The voltage across the terminals of a typical electrical outlet is approximated by V(t) = 152 sin (120xt), where t is measured in seconds. AV 160- Answer parts (a) through (c). 120- (a) Find the amplitude and the period for V(t). 80- The amplitude of the voltage is 40- The period of the voltage is (Type an integer or a simplified fraction.) 0- (b) Find the frequency of V(t), that is, the number of cycles completed in one second. -40- The frequency of V(t) is (Type an integer or a simplified fraction.) -80- -120- 1 (c) Graph V(t) over the interval 0, 30 -160- Use the graphing tool to graph the equation. Click to enlarge
The voltage across the terminals of a typical electrical outlet is approximated by V(t) = 152 sin (120xt), where t is measured in seconds. AV 160- Answer parts (a) through (c). 120- (a) Find the amplitude and the period for V(t). 80- The amplitude of the voltage is 40- The period of the voltage is (Type an integer or a simplified fraction.) 0- (b) Find the frequency of V(t), that is, the number of cycles completed in one second. -40- The frequency of V(t) is (Type an integer or a simplified fraction.) -80- -120- 1 (c) Graph V(t) over the interval 0, 30 -160- Use the graphing tool to graph the equation. Click to enlarge
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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![### Electrical Outlet Voltage Analysis
The voltage across the terminals of a typical electrical outlet is approximated by the function:
\[ V(t) = 152 \sin (120\pi t) \]
where \( t \) is measured in seconds.
**Answer parts (a) through (c):**
**(a) Determine the amplitude and the period for \( V(t) \).**
- **Amplitude:**
The amplitude of the voltage is \( \boxed{152} \).
- **Period:**
The period of the voltage is \( \boxed{\frac{1}{60}} \) (Type an integer or a simplified fraction.)
**(b) Determine the frequency of \( V(t) \), which is the number of cycles completed in one second.**
- **Frequency:**
The frequency of \( V(t) \) is \( \boxed{60} \) (Type an integer or a simplified fraction.)
**(c) Graph \( V(t) \) over the interval \([0, \frac{1}{30}]\).**
Use the graphing tool to graph the equation.
#### Graph Instructions
**Click to enlarge graph**
The provided graph grid is labeled as follows:
- **Voltage Axis (V):** Spanning from -160V to 160V in intervals of 40V.
- **Time Axis (t):** Spanning from 0 to \(\frac{1}{30}\) seconds with an additional mark at \(\frac{1}{60}\) seconds.
Note: Click the graph, choose a tool in the palette, and follow the instructions to create your graph.
_Save for Later_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1668550e-16d3-480e-a17e-3f1198f7538c%2F47f6bc74-fc5d-47a2-9237-00a1857b3dd9%2F6yq0dwc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electrical Outlet Voltage Analysis
The voltage across the terminals of a typical electrical outlet is approximated by the function:
\[ V(t) = 152 \sin (120\pi t) \]
where \( t \) is measured in seconds.
**Answer parts (a) through (c):**
**(a) Determine the amplitude and the period for \( V(t) \).**
- **Amplitude:**
The amplitude of the voltage is \( \boxed{152} \).
- **Period:**
The period of the voltage is \( \boxed{\frac{1}{60}} \) (Type an integer or a simplified fraction.)
**(b) Determine the frequency of \( V(t) \), which is the number of cycles completed in one second.**
- **Frequency:**
The frequency of \( V(t) \) is \( \boxed{60} \) (Type an integer or a simplified fraction.)
**(c) Graph \( V(t) \) over the interval \([0, \frac{1}{30}]\).**
Use the graphing tool to graph the equation.
#### Graph Instructions
**Click to enlarge graph**
The provided graph grid is labeled as follows:
- **Voltage Axis (V):** Spanning from -160V to 160V in intervals of 40V.
- **Time Axis (t):** Spanning from 0 to \(\frac{1}{30}\) seconds with an additional mark at \(\frac{1}{60}\) seconds.
Note: Click the graph, choose a tool in the palette, and follow the instructions to create your graph.
_Save for Later_
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