Can someone help me with this math problem :)!? I added some pictures.
1 answer:
Answer:
V = 4x^3-39x^2+93.5x
Domain: 0 < x < 4.25
Using the graph the maximum volume is about V = 66 inches ^3 at about x = 1.6
Step-by-step explanation:
V = l*w*h
The length is 11 -2x
The width is 8.5 -2x
The height is x
V = ( 11 -2x) ( 8.5 -2x) x
FOIL ( first outer inner last)
V = (93.5 -22x - 17x +4x^2) x
Combine like terms
V =( 4x^2-39x+93.5)x
Distribute the x
V = 4x^3-39x^2+93.5x
The domain is the values that x can take
Looking at the picture
2x can be no largest than 8.5 or there will be no width
2x < 8.5
x < 4.25
If x ≤ 0 there is no height so x > 0
0 < x < 4.25
Using the graph the maximum volume is about V = 66 inches ^3 at about x = 1.6
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After 85 minutes of calls, there are $27.25 left on the card.
<h3>What is the remaining credit after 85 minutes of calls?</h3>
A linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:
In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)
(points of the form (time, dollars)).
So the slope is:
The linear equation is then:
y = -0.15*x + b
To find the value of b, we use the point (22. 36.7)
36.7 = -0.15*22 + b
36.7 + 0.15*22 = b = 40
Then the linear equation is:
y = -0.15*x +40
The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.
y = -0.15*85 + 40 = 27.25
This means that after 85 minutes of calls, there are $27.25 left on the card.
If you want to learn more about linear equations:
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