Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x = 125, y = 8. 6 TE Pa sin (a) ∞ a Submit Assignment Quit & Save Bac
Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x = 125, y = 8. 6 TE Pa sin (a) ∞ a Submit Assignment Quit & Save Bac
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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![### Assignment: Relationship of Variables
**Problem Statement:**
Write an equation describing the relationship of the given variables.
Given: \( y \) varies inversely as the cube root of \( x \) and when \( x = 125 \), \( y = 8 \).
**Solution:**
To find the equation that describes this relationship.
**Details:**
There is a LaTeX-like editor open on the screen showing mathematical symbols and expressions such as \( a^b \), \( \sin(a) \), \( \infty \), and \( \alpha \), indicating that this editor is likely being used to form the equation or calculate the given problem’s answer.
The relationship given suggests that \( y \) varies inversely with the cube root of \( x \), which can be expressed as:
\[
y = \frac{k}{\sqrt[3]{x}}
\]
**Next Steps:**
1. Use the values provided \( x = 125 \) and \( y = 8 \) to solve for the constant \( k \).
2. Substitute \( x = 125 \) and \( y = 8 \) into the equation \( y = \frac{k}{\sqrt[3]{x}} \):
\[
8 = \frac{k}{\sqrt[3]{125}}
\]
3. Calculate the cube root of 125, which is 5:
\[
\sqrt[3]{125} = 5
\]
4. Now, substitute and solve for \( k \):
\[
8 = \frac{k}{5}
\]
\[
k = 8 \times 5
\]
\[
k = 40
\]
5. Substitute the value of \( k \) back into the equation:
\[
y = \frac{40}{\sqrt[3]{x}}
\]
Thus, the equation describing the relationship of the given variables is:
\[
y = \frac{40}{\sqrt[3]{x}}
\]
By following these steps, we can determine the mathematical relationship between \( y \) and \( x \) in this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f332ee6-3ef6-4e55-bad3-1cebde5ee541%2Fbd891a69-7ca7-4688-93af-ffa18e9c22b6%2F4drwpkm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Assignment: Relationship of Variables
**Problem Statement:**
Write an equation describing the relationship of the given variables.
Given: \( y \) varies inversely as the cube root of \( x \) and when \( x = 125 \), \( y = 8 \).
**Solution:**
To find the equation that describes this relationship.
**Details:**
There is a LaTeX-like editor open on the screen showing mathematical symbols and expressions such as \( a^b \), \( \sin(a) \), \( \infty \), and \( \alpha \), indicating that this editor is likely being used to form the equation or calculate the given problem’s answer.
The relationship given suggests that \( y \) varies inversely with the cube root of \( x \), which can be expressed as:
\[
y = \frac{k}{\sqrt[3]{x}}
\]
**Next Steps:**
1. Use the values provided \( x = 125 \) and \( y = 8 \) to solve for the constant \( k \).
2. Substitute \( x = 125 \) and \( y = 8 \) into the equation \( y = \frac{k}{\sqrt[3]{x}} \):
\[
8 = \frac{k}{\sqrt[3]{125}}
\]
3. Calculate the cube root of 125, which is 5:
\[
\sqrt[3]{125} = 5
\]
4. Now, substitute and solve for \( k \):
\[
8 = \frac{k}{5}
\]
\[
k = 8 \times 5
\]
\[
k = 40
\]
5. Substitute the value of \( k \) back into the equation:
\[
y = \frac{40}{\sqrt[3]{x}}
\]
Thus, the equation describing the relationship of the given variables is:
\[
y = \frac{40}{\sqrt[3]{x}}
\]
By following these steps, we can determine the mathematical relationship between \( y \) and \( x \) in this problem.
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