A variable force has the function $F=(7\mathrm{.}5x^2+5\mathrm{.}2x+2\mathrm{.}8)hat(i)+(14\mathrm{.}1y)hat(j)+(4\mathrm{.}8z-9\mathrm{.}6)hat(k)$ where $F$ is in $N.$

This force acts on a particle as it moves from position $r_1=-7\mathrm{.}8$hat$(i)+6\mathrm{.}2$hat$(j)+16\mathrm{.}3$hat$(k)$ to position $r_2=6\mathrm{.}7$hat$(i)-14\mathrm{.}8$hat$(j)+20$hat$(k),$ both positions in meters.

A$.$ What is the expression for the work done by the $x$ component of the force intierms of $x?$

B$.$ What is the expression for the work done by the $y$ component of the force in terms of $y?$

C$.$ What is the expression for the work done by the $z$ component of the force in terms of $z?$

Precision for the following calculations is to $4$ significant figures.

D$.$ Evaluate the work done by the $x$ component of the force between $r_1$ and $r_2.4\mathrm{.}9$

E$.$ Evaluate the work done by the $y$ component of the force between $r_1$ and $r_2,4,0$

F$.$ Evaluate the work done by the $z$ component of the force between $r_1$ and $r_2,4\mathrm{.}0$

G$.$ Evaluate the total work done by the force between $r_1$ and $r_2.4\mathrm{.}0$