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dybincka [34]
3 years ago
15

Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of th

e kite from the ground is (20.27,61,77.27) meters.
Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0
We have to calculate the height of the kite from the ground.
Using trigonometry:
sin 75° = h / 80
h = 80 · sin 75°
h = 80 · 0.96529
Answer:
<span>h = 77.27 m</span>
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Leno4ka [110]

Answer:

\frac{s^2-25}{(s^2+25)^2}

Step-by-step explanation:

Let's use the definition of the Laplace transform and the identity given:\mathcal{L}[t \cos 5t]=(-1)F'(s) with F(s)=\mathcal{L}[\cos 5t].

Now, F(s)=\int_0 ^{+ \infty}e^{-st}\cos(5t) dt. Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that F(s)=\frac{1}{5}\sin(5t)e^{-st} |_{0}^{+\infty}+\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt=\int_0 ^{+ \infty}e^{-st}\sin(5t) dt.

Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that

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Solving for F(s) on the last equation, F(s)=\frac{s}{s^2+25}, then the Laplace transform we were searching is -F'(s)=\frac{s^2-25}{(s^2+25)^2}

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3 years ago
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