Math Problem Statement
\frac{568}{\left[1+\left(\frac{0.17}{4}\right)^{\left(4\cdot 4\right)}\right]}-\frac{81}{\left[1+\left(\frac{0.07}{2}\right)^{\left(15\cdot 2\right)}\right]}+76\cdot \left[1+\left(\frac{0.04}{12}\right)^{\left(13\cdot 12\right)}\right]. ROUND TO 4 DECIMAL PLACES FOR FINAL ANSWER OF Y
Solution
To solve the given expression step by step, let's break it down:
[ Y = \frac{568}{\left[1+\left(\frac{0.17}{4}\right)^{\left(4\cdot 4\right)}\right]}-\frac{81}{\left[1+\left(\frac{0.07}{2}\right)^{\left(15\cdot 2\right)}\right]}+76\cdot \left[1+\left(\frac{0.04}{12}\right)^{\left(13\cdot 12\right)}\right] ]
Step 1: Simplify each component inside the brackets
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Calculate the first term in the denominator of the first fraction:
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Calculate the first term in the denominator of the second fraction:
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Calculate the exponent in the third term:
Step 2: Substitute these values back into the equation
Now, let's compute each component using a calculator and round them appropriately.
I'll do these calculations now.The final rounded value of is .
Would you like to delve into the details of this solution, or do you have any questions?
Here are some related questions to explore:
- How do exponentiation and powers affect small decimal numbers?
- Why is it important to round to a specific number of decimal places in mathematical calculations?
- How does changing the values in the equation affect the final outcome?
- What are some practical applications of such calculations?
- How would the result change if we altered the operation from subtraction to addition?
Tip: Always double-check your calculations when dealing with multiple operations to avoid errors, especially with exponents and small decimals.
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Math Problem Analysis
Mathematical Concepts
Fractional calculations
Exponentiation
Formulas
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Theorems
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Suitable Grade Level
Advanced High School
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