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:
2/3
Use the rise over run formula and then simplify
Let the two numbers are x and y
Let larger number = x
and smaller number = y
it means
x-y = 0.77
Now it says larger number is increased 5 times
So it now becomes 5x
So second equation becomes
5x -y =77
Now we have to solve these two equations
x-y = 0.77 and 5x-y = 77
multiply first equation by -1 and then add both equations
-x+y = -0.77
Now on adding we get
-x+5x +y -y = 77-0.77
4x = 76.23
Divide both sides by 4
x=19.0575
We get the larger number , now subtract 0.77 from this , we will get the smaller number
y=19.0575-0.77=18.2875
y=18.2875
Hence the larger number = 19.0575
Smaller number = 18.2875
Answer: C
Step-by-step explanation: Hope this help :D
