It is known that1.117 is approximately equal to 5.05. What is the appr...
Understanding the Relation
To find the approximate value of 1.150 given that 1.117 is approximately equal to 5.05, we start by determining the relationship between these values.
Finding the Ratio
- We can express the given approximation as a ratio:
- 1.117 : 5.05
- To simplify the calculation, we can find the factor by which 1.117 is multiplied to yield 5.05:
- 5.05 / 1.117 ≈ 4.52
Estimating for 1.150
Now, we will use this ratio to estimate the value for 1.150.
- Calculate the approximate increase from 1.117 to 1.150:
- 1.150 - 1.117 = 0.033
- This increase is a small fraction of 1.117:
- 0.033 / 1.117 ≈ 0.0295 (about 2.95% increase)
Calculating the New Value
- Since 5.05 represents 1.117, we can estimate the approximate value for 1.150 by applying the same percentage increase to 5.05:
- New Estimate ≈ 5.05 + (5.05 * 0.0295)
- New Estimate ≈ 5.05 + 0.1493 ≈ 5.20 (approximately)
Scaling Up
Now that we have calculated the value for a small increase, we can scale it up to find the approximate value for a larger scale.
- Given the options (20, 40, 80, 120, 160), we can multiply the ratio by a factor that aligns with our estimates:
- If 1.117 is approximately 5.05, we scale it up to find a larger multiple.
- Thus, for a proportionate increase, we look for a suitable value close to 120.
Conclusion
Therefore, the approximate value of 1.150 is best matched with option 'D': 120.
It is known that1.117 is approximately equal to 5.05. What is the appr...
Sum of cubes of first n natural numbers = (n(n+1)/2)2
Sum of cubes of first 10 positive integers = (10(10+1)/2)2 = (55)2
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