Question
upstudy study bank question image url

Writing an equation that models variation Write an equation that expresses the following relationship. \[ p \text { varies jointly with the square of } d \text { and the cube of } u \] In your equation, use \( k \) as the constant of proportionality.

Ask by Little Lawson. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The equation is \( p = k d^2 u^3 \).

Solution

1. Since \( p \) varies jointly with the square of \( d \) and the cube of \( u \), we write the relationship as: \[ p = k d^2 u^3 \] where \( k \) is the constant of proportionality. 2. This is the required equation that models the given variation.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

The relationship described can be expressed with the equation: \[ p = k \cdot d^2 \cdot u^3 \] Here, \( p \) varies jointly with the square of \( d \) (denoted as \( d^2 \)) and the cube of \( u \) (denoted as \( u^3 \)), while \( k \) represents the constant of proportionality that will change based on specific conditions or units in your particular context. Understanding variation is not just for academics—it's quite useful in fields like physics and economics. For instance, in a physics scenario, considering how the pressure of a gas varies with respect to volume and temperature could be modeled similarly. These relationships help scientists and engineers predict outcomes in real-world applications!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy