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.
<span>Together with triangles, circles comprise most of the GMAT Geometry problems.
A circle is the set of all points on a plane at the same distance from a single point ("the center").
The boundary line of a circle is called the circumference.</span>
In order to find a percentage, you divide the sample by the total amount.
For example: Tess has 3 cookies out of the total amount of 9. 3/9 = 33.3%
For find f(-2) of f(x)=7x+3, plug in -2 for x.
7(-2)+3=y
-14+3=y
y=-11
To find the rate, or the slope, you divide x/y. So 2/6 is 1/3. 3 over 9 is also 1/3. So the rate is 1/3. In rates you always divide, you don't mulitply or subtract or add to find the rate.
To answer this question you must find the percentage of the children that read before bed and compare it to the adults bag read before bed’s percentage.
To do this, start by dividing the number of children that read before bed by the total number of children surveyed.
This leaves you with:
6/13= 0.4615
To find the actual percentage, multiply this result by 100.
0.4615 x 100 = 46.15
This percentage rounded is 46%
So, now you can compare the percentages. The percentage of children that read before bed is 46% and the percentage of adults that read before bed is 54%. So, the group with the greatest percentage was the adults.
I hope this helps!
