3 years ago

Can someone help me with these last two questions? Worth 6 points

Mathematics

1 answer:

Usimov [2.4K]3 years ago

5 0

Image containing examples of all three: https://www.mathsisfun.com/algebra/images/variable-constant.svg

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Answer:

The curve is given by r(s)= $3\frac{s}{\sqrt{29}} i + (7 - 4\frac{s}{\sqrt{29}} ) j + (3 + 2\frac{s}{\sqrt{29}} ) k$

Step-by-step explanation:

The aec length of the curve is given by:

L= $\int\limits^t_0 {|r'(t)|} \, dt$

r(t) = 3t i + (7 − 4t) j + (3 + 2t) k

r'(t)= 3 i -4 j + 2 k

|r'(t)|= $\sqrt{3^2+(-4)^2+2^2} =\sqrt{9+16+4} =\sqrt{29}$

L= $\int\limits^t_0 {\sqrt{29}} \, dt=\sqrt{29}\int\limits^t_0 \, dt$

L= $\sqrt{29}t|^t_0=\sqrt{29}t-\sqrt{29}0=\sqrt{29}t$

s(t)= $\sqrt{29}t$

We have to obtain t in terms of s, hence:

t= $\frac{s}{\sqrt{29}}$

Finally,

r(s)= $3\frac{s}{\sqrt{29}} i + (7 - 4\frac{s}{\sqrt{29}} ) j + (3 + 2\frac{s}{\sqrt{29}} ) k$

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