In this question, you have to form the equation given the formula of the volume : L x W x D
L = W+5
W = W
D = W-1
(W+5)(W)(W-1) = 20
(W^2+5W)(W-1) = 20
W^3+4W^2-5W-20 = 0
Get the roots by factoring it out.
<span>(w +4) *(w +2.236) *(w -2.236)
</span>
So the roots are: -4, -2.236, 2.236.
Since we're talking about dimensions, let's use the positive root..
L = 7.24
W = 2.24
D = 1.24
Answer:
D.
Step-by-step explanation:
The x-axis of the graph isn't constant with the years. It cannot be consistent if the first twenty years are scaled together and the last 10 are put in increments of 2 years.
I'm not sure but I think it is the first one
You should have drawn1 - x-axis and y-axis in light pencil.2 - graphed a down-facing parabola with the top of the frown on the y-axis at y = 2. It should be crossing the x-axis at ±√2. This should be in dark pencil or another color.3 - In dark pencil or a completely new color, draw a rectangle with one of the horizontal sides sitting on top of the x-axis and the other horizontal side touching the parabola at each of the top corners of the rectangle. The rectangle will have half of its base in the positive x-axis and the other half on the negative x-axis. It should be split right down the middle by the y-axis. So each half of the base we will say is "x" units long. So the whole base is 2x units long (the x units to the right of the y-axis, and the x units to the left of the y-axis) I so wish I could draw you this picture... In the vertical direction, both vertical edges are the same length and we will call that y. The area that we want to maximize has a width 2x long, and a height of y tall. So A = 2xy This is the equation we want to maximize (take derivative and set it = 0), we call it the "primary equation", but we need it in one variable. This is where the "secondary equation" comes in. We need to find a way to change the area formula to all x's or all y's. Since it is constrained to having its height limited by the parabola, we could use the fact that y=2 - x2 to make the area formula in only x's. Substitute in place of the "y", "2 - x2" into the area formula. A = 2xy = 2x(2 - x2) then simplify A = 4x - 2x3 NOW you are ready to take the deriv and set it = 0 dA/dx = 4 - 6x2 0 = 4 - 6x2 6x2 = 4 x2 = 4/6 or 2/3 So x = ±√(2/3) Width remember was 2x. So the width is 2[√(2/3)]Height is y which is 2 - x2 = 2 - 2/3 =4/3
Plug in the known x value
2(-1/2)-3y=6
-1-3y=6
-3y=7
y=-7/3
Final answer: -7/3
