The formula for circumference is C = 2πr, where r is the radius of the circle. However, the radius is half the diameter, so the circumference could also be calculated using the formula C = πd, where d is the diameter of the circle. π is commonly shortened to 3.14.
If the diameter of the circle is 6 feet, an estimate of the circle's circumference is 6 times 3 feet or 18 feet.
Answer:
18 ft
<span>you need to set up the equations solve for x or y. and substitute. I can give you the starting equations, but i cant find the answer and I don't remember how to do all the steps, but the first two equations (the ones you use to solve for x or y to use to solve for a number to subsitute. x-12=y y-14=3x and there should be one more for that they met two years ago.</span>
OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0
Because the roots of the equation are 0 and 12, we know the formula is therefore of the form
y = ax(x - 12), for some a
So put in x = 6
-9 = 6a(-6)
9 = 36a
a = 1/4
So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x
The gradient of this is dy/dx = 0.5x - 3
The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8
Gradient of the parabolic mirror at x = 4 is -1
So the gradient of the normal to the mirror at x = 4 is therefore 1.
Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.
So the focal point is at y = -8, i.e. 1 metre above the back of the dish.
The sides of the rectangle are:
xy = 39
2x + 2y
Solve by simultaneous equation:
ysquared -17y + 30 = 0
Solution:
The sides are equal to 15 and 2
