Question

I need all parts of 2) done. (a, b, c, and d.)

Answer 1

your equations for part a) are semi-correct, let's recall that the x-axis has the number of cows and y-axis is how long it takes.

if the setup for Wesly is 0.3 hours, then he takes 0.2(1) for one cow and for a second one is 0.2(2) and so on, that'll be 0.2x, and how long it takes will be "y".

so we're looking at

y = 0.3 + 0.2x

y = 0.4 + 0.05x

now let's do part c)

`\begin{cases}y=0.3+0.2x\\\\ y=0.4+0.05x \end{cases}\qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{\underset{y}{0.3+0.2x}~~ = ~~0.4+0.05x} \\\\\\ 0.2x=0.1+0.05x\implies 0.15x=0.1\implies x=\cfrac{0.1}{0.15}\implies \boxed{x=\cfrac{2}{3}} \\\\\\ \stackrel{\textit{substituting the 1st equation}}{y=0.3+0.2((2)/(3))}\implies \boxed{y=\cfrac{13}{30}}`

now le's do part b), Check the picture below.

now onto part d)

does it make any sense?

well, let's look at the picture, with the closeup

the blue line touches the red line and then it keeps on going UP, meaning, after they touch each other, it takes more hours on the blue line than it'd on the red line, so the red line takes less hours after that intersection, why's that?

well, the machine takes longer to setup, because he has to grab the mechanical pieces, put them together, assemble any parts, hook it up to the barn maybe, and so forth, however, once he's done with all that jazz, the machine can milk a cow in 0.05 of an hour, something he'd take 0.2 by himself, that machine is four times faster, hell yeah.

you can think of say hmm a tractor for plowing a land for say corn, same thing, it takes a while to setup maybe even weeks, but once is going it moves like a bee, plus it doesn't get tired, you simple give it some tune up and more gas and off you go.

I bet Wesley after milking about 5 cows, he's going to go watch Pokemon for a few to relax a bit, the machine won't.