Question

Math

Posted 2 months ago

```
$v(t)=(10 \cos (t), 10 \sin (t), 100-t)$
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) $(10 \cos (t), 10 \sin (t),-1)$
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

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.

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