Answer:
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Answer:
x = -3, 
Step-by-step explanation:
The given quadratic equation is: 
This can be written as: 
To solve a quadratic equation of the form 
we use the formula:
Here, a = 2; b = 3; c = - 9
Therefore, the roots of the equation are:
We get two values of 'x', viz.,
x = 
and 
⇒ x = -3, 3/2
Since the factors of the quadratic equation is asked, we write it as:
(x + 3)(x - ) = 0
because, if (x - a)(x - b) are the factors of a quadratic equation, then 'a' and 'b' are its roots.
Multiply (x + 3) and (x - to see that this indeed is the given quadratic equation.
Answer:
I think the answer is m=3
Step-by-step explanation:
Hope this helps :D
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.
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