Answer:
Answers are in bold type
Step-by-step explanation:
f(x) = 
The parabola opens up, so has a minimum at the vertex.
Let (h, k) be the vertex
h = -b/2a = - (-144)/2(1) = 57
k = 57^2 - 144(57) = 3249 - 6498 = -3249
Therefore, the vertex is (57, -3249)
The minimum value is -3249
The domain is the set of real numbers.
The range = {y | y ≥ -3249}
The function decreases when -∞ < x < 57 and increases when 57 > x > ∞
The x - intercepts:
= 0
x(x - 114x) = 0
x = 0 or x = 114
x-intercepts are (0, 0) and (0, 114)
When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0
y-intercept is (0, 0)
Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Step-by-step explanation:
Since we have given that
Height = 9 inches
Diameter = 6 inches
Radius = 3 inches
So, 
Volume of cone is given by

By differentiating with respect to time t, we get that

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie 
and h = 2 inches deep.

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Answer:
6 3/8 inches (6.375 inches)
Step-by-step explanation:
For simplicity we'll assume that both the photo and the poster board are square. To determine the width of the border, subtract 8.5 inches from the poster board width 21.25 inches, obtaining 12.75 inches, and then divide that 12.75 inches by 2: 6.375 inches (6 3/8 inches).
Set the photo 6 3/8 inches from each edge of the poster board.
Answer:
(6,15)
Step-by-step explanation: