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Murljashka [212]
3 years ago
6

In a rectangular park that measures 80 yards by 18 yards, a dog runs from one corner to the

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
6 0
Pythagoras
a^2 + b^2 = c^2
80^2 + 18^2 = Answer^2
Answer= The square root of 6724
= 82 yards
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Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
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\mathbf r(t)=\displaystyle\int(5t^4\,\mathbf i+6t^5\,\mathbf j+t\,\mathbf k)\,\mathrm dt
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Given \mathbf r(1)=\mathbf i+\mathbf j, we have

\begin{cases}1^5+C_1=1\\\\1^6+C_2=1\\\\\dfrac121^2+C_3=0\end{cases}\implies C_1=0,C_2=0,C_3=-\dfrac12

so that the particular solution is

\mathbf r(t)=t^5\,\mathbf i+t^6\,\mathbf j+\dfrac12(t^2-1)\,\mathbf k
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~ = about
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