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Question
Math
Posted 2 months ago

v(t)=(10cos(t),10sin(t),100t)
v(t)=(10 \cos (t), 10 \sin (t), 100-t)


What is the velocity of v(t)v(t) ?

Choose 1 answer:
(A) 10210 \sqrt{2}
(B) (10sin(t),10cos(t),1)(-10 \sin (t), 10 \cos (t),-1)
(c) 101\sqrt{101}
(D) (10cos(t),10sin(t),1)(10 \cos (t), 10 \sin (t),-1)
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
The function v(t)v(t) is given by (10cos(t),10sin(t),100t)(10 \cos(t), 10 \sin(t), 100 - t)
step 3
Differentiating 10cos(t)10 \cos(t) with respect to tt gives 10sin(t)-10 \sin(t)
step 4
Differentiating 10sin(t)10 \sin(t) with respect to tt gives 10cos(t)10 \cos(t)
step 5
Differentiating 100t100 - t with respect to tt gives 1-1
step 6
Therefore, the velocity of v(t)v(t) is (10sin(t),10cos(t),1)(-10 \sin(t), 10 \cos(t), -1)
[question 1] Answer
B
Key Concept
Velocity of a function
Explanation
The velocity of a function is found by differentiating its components with respect to time.

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