Answer:
140 deg
Step-by-step explanation:
The sum of the measures of the interior angles of an n-gon is
(n - 2)180
In a 9-gon, there are 9 sides, so n = 9.
The sum of the measures of the interior angles of a 9-gon is
(n - 2)180 =
= (9 - 2)(180)
= 7(180)
= 1260
A regular polygon has congruent interior angles. A 9-gon has 9 congruent interior angles. The measure of each interior angle is the sum of the measures of the interior angles divided by the number of angles.
1260/9 = 140
The key piece of information for these questions is the Fundamental Theorem of Algebra, which states that a degree n polynomial has n complex roots. A complex root can be either real or imaginary.
First question, regarding the polynomial y = x^3 - 3x^2 + 16x - 48:
We know there is one real root, the x-intercept.
Since it's a third degree polynomial, there are three complex roots in total.
Therefore, there is one real root and two imaginary roots.
Answer is B
Second question:
You probably can guess the answer, now that you know the Fundamental Theorem of Alegebra:
There are 3 real zeros, each with multiplicity one, meaning each root only happens once. It's a 5th degree polynomial, so there are a total of 5 roots, implying 2 imaginary roots.
Answer is C) 3 real and 2 imaginary zeroes.
The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft
50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt
