Michael found a stock fund he wanted to purchase. He can make an initial investment of $10,000. The fund
0.07t
has a continuous compounding rate of 7%. Michael uses the equation 20000 = 10000e
to determine how
long he will need to plan to invest for his money to double in value. How long will Michael’s investment need
to be?

We have enough material to build a fence around a station that has a perimeter of 180 feet the width of the rectangular space must be 3 1/4 feet what must the length be

According to the 2008 u.s. census, california had a population of approximately 4 × 10^7 people and florida had a population of approximately 2 × 10^7 people. which of the following is true? a. the population of florida was approximately two times the population of california. b. the population of florida was approximately twenty times the population of california. c. the population of california was approximately twenty times the population of florida. d. the population of california was approximately two times the population of florida.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .