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:
Equation: y = -3x -2
Graph: Attached below ↓↓↓↓↓
Step-by-step explanation:
The equation is y = -3x + b
We need B at this point.
Since we have a point given to us,( -2, 4)we can input the x and y
Solve:
4 = -3(-2) + b
4 = 6 + b
b = -2
So the equation we have is y = -3x -2
Let's graph the line.
We go 2 units below the x-axis, because the y-intercept is -2, and the slope is -3, so we go down 3 units, and to the right 1.
Picture attached:
-Chetan K
Answer:
$477
Step-by-step explanation:
63 hours x $6 = $378
9 hours x $11 = $99
378+99= $477
Answer:
13 feet
Step-by-step explanation:
1 yard = 3 feet
4 yards = 12 feet
1/3 yard = 1 foot
12 feet + 1 foot = 13 feet
The answer is one kilogram. one kilogram is about the same as 2 pounds, while one gram is less than an ounce.
Hope this helps!
