After determining whether the variation model below is of the form y = kx or y =4₁ x find the value of k. x20 y 1 30 02-² 5 0k-¹ 4 Ok=1/ 02-²713 O 40 1 60 60 1 90 80 100 1 1 120 150
After determining whether the variation model below is of the form y = kx or y =4₁ x find the value of k. x20 y 1 30 02-² 5 0k-¹ 4 Ok=1/ 02-²713 O 40 1 60 60 1 90 80 100 1 1 120 150
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![After determining whether the variation model below is of the form \( y = kx \) or \( y = \frac{k}{x} \), find the value of \( k \).
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 20 & 40 & 60 & 80 & 100 \\
\hline
y & \frac{1}{30} & \frac{1}{60} & \frac{1}{90} & \frac{1}{120} & \frac{1}{150} \\
\hline
\end{array}
\]
Possible values of \( k \):
- \( \circ \, k = \frac{3}{2} \)
- \( \circ \, k = \frac{5}{4} \)
- \( \circ \, k = \frac{1}{20} \)
- \( \circ \, k = \frac{2}{3} \)
- \( \circ \, k = \frac{1}{10} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F556d7fe8-ec0a-4648-8d64-f7fe013c7dbe%2Fef720558-1ac1-41c7-bd76-a52f0b618819%2F5eqim7_processed.png&w=3840&q=75)
Transcribed Image Text:After determining whether the variation model below is of the form \( y = kx \) or \( y = \frac{k}{x} \), find the value of \( k \).
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 20 & 40 & 60 & 80 & 100 \\
\hline
y & \frac{1}{30} & \frac{1}{60} & \frac{1}{90} & \frac{1}{120} & \frac{1}{150} \\
\hline
\end{array}
\]
Possible values of \( k \):
- \( \circ \, k = \frac{3}{2} \)
- \( \circ \, k = \frac{5}{4} \)
- \( \circ \, k = \frac{1}{20} \)
- \( \circ \, k = \frac{2}{3} \)
- \( \circ \, k = \frac{1}{10} \)
![**Direct Variation Model**
Use the given value of \( k \) to complete the table for the direct variation model:
\[ y = kx^2. \]
**Instructions:**
1. Use the value of \( k = 1 \).
2. Complete the table with the given \( x \) values.
3. Plot the points on a rectangular coordinate system.
**Table:**
| \( x \) | 8 | 10 | 12 | 14 | 16 |
|---------|-----|-----|-----|-----|-----|
| \( y = kx^2 \) | | | | | |
**Solution:**
Apply the formula \( y = kx^2 \) with \( k = 1 \) to find the \( y \) values.
- For \( x = 8 \), \( y = 1 \times 8^2 = 64 \)
- For \( x = 10 \), \( y = 1 \times 10^2 = 100 \)
- For \( x = 12 \), \( y = 1 \times 12^2 = 144 \)
- For \( x = 14 \), \( y = 1 \times 14^2 = 196 \)
- For \( x = 16 \), \( y = 1 \times 16^2 = 256 \)
Complete the table as follows:
| \( x \) | 8 | 10 | 12 | 14 | 16 |
|---------|-----|-----|-----|-----|-----|
| \( y = kx^2 \) | 64 | 100 | 144 | 196 | 256 |
**Graphing:**
Plot these points on a graph with \( x \)-axis for values of \( x \) and \( y \)-axis for the corresponding \( y \) values. The plotted points (8, 64), (10, 100), (12, 144), (14, 196), (16, 256) should form a parabola opening upwards.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F556d7fe8-ec0a-4648-8d64-f7fe013c7dbe%2Fef720558-1ac1-41c7-bd76-a52f0b618819%2Fuho3wu_processed.png&w=3840&q=75)
Transcribed Image Text:**Direct Variation Model**
Use the given value of \( k \) to complete the table for the direct variation model:
\[ y = kx^2. \]
**Instructions:**
1. Use the value of \( k = 1 \).
2. Complete the table with the given \( x \) values.
3. Plot the points on a rectangular coordinate system.
**Table:**
| \( x \) | 8 | 10 | 12 | 14 | 16 |
|---------|-----|-----|-----|-----|-----|
| \( y = kx^2 \) | | | | | |
**Solution:**
Apply the formula \( y = kx^2 \) with \( k = 1 \) to find the \( y \) values.
- For \( x = 8 \), \( y = 1 \times 8^2 = 64 \)
- For \( x = 10 \), \( y = 1 \times 10^2 = 100 \)
- For \( x = 12 \), \( y = 1 \times 12^2 = 144 \)
- For \( x = 14 \), \( y = 1 \times 14^2 = 196 \)
- For \( x = 16 \), \( y = 1 \times 16^2 = 256 \)
Complete the table as follows:
| \( x \) | 8 | 10 | 12 | 14 | 16 |
|---------|-----|-----|-----|-----|-----|
| \( y = kx^2 \) | 64 | 100 | 144 | 196 | 256 |
**Graphing:**
Plot these points on a graph with \( x \)-axis for values of \( x \) and \( y \)-axis for the corresponding \( y \) values. The plotted points (8, 64), (10, 100), (12, 144), (14, 196), (16, 256) should form a parabola opening upwards.
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