Question
upstudy study bank question image url

Solve the formula for the given variable. \[ Z=\frac{9}{f-s} \] Solve for \( f \), then solve for \( s \). \( f=\square \) (Simplify your answer.)

Ask by Marshall Reed. in the United States
Feb 26,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( f = \frac{9 + Zs}{Z} \) and \( s = \frac{-9 + Zf}{Z} \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To solve for \( f \), we start with the equation \( Z=\frac{9}{f-s} \). First, we multiply both sides by \( (f-s) \) to eliminate the fraction: \[ Z(f-s) = 9. \] Now, we can distribute \( Z \): \[ Zf - Zs = 9. \] Next, we want to isolate \( f \): \[ Zf = 9 + Zs. \] Now, dividing by \( Z \): \[ f = \frac{9 + Zs}{Z}. \] Now, to solve for \( s \), we start again from the original formula: \[ Z=\frac{9}{f-s}. \] Multiplying both sides by \( (f-s) \): \[ Z(f-s) = 9. \] Distributing again gives: \[ Zf - Zs = 9. \] Rearranging to isolate \( s \): \[ Zs = Zf - 9. \] Now we divide by \( Z \): \[ s = \frac{Zf - 9}{Z}. \] Thus, we have the solutions as follows: \( f=\frac{9 + Zs}{Z} \) and \( s=\frac{Zf - 9}{Z}. \)

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