Step-by-step explanation:
A)
The length of the box is 30 − 2x inches.
The width of the box is 30 − 2x inches.
The height of the box is x inches.
So the volume is:
V = x (30 − 2x)²
B)
V(3) = 3 (30 − 6)² = 1728
V(4) = 4 (30 − 8)² = 1936
V(5) = 5 (30 − 10)² = 2000
V(6) = 6 (30 − 12)² = 1944
V(7) = 7 (30 − 14)² = 1792
As x increases, the volume of the box increases to a maximum and then decreases.
C)
The ends of the domain occur when V = 0.
0 = x (30 − 2x)²
x = 0 or 15
So the domain is (0, 15).
Since we don't know the length of the trip, we can't find an exact answer.
However, we can write an expression for it. First, we let, T, represent the total number of miles for the trip.
Now, just divide T by 33. So our expression is T/33.
If you know the total miles of the trip, just divide it by 33 and you will have the answer.
Answer:
Step-by-step explanation:
If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex. Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards). The formula for this type of a parabola is, in vertex form,

where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex. For us, p = .25, h = 7, and k = -6. Filling in our formula:

Simplify the left side to
which simplifies, in its entirety, to

Answer:
150 degrees
Step-by-step explanation:
- Let the supplement = x
- So the angle you want is 5x
- Then [x + 5x] = 180 because they are supplementary.
- Solving. 6x = 180. Then x = 30.
- So the angle is 5x = 5×30 = 150 degrees
If it's adding to the 4,900 in the bank just add the numbers to 4,900.
After 4 years. 1,176.
Year 1: 294
Year 2: 588
Year 3: 882
Year 4: 1176
Year 5: 1470
Year 6: 1764