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
can you please show how to do these? thanxx =)
All this means is to re-arrange the equation so F and R are alone on one side of the equation.
I hope this helps. Thanks for asking.
a. To solve for F in the given equation K = (5/9)(F-32) + 273:
1. Distribute the (5/9) to both terms inside the parentheses:
K = (5/9)F - (5/9)(32) + 273
2. Simplify the expression (5/9)(32):
K = (5/9)F - 160/9 + 273
3. Combine like terms -160/9 and 273:
K = (5/9)F + 113/9
4. To isolate the variable F, subtract 113/9 from both sides of the equation:
K - 113/9 = (5/9)F
5. To get F alone, divide both sides of the equation by (5/9) or multiply both sides by its reciprocal (9/5):
[(9/5)(K - 113/9)] = F
Therefore, the formula for converting temperature from Kelvin (K) to Fahrenheit (F) is:
F = (9/5)(K - 113/9)
b. To solve for R in the equation A = P + Prt:
1. Factor out P from the right side:
A = P(1 + rt)
2. Divide both sides of the equation by (1 + rt):
A / (1 + rt) = P
3. To solve for R, subtract 1 from both sides of the equation:
A / (1 + rt) - 1 = P - 1
4. Simplify the left side by finding a common denominator:
A / (1 + rt) - (1 + rt) / (1 + rt) = P - 1
5. Combine the fractions on the left side:
(A - (1 + rt)) / (1 + rt) = P - 1
6. Multiply both sides of the equation by (1 + rt) to isolate R:
(A - (1 + rt)) = (P - 1)(1 + rt)
7. Expand the right side using distributive property on (P - 1)(1 + rt):
A - 1 - rt = P + Prt - 1 - rt
8. Cancel out the -1 and +1 terms on both sides of the equation:
A - rt = P + Prt - rt
9. Group the terms involving R on one side:
A - rt = P + (P - r)t
10. Factor out t:
A - rt = P + (P - r)t
11. Finally, solve for R:
R = (A - P) / (Pt)
Therefore, the formula for calculating the annual interest rate (R) in the equation A = P + Prt is:
R = (A - P) / (Pt)