Question
Solve \( m=(a+d) T \) (a) for \( T \) \( T=\square \) (b) for \( d \) \( d=\square \)
Ask by Schmidt Edwards. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( T = \frac{m}{a + d} \)
\( d = \frac{m - aT}{T} \)
Solution
Solve the equation \( m=(a+d)T \).
Solve the equation by following steps:
- step0: Solve for \(T\):
\(m=\left(a+d\right)T\)
- step1: Swap the sides:
\(\left(a+d\right)T=m\)
- step2: Divide both sides:
\(\frac{\left(a+d\right)T}{a+d}=\frac{m}{a+d}\)
- step3: Divide the numbers:
\(T=\frac{m}{a+d}\)
Solve the equation \( m=(a+d)T \).
Solve the equation by following steps:
- step0: Solve for \(d\):
\(m=\left(a+d\right)T\)
- step1: Multiply the terms:
\(m=T\left(a+d\right)\)
- step2: Swap the sides:
\(T\left(a+d\right)=m\)
- step3: Divide both sides:
\(\frac{T\left(a+d\right)}{T}=\frac{m}{T}\)
- step4: Divide the numbers:
\(a+d=\frac{m}{T}\)
- step5: Move the constant to the right side:
\(d=\frac{m}{T}-a\)
- step6: Subtract the terms:
\(d=\frac{m-aT}{T}\)
- step7: Simplify:
\(d=\frac{m-Ta}{T}\)
The solution to the equation \( m = (a + d)T \) for \( T \) is \( T = \frac{m}{a + d} \).
The solution to the equation \( m = (a + d)T \) for \( d \) is \( d = \frac{m - aT}{T} \).
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Bonus Knowledge
To solve for \( T \) in the equation \( m = (a + d) T \), we can isolate \( T \) by dividing both sides by \( (a + d) \): \[ T = \frac{m}{a + d} \] Now, solving for \( d \), we start from the original equation \( m = (a + d) T \) and first divide both sides by \( T \): \[ \frac{m}{T} = a + d \] Next, to isolate \( d \), we subtract \( a \) from both sides: \[ d = \frac{m}{T} - a \]