Question
show me step bt step on how to solve this problem. don't use [and { in the steps.
(3094/r)=5927(((1+r)^27)/r)
(3094/r)=5927(((1+r)^27)/r)
Answers
GPT-4o mini
To solve the equation (3094/r) = 5927(((1+r)^27)/r), we will follow these steps:
1. **Eliminate the fraction**: Multiply both sides by r to get rid of the denominator:
3094 = 5927 * (1 + r)^27
2. **Isolate the term with the variable**: Divide both sides by 5927:
(3094/5927) = (1 + r)^27
3. **Simplify the left side**: Calculate the fraction and express it in decimal form:
x = 3094/5927
x ≈ 0.522
Now the equation looks like:
0.522 = (1 + r)^27
4. **Take the 27th root**: To isolate (1 + r), take the 27th root of both sides:
1 + r = (0.522)^(1/27)
5. **Calculate the right side**: Using a calculator to find the 27th root:
1 + r ≈ 0.998
6. **Isolate r**: Subtract 1 from both sides:
r ≈ 0.998 - 1
r ≈ -0.002
7. **Result**: Therefore, the solution is:
r ≈ -0.002, or in percentage terms, r ≈ -0.2%.
Remember to check the initial equation using this value of r to ensure that the solution is valid.
1. **Eliminate the fraction**: Multiply both sides by r to get rid of the denominator:
3094 = 5927 * (1 + r)^27
2. **Isolate the term with the variable**: Divide both sides by 5927:
(3094/5927) = (1 + r)^27
3. **Simplify the left side**: Calculate the fraction and express it in decimal form:
x = 3094/5927
x ≈ 0.522
Now the equation looks like:
0.522 = (1 + r)^27
4. **Take the 27th root**: To isolate (1 + r), take the 27th root of both sides:
1 + r = (0.522)^(1/27)
5. **Calculate the right side**: Using a calculator to find the 27th root:
1 + r ≈ 0.998
6. **Isolate r**: Subtract 1 from both sides:
r ≈ 0.998 - 1
r ≈ -0.002
7. **Result**: Therefore, the solution is:
r ≈ -0.002, or in percentage terms, r ≈ -0.2%.
Remember to check the initial equation using this value of r to ensure that the solution is valid.