF changing when the body is 7000 km away?

Problem 2:

Approximate the value of sin(31∘)sin⁡(31∘)sinsin ⁡ ( 31 ∘ ) using linear approximations. [Hint: Convert 31∘31∘3131 ∘ to radians].