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
Assuming that the mix disolves into the 20 gallons and doesn't take up space
1:2
x:20
1/2=x/20
multiply btoh sides by 20
10=x
answer is 10 cups of mixture
Answer:
4.1 billion
Step-by-step explanation:
1 ft = 30.48 cm
1 in = 2.54 cm
The volume of rain that fell on the roof is given by ...
V = LWH
V = (175 ft × 30.48 cm/ft)(45 ft × 30.48 cm/ft)(11 in × 2.54 cm/in)
= 175×45×11×30.48²×2.54 cm³ = 204,412,236.336 cm³
At 20 drops per cm³, this will be ...
20×204,412,236.336 ≈ 4,088,244,727 . . . . raindrops
About 4.1 billion raindrops fell on your roof.
You need to find x so that then you can do it and you didn’t share a answer so how are we supposed to know??
