Approximate the magnitude of the vector and the angle 0, 0° ≤ 0 < 360°, that the vector makes with the positive x-axis. Round your answers to the nearest tenth. W = √15i - 7j |W| = 8 0= Need Help? Submit Answer X° Read It K
Approximate the magnitude of the vector and the angle 0, 0° ≤ 0 < 360°, that the vector makes with the positive x-axis. Round your answers to the nearest tenth. W = √15i - 7j |W| = 8 0= Need Help? Submit Answer X° Read It K
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section1.8: Applications And Models
Problem 4ECP: From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the...
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Section 7.5 question 17
![**Title: Vector Magnitude and Angle Calculation**
**Objective:**
Approximate the magnitude of the vector and the angle \( \theta \), in the range \( 0^\circ \leq \theta < 360^\circ \), that the vector makes with the positive x-axis. Round your answers to the nearest tenth.
**Given Vector:**
\[ \mathbf{W} = \sqrt{15} \mathbf{i} - 7 \mathbf{j} \]
**Instructions:**
1. Calculate the magnitude of the vector \( |\mathbf{W}| \) using the formula:
\[ |\mathbf{W}| = \sqrt{( \text{component of } \mathbf{i} )^2 + (\text{component of } \mathbf{j} )^2} \]
2. Determine the angle \( \theta \) that the vector makes with the positive x-axis using the inverse tangent function:
\[ \theta = \tan^{-1} \left( \frac{\text{component of } \mathbf{j}}{\text{component of } \mathbf{i}} \right) \]
**Solution:**
- **Magnitude:**
The field for the magnitude \( |\mathbf{W}| \) is correctly filled with 8.
- **Angle:**
The field for the angle \( \theta \) is currently empty and marked incorrect.
**Steps to input the answer:**
1. Calculate and verify the magnitude using the provided formula.
2. Use the arctangent function to find the angle \( \theta \).
3. Ensure to adjust the angle if necessary, depending on the quadrant in which the vector lies.
4. Enter your answers in the respective fields and click "Submit Answer."
**Assistance:**
If you need further help, click on the "Read It" button for additional resources and explanations.
**Submission:**
- After completing the calculations, enter your answers and click the "Submit Answer" button.
**Output:**
The interface contains a section for the submission of the calculated values. A green checkmark and a red cross are beside the fields, indicating the correctness of the entered magnitude and the incorrectness of the angle, respectively.
Remember to double-check your calculations to ensure accurate results.
**Image Description:**
The image is a screenshot of an educational platform showing a problem that requires determining the magnitude and angle of a given vector. The vector components \( \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29eaf221-c72e-4b9c-a681-25e14c4a1cc7%2F66e70200-7596-44c1-bd4d-732c627c5060%2Fr6lgvps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Vector Magnitude and Angle Calculation**
**Objective:**
Approximate the magnitude of the vector and the angle \( \theta \), in the range \( 0^\circ \leq \theta < 360^\circ \), that the vector makes with the positive x-axis. Round your answers to the nearest tenth.
**Given Vector:**
\[ \mathbf{W} = \sqrt{15} \mathbf{i} - 7 \mathbf{j} \]
**Instructions:**
1. Calculate the magnitude of the vector \( |\mathbf{W}| \) using the formula:
\[ |\mathbf{W}| = \sqrt{( \text{component of } \mathbf{i} )^2 + (\text{component of } \mathbf{j} )^2} \]
2. Determine the angle \( \theta \) that the vector makes with the positive x-axis using the inverse tangent function:
\[ \theta = \tan^{-1} \left( \frac{\text{component of } \mathbf{j}}{\text{component of } \mathbf{i}} \right) \]
**Solution:**
- **Magnitude:**
The field for the magnitude \( |\mathbf{W}| \) is correctly filled with 8.
- **Angle:**
The field for the angle \( \theta \) is currently empty and marked incorrect.
**Steps to input the answer:**
1. Calculate and verify the magnitude using the provided formula.
2. Use the arctangent function to find the angle \( \theta \).
3. Ensure to adjust the angle if necessary, depending on the quadrant in which the vector lies.
4. Enter your answers in the respective fields and click "Submit Answer."
**Assistance:**
If you need further help, click on the "Read It" button for additional resources and explanations.
**Submission:**
- After completing the calculations, enter your answers and click the "Submit Answer" button.
**Output:**
The interface contains a section for the submission of the calculated values. A green checkmark and a red cross are beside the fields, indicating the correctness of the entered magnitude and the incorrectness of the angle, respectively.
Remember to double-check your calculations to ensure accurate results.
**Image Description:**
The image is a screenshot of an educational platform showing a problem that requires determining the magnitude and angle of a given vector. The vector components \( \
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