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) 1000 1402 998 1482 992 1529 983 1551 972 1554 1543 6-8 20 40 60 80 100 958 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) 1000 1402 998 1482 992 1529 983 1551 972 1554 1543 6-8 20 40 60 80 100 958 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve for c and d
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
998
1482
992
1529
983
1551
972 1554
1543
20
40
60
80
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.
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