Answer:
Step-by-step explanation:
Simplifying
W + -2 + 2w = 6 + 5w
Reorder the terms:
-2 + W + 2w = 6 + 5w
Solving
-2 + W + 2w = 6 + 5w
Solving for variable 'W'.
Move all terms containing W to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + W + 2 + 2w = 6 + 2 + 5w
Reorder the terms:
-2 + 2 + W + 2w = 6 + 2 + 5w
Combine like terms: -2 + 2 = 0
0 + W + 2w = 6 + 2 + 5w
W + 2w = 6 + 2 + 5w
Combine like terms: 6 + 2 = 8
W + 2w = 8 + 5w
Add '-2w' to each side of the equation.
W + 2w + -2w = 8 + 5w + -2w
Combine like terms: 2w + -2w = 0
W + 0 = 8 + 5w + -2w
W = 8 + 5w + -2w
Combine like terms: 5w + -2w = 3w
W = 8 + 3w
Simplifying
W = 8 + 3w
1:24 and 2:20 and 3:30 and 4:16 and 5:12
Notes:
- The sign of the coefficient of the quadratic equation determines if the vertex is a minimum or maximum. Positive looks like ∪ so has a minimum. Negative looks like ∩ so has a maximum.
- Maximum/minimum height is the y-value of the vertex.
- Time to reach maximum height is the x-value of the vertex (which is also the Axis-Of-Symmetry).
Answer: 4) maximum
5) 20.1 ft
6) 2 seconds
<u>Step-by-step explanation:</u>
4) h(t) = -16t² + 256t
↓
the coefficient is negative so it looks like ∩.
Therefore, it has a maximum.
5) h(t) = -16t² + 30t + 6

6) h(t)=-16t²+64t+80

The volume of a cuboid is given by length × width × height
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches