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.
<h3>Let the number be x</h3>
- Multiply all terms by the same value to eliminate fraction denominators
- Cancel multiplied terms that are in the denominator
<h2>Solved ✔︎</h2>
Answer:
78
Step-by-step explanation:
for the right side we can just do 14*2 since there are two people per seat and 14 rows
14 *2 is 28
for the left side we just do 14*3 since there are three people per seat and 14 rows
14*3 is 42
Then we have to add the 8 students that can fit in the very back seat
42 + 28 + 8
28 + 8 is 36
42 + 36 = 78
0.50x+0.75b is greater than or equal to 200
(idk how to put the greater than or equal to sign but make sure you put the sign)
X is the bag of chips
B is the sodas
She's be using 12 cups of sugar. Heres the explanation to how i got that, i figured out what number 16 would multiply by to get 64 which was 4, so then i also multiplied 3 by 4 which is how i got 12. Hope this helps
