Questions: Match each graph with its equation. vecr(t)=⟨cos(t), 2, sin(t)⟩ vecr(t)=⟨t, sin(t), 2⟩ vecr(t)=⟨cos(t), sin(t), t⟩ vecr(t)=⟨t, 2,(t-2)^2⟩ vecr(t)=⟨2, sin(t), cos(t)⟩

Match each graph with its equation.

vecr(t)=⟨cos(t), 2, sin(t)⟩
vecr(t)=⟨t, sin(t), 2⟩
vecr(t)=⟨cos(t), sin(t), t⟩
vecr(t)=⟨t, 2,(t-2)^2⟩
vecr(t)=⟨2, sin(t), cos(t)⟩
Transcript text: -- wamap.org/assess2/?cid=386328aid=2203120\#/skip/2 Review 2 Score: 1.6/4 Answered: 1/4 Question 2 Match each graph with its equation. \[ \begin{array}{l} \vec{r}(t)=\langle\cos (t), 2, \sin (t)\rangle \\ \vec{r}(t)=\langle t, \sin (t), 2\rangle \\ \vec{r}(t)=\langle\cos (t), \sin (t), t\rangle \\ \vec{r}(t)=\left\langle t, 2,(t-2)^{2}\right\rangle \\ \vec{r}(t)=\langle 2, \sin (t), \cos (t)\rangle \end{array} \] a. b. Search
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze Graph A

The graph for 'a' appears to be a parabola in the y-z plane, which suggests that y and z coordinates are quadratic functions and the x coordinate is constant.

Step 2: Analyze Graph B

The graph for 'b' shows a sinusoidal curve in the x-z plane, with a constant y value, suggesting that x and z are trigonometric functions of t, and y is a constant.

Step 3: Analyze Graph C

Graph 'c' resembles a semi-circle in the x-y plane, suggesting x and y coordinates are trigonometric functions and z is linearly dependent on the parameter t.

Final Answer:

a. $\vec{r}(t) = \langle 1, 2, (t-2)^2 \rangle$

b. $\vec{r}(t) = \langle t, \sin(t), 2 \rangle$

c. $\vec{r}(t) = \langle \cos(t), 2\sin(t), t \rangle$

Was this solution helpful?
failed
Unhelpful
failed
Helpful