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This problem is based on the following data for the density, p, and sound speed, a, of water as a Function of temperature. T P a (°C) (kg/m³) (m/s) 0 1000 1402 20 998 1482 40 992 1529 60 983 1551 80 972 1554 1543 100 958 Estimate, using a piecewise linear interpolation, (a) the density and sound of speed of water when T = 35° C; (b) the temperature and density of water when a = 1545 m/s. Moreover, find (c) a least squares line a(T) = c₁T + co fitting the data; (d) a least squares parabola p(T) = c₂T² + c₁T + co fitting the data.

This problem is based on the following data for the density, p, and sound speed, a, of water as a Function of temperature. T P a (°C) (kg/m³) (m/s) 0 1000 1402 20 998 1482 40 992 1529 60 983 1551 80 972 1554 1543 100 958 Estimate, using a piecewise linear interpolation, (a) the density and sound of speed of water when T = 35° C; (b) the temperature and density of water when a = 1545 m/s. Moreover, find (c) a least squares line a(T) = c₁T + co fitting the data; (d) a least squares parabola p(T) = c₂T² + c₁T + co fitting the data.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This problem is based on the following data for the density, p, and sound speed, a, of water as a function of temperature. T р a (°C) (kg/m³) (m/s) 0 1000 1402 20 998 1482 40 992 1529 60 983 1551 80 972 1554 100 958 1543 Estimate, using a piecewise linear interpolation, (a) the density and sound of speed of water when T = 35° C; (b) the temperature and density of water when a = Moreover, find 1545 m/s. a least squares line a(T) = c₁T+ Co fitting the data; (d) a least squares parabola p(T) = c₂T² + c₁T + co fitting the data.
Transcribed Image Text:This problem is based on the following data for the density, p, and sound speed, a, of water as a function of temperature. T р a (°C) (kg/m³) (m/s) 0 1000 1402 20 998 1482 40 992 1529 60 983 1551 80 972 1554 100 958 1543 Estimate, using a piecewise linear interpolation, (a) the density and sound of speed of water when T = 35° C; (b) the temperature and density of water when a = Moreover, find 1545 m/s. a least squares line a(T) = c₁T+ Co fitting the data; (d) a least squares parabola p(T) = c₂T² + c₁T + co fitting the data.
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