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Answer :
The interpolated value at x = 55 is 44.
To compute the value using linear interpolation, we need to use data points between which our value of interest lies. Let's assume we are looking to find the interpolated value for a given data set. Linear interpolation formula is given by:
y = y1 + (x - x1) * (y2 - y1) / (x2 - x1)
Where:
- x1, y1 are the coordinates of the first data point
- x2, y2 are the coordinates of the second data point
- x is the value at which we want to interpolate
As an example, assume we have data points (44, 44) and (76, 44) and want to find the interpolated value at x = 55. We would compute as follows:
- Identify data points: (x1, y1) = (44, 44); (x2, y2) = (76, 44)
- Apply the formula: y = 44 + (55 - 44) * (44 - 44) / (76 - 44)
- Simplify: y = 44
Therefore, the interpolated value at x = 55 is 44.
Complete Question:- Compute the values 69, 55, 35, 47, 77, 69, 63, and 44 using linear interpolation.
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Rewritten by : Barada
Using linear interpolation, we can estimate that the value for 63 in this data set is approximately 54.38.
To compute the value of 63 using linear interpolation, we first need to identify the two closest data points to 63. In this case, those points are 55 and 69.
Next, we need to calculate the distance between those two points, which is 14.
We then calculate the proportion of that distance that 63 is from 55.
This can be done by subtracting 55 from 63 (which gives us 8), and then dividing by the distance between the two points (14).
This gives us 0.57 (rounded to two decimal places).
Finally, we can use this proportion to interpolate a value between the corresponding y-values (35 and 69) for those two data points.
To do this, we first calculate the difference between those two y-values (69-35=34).
We then multiply that difference by the proportion we calculated earlier (34 x 0.57 = 19.38).
Finally, we add this result to the y-value for the closest data point to 63 (35 + 19.38 = 54.38).
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