Suppose f(x) is a function such that for some positive integer n, f has n linearly dependent derivatives. In other words, if f(x),f′(x),…,f(n−1)(x),f(n)(x) are all linearly dependent functions, then f(x) is expressible in terms of a, xk, eax, sin(ax),cos⁡(ax), and any combination of such functions, where a is a constant and k is a positive integer. Prove this statement

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.

If you apply the changes below to the linear parent function f(x)=x what is the equation of the new function vertically stretched by a factor of 3 flip over the x axis

Prove the following(cot0+cosec0)[tex](cot0 + cosec0) { }^{2} = \frac{1 + cos0}{1 - cos0} [/tex]