Find Root of Equation Using Newton’s Method: a) Explain how we know that the given equation must have a root in the given interval.
b) Use Newtons method to approximate the root correct to six decimal places.

x^4-x^3-1=0 [1,2]

A80-foot piece of siding is cut into three pieces so that the second piece is four times four times as long as the first piece and the third piece is five times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces.

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

Joanie wrote a letter that was 1 1/4 pages long. katie wrote a letter that was 3/4 page shorter then joagies letter. how long was katies letter