Volume = length x width x height:
Volume = 3 x 6 x 2 = 36 cubic inches.
Answer:
5/9
Step-by-step explanation:
complement means not choosing an orange
P( not choosing orange) = (apple and fruit) / total
= (4+6) / (4+6+8)
=10/18
= 5/9
Answer:
9.268
Step-by-step explanation:
Answer:
32 and 40
Step-by-step explanation:
Let's call the smaller number x. If the smaller number is x, the equation for this problem is 2x + 8 = 72
Equation:
2x + 8 = 72
2x = 64
x = 32
So now we know the smaller number is 32, so now add 8 and we get 40.
Therefore the 2 numbers are 32 and 40
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.
