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
Answer:
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if we asked questions and somone just ans the question wrongly for free points
therefore you can report the ans and delete the ans..
now a days many people are doing this...
Good Morning!
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
She can swim 1 1/4 per hour.
I hope this helps! :)
Answer:
Step-by-step explanation:
A parabola has a focus of F(8.5,−4) and a directrix of x=9.5.
General form of horizontal parabola is
the distance between directrix and focus is the value of p
so p = 8.5 - 9.5 = -0.5
Focus is (h+p , k), given focus is (8.5, -4)
So k = -4 and h+p = 8.5
we know p = -0.5
h +p = 8.5
h - 0.5 = 8.5
so h= 9 and k = -4
vertex is (h,k) that is (9, -4)
Now plug in the value in the general equation
, k= -4, h= 9 , p = -0.5
subtract 18 on both sides
Divide whole equation by -2
Why?
Because if you draw a line from A to D to make a triangle AED, then triangle all angle add up equal 180.
