For the function f(x) = 1 4 ex + e−x, prove that the arc length on any interval has the same value as the area under the curve. f(x) = 1 4 ex + e−x ⇒ f '(x) = ⇒ 1 + [f '(x)]2 = 1 + = 2 = [f(x)]2 The arc length of the curve y = f(x) on the interval [a, b] is L = b a 1 + [f '(x)]2 dx = b a [f(x)]2 dx = b a f(x) dx, which is the area under the curve y = f(x) on the interval [a, b].

Asmall business produces and sells balls. the fixed costs are $20 and each ball costs $4.32 to produce. each ball sells for $8.32. write the equations for the total cost, c, and the revenue, r, then use the graphing method to determine how many balls must be sold to break even.

Mat bought a phone for $100. he has to pay $30 per mouth. if he has paid $640 in total, how many mouth has he had the phone?

He ! a group of farmers planned to clean 80 acres of wheat per day to finish the work on schedule. right before the work started, they received a new piece of machinery that them clean 10 more acres per day than originally planned. as a result of increased productivity in the last day before the deadline they only had to clean 30 acres. how many acres of wheat did the group of farmers have to clean?