Find the Work Done by F Over the Curve in the Direction

question 244

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = \frac { \mathrm { y } } { \mathrm { z } } \mathbf { i } + \frac { \mathrm { x } } { \mathrm { z } } \mathbf { j } + \frac { \mathrm { x } } { \mathrm { y } } \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { t } ^ { 7 } \mathbf { i } + \mathrm { t } ^ { 5 } \mathbf { j } + \mathrm { t } ^ { 2 } \mathbf { k } , 0 \leq \mathrm { t } \leq 1$$

• A) \(W = \frac { 17 } { 10 }\)
• B) \(W = 14\)
• C) \(W = 0\)
• D) \(W = 1\)

---

Definitions:

Mutagens

Agents, such as chemicals or radiation, that cause mutations or changes in the DNA of organisms.

Transcription Factors

Proteins that regulate the transcription of genes by binding to specific DNA sequences, thus controlling the flow of genetic information from DNA to mRNA.

RNA Polymerase

An enzyme responsible for synthesizing RNA from a DNA template during the process of transcription.

Promoter

A region of DNA that initiates transcription of a particular gene.