The angle measured from the normal to the mirror will be
.. arctan(14/11.5) ≈ 50.6°
Since
is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.
So, if we think of 15 as 9+6, we have

Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).
Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.
Answer:
A = 0
B = π/4
C = 0
D = 4
Volume = 16
Step-by-step explanation:
∫BA∫DC∫AB∫CD is shown in the picture attached
By definition, the average rate of change is given by:

We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:

Evaluating for x = 3:

Then, the AVR is:




For f (x) = 3x - 8:
Evaluating for x =4:

Evaluating for x = 5:

Then, the AVR is:



For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:

Evaluating for x = 4:

Then, the AVR is:




For f (x) = x ^ 2 - 5:
Evaluating for x = -1:

Evaluating for x = 1:

Then, the AVR is:




Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]
Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.
8 goes into 40 five times
3/8= (3*5)/40 = 15/40
10 goes into 40 four times
7/10= (7*4)/40= 28/40
ANSWER: A) 15/40 and 28/40
Hope this helps! :)