X = 2
A square has 4 sides. To get the perimeter of a square, you could multiply the length of one side by 4.
One side of the larger triangle is x inches plus an additional 8 inches, which can be written as (x+8)
To get the perimeter of the larger square, multiply the expression (x+8) by 4. The question states the larger square’s perimeter is 40 inches.
You end up with this equation: 4(x + 8) = 40
To solve first distribution 4 into (x + 8).
4x + 32 = 40 | subtract 32 from both sides
4x = 8 | divide each side by 4
x = 2 inches
So the side length of the original square is 2 inches. To check your work, go back and plug x = 2 into the original equation. 8 in + 2 in = 10 inches, and 10 inches x 4 = 40 inches, so x = 2 is the solution
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
90/2 = 45
45/1700 = 0.02647
0.02647 x 100 = 2.64
2.46%
