solve for the indicated variable:
a. temperature formula
solve for F: K=5/9(F-32)+273
b. annual interest rate
solve for R: A=P+Prt
K=5/9(F-32)+273
K-273=5/9(F-32)
9(K-273)=5(F-32)
9K-2457=5F-160
9K-2457+160=5F
(9K-2297)/5 = F
A=P + Prt
A-P=Prt
(A-P)/Pt = r
Check my work carefully.
C=k-273. Am i correct
a. To solve for F in the temperature formula K = 5/9(F-32) + 273, we need to isolate F.
First, distribute the 5/9 through the parentheses:
K = (5/9)F - (5/9)(32) + 273
Simplify the expression:
K = (5/9)F - 160/9 + 273
Combine like terms:
K = (5/9)F + (1173 - 160)/9
Simplify further:
K = (5/9)F + 1013/9
To isolate F, subtract 1013/9 from both sides:
K - 1013/9 = (5/9)F
Finally, multiply both sides by 9/5 to solve for F:
(9/5)(K - 1013/9) = F
Therefore, F = (9/5)(K - 1013/9).
b. To solve for R in the annual interest rate formula A = P + Prt, we need to isolate R.
First, factor out the common factor of P from the right side:
A = P(1 + rt)
Next, divide both sides by P:
A/P = 1 + rt
Subtract 1 from both sides:
(A/P) - 1 = rt
To isolate R, divide both sides by t:
((A/P) - 1)/t = r
Finally, simplify the expression:
((A - P)/P)/t = r
Therefore, R = ((A - P)/P)/t.
Note: In this context, it is common to express the interest rate as a decimal rather than a percentage.