Write a polynomial in factored form with least possible degree having zeros at 5, -2 multiplicity 3, -3 multiplicity 2, 3i multiplicity 2, and f(-1)=-800.

Polynomial:

Step-by-step explanation:

Zeros are at 5, (-2 * 3 = -6), (-3 * 2 = -6), (3i * 2 = 6i)

= 5, -6, -6, and 6i

The factors are (x-5), (x-(-6)), (x-(-6)), (x-6i)

= (x-5), (x+6), (x+6), (x-6i)

For f(-1) = -800, x = -1 which gives a factor of (x - (-1)) = x + 1. The remainder is -800

The polynomial is thus:

f(x) = (x+1)(x-5)(x+6)(x+6)(x-6i) - 800

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

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm