Let α represent the acute angle between the horizontal and the straight line from the plane to the station. If the 4-mile measure is the straight-line distance from the plane to the station, then
sin(α) = 3/4
and
cos(α) = √(1 - (3/4)²) = (√7)/4
The distance from the station to the plane is increasing at a rate that is the plane's speed multiplied by the cosine of the angle α. Hence the plane–station distance is increasing at the rate of
(440 mph)×(√7)/4 ≈ 291 mph
Answer: x=6
Step-by-step explanation:
We’re going to use the formula for area of a rectangle, which is length x width. We are also going to use the formula for area of a triangle which is 1/2 x base x height.
Let’s start with the rectangle under the triangle ends of the roof. They are 11mm wide, 10mm high, and there are two of them.
11 x 10 x 2 = 220
Then the other sides that are 16 x 10. There are 2 of them.
16 x 10 x 2 = 320
Then the rectangular pieces of roof, 9.7 x 16, and there are 2 of them.
9.7 x 16 x 2 = 310.4
Lastly, the triangle pieces of roof. (1/2)(base)(height), but there are 2 of them
1/2 x 11 x 8 x 2 = 88
Add up all the parts:
220 + 320 + 310.4 + 88 = 938.4 mm
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