Hi there!
Find the value of 8 by substituting in -18 for g(x):
-18 = 2x - 8
Add 8 to both sides:
-10 = 2x
Divide both sides by 2:
-10/2 = 2x/2
x = -5
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
Answer:
period = 2
Step-by-step explanation:
The period is the measure of 1 complete cycle of the wave
The wave enters at x = 0 , y = - 0.5
After 1 cycle the wave is at x = 2, y = - 0.5
period = 2 - 0 = 2
Answer:
She pays $566.10
Step-by-step explanation:
The mattress store marks a mattress up 100%. 100% of $225 is 225. We add 225 to 225 and get 510. Therefore, the store sells the mattress for $510 without tax. When Cassie buys the mattress, we have to add 11% tax. We change 11% to 0.11 and multiply that by the selling price (510). We get 56.10, so that is the tax. We add the tax to the selling price and get $566.10. Cassie pays $566.10 for the mattress.
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