Computer science question don't use any AI I need solution very fast pls

Consider a consumer whose utility function and budget constraint are given by $u(x,y)=x^{\text{'}\text{'}}{y}^{2\text{'}}$ and $px+py=1,$ respectively, where $p$ is the price of good $x,p_i$ is the price of good $y,$ and $\frac{?}{?}$ is the consumer's income.

a$)$ Derive the ordinary demand functions, $x^{**}(p_t,p,l)$ and $y^{**}(pt,p,h)$

b$)$ Derive the consumer's indirect utility function, $u(p_5,p_1,h)$ that this term in the ordinary demand function from part a $($Roy$\text{'}$s identity$).$

d$)$ Minimize the expenditure level necessary to achieve some arbitrary utility target $u$ and solve the first$-$order conditions for the compensated $($or Hicksian$)$ demand functions, $x^{\text{'}}(p_s,p_p,u^{**})$ and $y^{\text{'}}(p_s,p_{,},u^{**}).$

e$)$ Calculate the value of $\frac{{}^{\text{'}}}{h}at(c{)}_p,$ and $\frac{{}^{\text{'}}}{h}at(c{)}_p,$ and show that $x$ and $y$ are net substitutes. Explain with the use of a diagram how $x$ and $y$ can be net substitutes but not gross substitutes.

f$)$ Derive the expenditure function, e $(($:$p$;$p,p,u^f\}.$

g$)$ Calculate the partial derivative, $\frac{?}{{?}_e}\frac{p_3,p_y,u^{TT}}{d}el{p}_{,},$ and verify that the resulting term is the compensated demand for good $x($Shepherf$\text{'}$s lemma$).$

h$)$ Invert the expenditure function to solve for $u^{\text{'}\text{'}}(p,n,p,n).$ Verify that this is indirect utility $u^{**}(p_n,p,n).$

i$)$ Suppose $P_Y=$$$1$ and the individual's income is $$330.$ If the price of good $x$ falls from $$5$ to $$4,$ evaluate the individual's gain in terms of compensating variation.

j$)$ Suppose $P_y=$$$1$ and the individual's income is $$330.$ If the price of good $x$ falls from $S to $$4,$ evaluate the individual's gain in terms of equivalent variation.

k$)$ Draw a graph that shows compensating variation, equivalent variation, and the change in consumer surplus. What range of values can the change in consumer surplus take?

An individual derives utility from consumption goods, $x,$ and leisure time, $N,$ to maximize the daily utility level, $u=N.$ Outside income per day is $Sm$ and the price of consumption goods is $Sp.$ The individual can earn money each day by working at a wage rate of $Sw$ per hour, but working of course takes away from leisure time $($which implies it causes disutility$).$ The individual's utility maximization problem is constrained by two things: $($i$)$ the budget constraint, $px=m+wL,$ and $($ii$)$ the "time constraint", $L+N=24.$ The budget constraint can be written in terms of $N,x,$ and $m$ by substituting for $L=24-N.$

a$)$ Write a single equation for the budget constraint in terms of $N,x,$ and $m$ and interpret.

b$)$ Derive the demands for goods and leisure $(x$ and $N)$

c$)$ Solve for the individual's labor supply function, $L^{**}=24-N.$ Graph the labor supply function and verify that labor supply slopes upward in the wage rate.

d$)$ What is the effect of an increase in outside income $(m)$ on labor supply? Show the effect of a decrease in $m($say due to graduation$)$ on the individual's labor supply.

ASSIGNMIENI #$02$

Question $=01121$

The following polynomial can be used to relate the zero$-$pressure spocific heat of dry air, Cp$,k*(kgK),$ to tempcraturs, $(K)$ :

$C_p=0\mathrm{.}99403+1\mathrm{.}671{10}^{-4}T+9\mathrm{.}7215{10}^{-2}{T}^2-9\mathrm{.}5838{10}^{-11}{T}^3+1\mathrm{.}9520{10}^{-14}{T}^4$

Apply Secant method to determine the temperature that comesponds to the specific heat of