Answer:
8:1
Step-by-step explanation:
the actual table's height in inches is 4*12 = 48 inches.
48/6 = 8
so the ratio is 8:1.
1. X(0,0) --> X'(3,-5).
To go from (0,0) to (3,-5), you must go to the right 3 and down 5.
I cannot answer 2 or 3, as rotations are not my strong suit.
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.
This question has to do with making an approximation based on the diagram of the angle. Angle KLM is an obtuse angle meaning it is larger then 90° but is also less than 180°. The only choices that lie within this range are choices B and D. However, it is safe to assume that angle KLM is closer to 180° than to 90° based on the diagram, therefore the answer must be choice B.
I hope this helps.
Let's form the difference of the two expressions and see what we can learn.
(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)
Since y > x, this is positive, so 2y -x is greater than 2x -y.
