adarianmcintosh
26.09.2019 •
Mathematics
Arotating light is located 15 feet from a wall. the light completes one rotation every 2 seconds. find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
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Ответ:
This is about differential calculus.
Rate = dy/dt = 41.61 ft/s
We are told that the light is located 15 ft from the wall and completes rotation every 2 seconds. Thus; we can say that the distance of the light's projection onto the given wall is expressed as;
y = 15 tan θ
where;
θ is the angle of light perpendicular to the wall.
One rotation is completed every 2 seconds and this means that;
Angular speed; ω = 2π/2 = π
Angular speed can also be expressed as;ω = θ/t
Thus;
θ = wt = πt
dθ/dt = π
Since y = 15 tan θThen
dy/dt = 15 sec² θ (dθ/dt)
(dy/dt) = 15π sec² θ
dy/dt = 15π sec²(20°)
dy/dt = 41.61 ft/s
Read more at; link
Ответ:
53.4 ft/s
Step-by-step explanation:
The distance from the point closest to the light is ...
d = (15 ft)tan(α)
where α is the angle from perpendicular. Since the light travels through an angle of 2π radians in 2 seconds, the angle can be represented by ...
α = πt . . . . radians
and the rate of change of α is ...
dα/dt = π . . . . radians/second
The rate of change of distance is ...
dd/dt = (15 ft)sec(α)²(dα/dt) = (15π)(sec(20°)²) ft/s ≈ 53.4 ft/s
Ответ:
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99