32.0=5.5x10^2(1/T)+14.2
Solve for T
I am confused about what the first step would be to solving for T. Would I divide 5.5x10^2(1/T) and move it to the left side?
Please help.
get all the T stuff together:
5.5*10^2(1/T) = 17.8
Now you can start working the numbers:
1/T = 17.8/550
T = 550/17.8
To solve for T in the equation 32.0 = 5.5x10^2(1/T) + 14.2, we can follow the steps below:
Step 1: Start by moving the constant term (14.2) to the right side of the equation by subtracting it from both sides:
32.0 - 14.2 = 5.5x10^2(1/T)
Simplifying this gives:
17.8 = 5.5x10^2(1/T)
Step 2: Divide both sides of the equation by 5.5x10^2 to isolate the term (1/T):
17.8 / (5.5x10^2) = 1/T
To divide by 5.5x10^2, you can divide the numerator (17.8) by 5.5 and then divide by 10^2 (or multiply by 0.01 since 10^2 equals 100).
17.8 ÷ 5.5 = 3.23636363636 (rounded to 11 decimal places)
3.23636363636 ÷ 0.01 = 32.3636363636 (rounded to 11 decimal places)
So, we have:
32.3636363636 = 1/T
Step 3: To solve for T, we can take the reciprocal of both sides to isolate T:
1/32.3636363636 = T
Calculating this gives:
T ≈ 0.0308880309 (rounded to 11 decimal places)
Therefore, solving the equation gives T ≈ 0.0309.