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

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

Choose 1 answer:
(A) $10 \sqrt{2}$
(B) $(-10 \sin (t), 10 \cos (t),-1)$
(c) $\sqrt{101}$
(D) $(10 \cos (t), 10 \sin (t),-1)$

Question

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

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

Choose 1 answer:
(A) $10 \sqrt{2}$
(B) $(-10 \sin (t), 10 \cos (t),-1)$
(c) $\sqrt{101}$
(D) $(10 \cos (t), 10 \sin (t),-1)$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the velocity of the function $v(t)$, we need to differentiate each component of the function with respect to $t$. ‖ ‖ step 2 ⋮ The function $v(t)$ is given by $(10 \cos(t), 10 \sin(t), 100 - t)$. ‖ ‖ step 3 ⋮ Differentiating $10 \cos(t)$ with respect to $t$ gives $-10 \sin(t)$. ‖ ‖ step 4 ⋮ Differentiating $10 \sin(t)$ with respect to $t$ gives $10 \cos(t)$. ‖ ‖ step 5 ⋮ Differentiating $100 - t$ with respect to $t$ gives $-1$. ‖ ‖ step 6 ⋮ Therefore, the velocity of $v(t)$ is $(-10 \sin(t), 10 \cos(t), -1)$. ‖ ∻[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.⚹◊What is the formula for calculating the magnitude of the velocity of the function $v(t)$?⍭ Generate me a similar question◊

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