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
![**Variation Problem**
**Write an equation that describes the following variation problem:**
3) \( Q \) varies directly with the square of \( t \). \( Q = 45 \) when \( t = 3 \).
**Explanation:**
In direct variation problems involving a square, the equation can be written as:
\[ Q = k \cdot t^2 \]
To find the constant of variation \( k \):
1. Substitute the given values \( Q = 45 \) and \( t = 3 \) into the equation:
\[ 45 = k \cdot (3)^2 \]
\[ 45 = k \cdot 9 \]
2. Solve for \( k \):
\[ k = \frac{45}{9} \]
\[ k = 5 \]
Hence, the equation describing the variation is:
\[ Q = 5t^2 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b3e2b09-123d-4bda-aba2-2450a44862a9%2Ff4503eba-9bc6-4cf2-8fde-37620fd31ddc%2Fdsrusxh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Variation Problem**
**Write an equation that describes the following variation problem:**
3) \( Q \) varies directly with the square of \( t \). \( Q = 45 \) when \( t = 3 \).
**Explanation:**
In direct variation problems involving a square, the equation can be written as:
\[ Q = k \cdot t^2 \]
To find the constant of variation \( k \):
1. Substitute the given values \( Q = 45 \) and \( t = 3 \) into the equation:
\[ 45 = k \cdot (3)^2 \]
\[ 45 = k \cdot 9 \]
2. Solve for \( k \):
\[ k = \frac{45}{9} \]
\[ k = 5 \]
Hence, the equation describing the variation is:
\[ Q = 5t^2 \]
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