9514 1404 393
Answer:
8√3 ≈ 13.86 ft
Step-by-step explanation:
The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
For y=4, the corresponding value of x is ...
4 = 1/12x^2
48 = x^2
√48 = x = 4√3
Then the width of the searchlight opening is ...
2(4√3 ft) = 8√3 ft ≈ 13.86 ft
you divide 12 by 25 which is 0.48 and multiply it by 48 and the answer is 48%
A simple answer is that any given trapezoid with height h and length of the parallel lines a and b, is half of a parallelogram with an area of (a+b) x h. Since the trapezoid is half of this, it is h(a+b)/2
In one revolution of the wheel, a point on the edge travels a distance equal to the circumference of the wheel.
The wheel has radius 1 ft, so its circumference is 2π (1 ft) = 2π ft.
Then the point has a linear speed of
(1/4 rev/s) * (2π ft/rev) = 2π/4 ft/s = π/2 ft/s
The original volume of the given prism is
l*w*h = 162
where l = length, w = width, h = height
Reducing 1/3 of each sides,
(1/3)l*(1/3)w*(1/3)h=(1/27)162
Thus,
The new volume is 162/27 = 6 cubic cm
