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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<u>Step-by-step explanation:</u>
Use the formula y = A cos (Bx - C) + D where
- A = amplitude
- Period = 2π/B
- Phase Shift = C/B
- D = vertical shift (aka midline)
Given: Max = 8, Min = 2, (1/2)Period = 20 → Period = 40
Amplitude (A) = (Max - Min)/2
= (8 - 2)/2
= 6/2
= 3
Midline (D) = (Max + Min)/2
= (8 + 2)/2
= 10/2
= 5
Period = 2π/B
→ B = 2π/Period
= 2π/40
= π/20
Notice that the Minimum touches the y-axis (not the Max) so there is no phase shift but there is a reflection → C-value = 0 & A-value is negative
Now, let's put it all together:
A = -3, B = π/20, C = 0, D = 5