Answer:
79.5 + 5.5x = Y
Step-by-step explanation:
Sumo wrestler gained 5.5 kg per month
After 11 month, he weighed 140 kg.
Let x be his current weight.
Then x + 11(5.5) = 140
x = 140 - 60.5
x = 79.5
If Y is the weight of the wrestler after t months, then the linear equation would be:
79.5 + 5.5t = Y
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:
the integers are 8 and 9
Step-by-step explanation:
consecutive means one right after the other. 9 is right after 8. and its product is 72, well 8x9 is 72.
Answer:
52.4
Step-by-step explanation:
Arc length = 2πr(θ/360)
r = 10
θ = 300°
Arc length = 2π(10)(300/360) = 20π(0.8333) = 16.666π ≈ 52.36
