Consider the following equation. 3x4 − 8x3 + 3 = 0, [2, 3] (a) explain how we know that the given equation must have a root in the given interval. let f(x) = 3x4 − 8x3 + 3. the polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the intermediate value theorem, there is a number c in (2, 3) such that f(c) = . in other words, the equation 3x4 − 8x3 + 3 = 0 has a root in [2, 3]. (b) use newton's method to approximate the root correct to six decimal places.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

c

step-by-step explanation:

there is no picture in order for this question to be answered

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."