Answer: 5.0625 or 5 1/16
Step-by-step explanation:
im smart
The options are wrong lol, it is -1/8
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: 65
Step-by-step explanation:
65 x 5= 325
Use substitution.
y = 2 - x and y = 4x + 7 can become
2 - x = 4x + 7
Now solve for x
-5 = 5x
-1 = x
Now plug -1 for x in either equation.
y = 2 - x -> y = 2 - (-1) -> y = 3
y = 4x + 7 -> y = 4*-1 + 7 -> y = -4 + 7 -> y = 3
So C) is the correct answer.
