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Kaylis [27]
2 years ago
8

If the endpoints of AB are A(-1,3), B(7,-1) What is the coordinate of the midpoint M

Mathematics
1 answer:
Kay [80]2 years ago
3 0

Answer:

b

Step-by-step explanation:

bbbnm

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Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4
arsen [322]

we are given

R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k

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Arc length calculation:

we can use formula

L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt

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now, we can plug these values

L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt

now, we can simplify it

L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt

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now, we can solve integral

\int \:8\sec \left(t\right)dt

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now, we can plug bounds

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=8\ln \left(\sqrt{2}+1\right)-0

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STatiana [176]

Answer:

K=2 that is the answer

6 0
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