Question

1.Suppose that a and b vary inversely and that b=5/3 when a=9. Write a function that models the inverse variation and find b when a=10. 2.What is a polynomial function in standard form with zeroes 1, 2, -2, and -3?

Answer 1

Answer:

a1) The model is a = 15/b

a2) When a = 10, b = 1.5

b) The polynomial function in standard form is $f(x) = x^{4} -4x^{3} - x^{2} + 16x -12$

Step-by-step explanation:

a1) Since a and b varies inversely and a = 9, b = 5/3. First find the constant of proportionality.

$a \alpha 1/b\\a = k/b\\9 = k /(5/3)\\9 = 3k/5\\45 = 3k\\k = 45/3\\k = 15$

The function that models the inverse variation is :

a = 15/b............(1)

a2) When a = 10, find b.

Substituting the value of a into equation (1)

10 = 15/b

b = 15/10

b = 1.5

b) Find the polynomial function with zeroes 1, 2, -2,3

The factors of the polynomials are x -1, x - 2, x + 2, x - 3.

The polynomial becomes:

$f(x) = (x-1)(x-2)(x+2)(x-3)\\f(x) = (x^{2} - 3x + 2) ( x^{2} - x -6)\\f(x) = x^{4} -x^{3} - 6x^{2} - 3x^{3} + 3x^{2} + 18x + 2x^{2} -2x - 12\\f(x) = x^{4} -4x^{3} - x^{2} + 16x -12$