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.
Answer:
9.0
Step-by-step explanation:
x = 7 / cos 39°
= 7 / 0.7771
= 9.0
It all just depends on how much it cost per foot, how much you need, the durability of the rope its self... I don’t see any numbers but if you put some numbers I can help lol
Answer:
The answer to your question is
Step-by-step explanation:
Data
f(x) = -2(x - 4)² + 2
Process
1) Assign values to x and evaluate the function to get y.
x f(x) y
0 -2(0 - 4)² + 2 -30
1 -2(1 - 4)² + 2 -16
2 -2(2 - 4)² + 2 - 6
3 -2(3 - 4)² + 2 0
4 -2(4 - 4)² + 2 2
5 -2(5 - 4)² + 2 0
6 -2(6 - 4)² + 2 -6
2.- Plot the points (see the graph below)
3.- Join the points (see the graph below)
Step-by-step explanation:
2b - 3/3 - 5 = 10
2b - 1 - 5 = 10
2b - 6 =10
2b -6 +6 = 10 +6
2b = 16
b = 8
