$(36)-$ Solve using Newton$-$Raphson method: $4x^4-3x^3-2x^2-x+2=1$

$(37)-$ Solve $8x^3-20x^2+14x-3=0$ by Newton$-$Raphson method assuming suitable value for $x.$

$(28)-$ Solve: $x+y+z=3$;$x-y+z=2$;$x+y-2z=0$

$(39-$ Solve: $a+b+c+d=4$;$a-b-c+d=0$;$a+2b-c+d=3$;$a=b$

$9.-$ Calculate stoichiometric coefficients in the reaction:

$C_6{H}_{12}{O}_6+a{O}_{2}bC{O}_2+cH{H}_{2}O$

$(41)-$ Calculate stoichiometric coefficients in the reaction:

$C_5{H}_{10}{O}_5+a{O}_{2}bC{O}_2+c{H}_{2}O$

Problems for practice...

$42.$ Stream $1$ contains $20\%HN{O}_3,30\%H_{2}S{O}_4,25\%HCl$ and $25\%H_{2}O.$ Stream $2$ contains $10\%HN{O}_3$ and $90\%H_{2}O.$ Stream $3$ contains $20\%H_{2}S{O}_4$ and $80\%H_{2}O.$ Stream $4$ contains $30\%HCl$ and $70\%H_{2}O.$ Four streams are mixed together to obtain a combined acid containing $7\%HN{O}_3,12\%H_{2}S{O}_4,14\%HCl$ and $67\%H_{2}O.$ All the percentages are by mass. Calculate the mass of streams $1,2,3$ and $4$ to produce $1000kg$ of combined acid.

$43.$ Fit an equation $=aP+b$ for the following data:

$\backslash$table$[[$Power$,P(W)$:$,1138,1470,1945,2168,2453,2513],[$Efficiency$.(\%)$:$,7\mathrm{.}87,9\mathrm{.}07,12\mathrm{.}34,14\mathrm{.}56,15\mathrm{.}56,15\mathrm{.}94]]$

$(45)-$ In the binary solution, density of solution $({}_s)$ is a function of mole fraction of water $(x_w).$ Develop a linear model for the variables. The data is as follows:

$\backslash$table$[[x_w$:$,0\mathrm{.}25,0\mathrm{.}5,1],[{}_s(k\frac{g}{m^3})$:$,850,900,1000]$