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: 411.6
Step-by-step explanation: What is 411.6 Million in Scientific Notation?
To answer the question what is 411.6 million in scientific notation let’s recall how to convert 411,600,000 to scientific notation as detailed on our home page.
If you split the number 411600000 into a coefficient and a power of 10 you do get 411.6 million in exponential form, but there is an indefinite number of possibilities.
As you probably want 411.6 million in normalized scientific notation, the coefficient or significand of 411.6m in scientific notation must be in the interval [1,10[.
As there are many ways to express 411.6 million in scientific notation, in this post we mean 411.6 million in normalized scientific notation, unless stated otherwise.
