R+9
Because Jessica rode 9 miles more than Roger, you would add 9 to Roger's number making the expression r+9
F(-10)=-2, f(-8)=5, and f is continuous. All these mean that f(x) is 0 for x in between -10 and -8.
That is, f at -10 is negative, then at -8 is positive. So the graph of f "cuts" the x-axis for an x value in (-10, -8).
Since there is only one value such that f(x)=0, x can only be -9.
Answer: -9
Answer:
x^2=-10
Step-by-step explanation:
x squared equals to negative 10
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.
