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:
2 pie r is the measure of its circumference.
Answer:
Trial- 2 shows the conservation of momentum in a closed system.
Step-by-step explanation:
Given: Mass of balls are 
Conservation of momentum in a closed system occurs when momentum before collision is equal to momentum after collision.
- Let initial velocity of ball
- Initial velocity of ball
- Final velocity of ball
- Final velocity of ball
- Momentum before collision
- Momentum after collision
Now, According to conservation of momentum.
Momentum before collision = Momentum after collision
We will plug each trial to this equation.
Trial 1
Trial 2
Trial 3
Trial 4
We can see only Trial 2 satisfies the princple of conservation of momentum. That is momentum before collison should equal to momentum after collision.
Answer:
100 - 20 = 80
original cost/100 X 80 = sale price
Answer:
When a shape is transformed by rigid transformation, the sides lengths and angles remain unchanged.
Rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.
Assume two sides of a triangle are:
And the angle between the two sides is:
When the triangle is transformed by a rigid transformation (such as translation, rotation or reflection), the corresponding side lengths and angle would be:
Notice that the sides and angles do not change.
Hence, rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.
Step-by-step explanation:
