how to solve this 3rd degree 1 Go points) The reciprocal of volume (1/v f(m)) is

Question

how to solve this 3rd degree

1 Go points) The reciprocal of volume (1/v f(m)) is a function of mass (m) (.e m dependent variable and 1/V dependent variable). Given the data points: mass and volume below, a) Solve for the coefficients of the polynomial nterpolation curve passing through all of these points and write the polynomial equation. m Igl volume em 50 22 62 t P3 13) Polynomial Interpolation Curve Coefficients and Equation: b Using the polynomial equation, estimate the volume at mass 3.55 g. What is the density foy

Explanation / Answer

Assume a three degree polynomial haing four unknown coefficients satisfy the given points
a(m)^3 + b(m^2) + cm + d = 1/V
then, the table gives us following values
m   V
2   50
4.6   22
10   9
13   6.2

PUTTING IN VALUES AND SOL VGIN FOR COEFFICIENTS BY USING 4 EQUATIONS AND 4 UNKNOWNS

a = 0.000022635092566052983
b = -0.00008019549596947946
c = 0.009543094473443198
d = 0.0010535122964630973

so, equation becomes
0.000022635092566052983 m^3 -0.00008019549596947946 m^2 + 0.009543094473443198 m + 0.0010535122964630973 = 1/V

b. m = 3.55 g
V = ?
from the equation
V = 28.625 CM^3

density = integrate from m = 3.55 and 11 (0.000022635092566052983 m^3 -0.00008019549596947946 m^2 + 0.009543094473443198 m + 0.0010535122964630973 )dm
density = 0.000022635092566052983 m^4/4 -0.00008019549596947946 m^3/3 + 0.009543094473443198 m^2/2 + 0.0010535122964630973m (from m = 3.55 to m = 11)
density = 1.749 g/cm^3

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