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.

5 0

2 years ago

Of the 100 entries in a costume contest, 39 entrants were dressed as heroes and 45 entrants were wearing a mask. If 21 entrants

ehidna [41]

Correct question with correct options has been attached

Answer:

Step-by-step explanation:

Let C represent those dressed as heroes and let B represent those wearing mask

Thus;

n(C) = 39

n(D) = 45

We are told that 21 entrants were dressed as heroes wearing a mask.

Thus; n(C n D) = 21

We are also told that there were a total of 100 entries.

Thus, n(T) = 100

Now, number of entrants neither dressed as heroes nor wearing a mask is given by;

n(T) - n(C u D)

n(C u D) = n(C) + n(D) - n(C n D)

n(C u D) = 39 + 45 - 21

n(C u D) = 63

Thus;number of entrants neither dressed as heroes nor wearing a mask is: 100 - 63 = 37

3 0

3 years ago