I still got the answer wrong, maybe because it's different because u(t)? what would be the answer for my version of this problem ## Vector-Valued Functions and TransformationsConsider the vector-valued function $ \mathbf{r}(t) = 4t^2\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} $. We are asked to write a vector-valued function $ \mathbf{u}(t) $ that is a specified transformation of $ \mathbf{r} $.### Transformation DescriptionWe need to apply a horizontal translation of **one unit in the direction of the positive x-axis** to the vector-valued function $ \mathbf{r}(t) $.### SolutionTo achieve a horizontal translation of one unit in the direction of the positive x-axis, we need to adjust the $ \mathbf{i} $ component of the function. The new vector-valued function $ \mathbf{u}(t) $ will be:\[ \mathbf{u}(t) = (4t^2 + 1)\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} \]### Final Answer\[ \mathbf{u}(t) = (4t^2 + 1)\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} \]

Consider the vector-valued function r(t) = 4t²i + (t5)j + tk. Write a vector-valued function u(t) that is the specified transformation of r. a horizontal translation one unit in the direction of the positive x-axis u(t) =

Consider the vector-valued function r(t) = 4t²i + (t5)j + tk. Write a vector-valued function u(t) that is the specified transformation of r. a horizontal translation one unit in the direction of the positive x-axis u(t) =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

I still got the answer wrong, maybe because it's different because u(t)? what would be the answer for my version of this problem

## Vector-Valued Functions and Transformations

Consider the vector-valued function $ \mathbf{r}(t) = 4t^2\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} $. We are asked to write a vector-valued function $ \mathbf{u}(t) $ that is a specified transformation of $ \mathbf{r} $.

### Transformation Description
We need to apply a horizontal translation of **one unit in the direction of the positive x-axis** to the vector-valued function $ \mathbf{r}(t) $.

### Solution
To achieve a horizontal translation of one unit in the direction of the positive x-axis, we need to adjust the $ \mathbf{i} $ component of the function. The new vector-valued function $ \mathbf{u}(t) $ will be:

\[ \mathbf{u}(t) = (4t^2 + 1)\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} \]

### Final Answer
\[ \mathbf{u}(t) = (4t^2 + 1)\mathbf{i} + (t - 5)\mathbf{j} + t\mathbf{k} \]

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