Very quick question..please help, exam tomorrow.

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WTF?

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Hey guys, I hope I'm not a pest by posting a question like this, but the truth is that it is confusing to me, so thanks for any help.

Carlita decides she wants to devote at least twice as many hours per day sleeping as she does working. Graph all the possible combinations of sleeping (s) and working time (w).

So the first step I think, is to get an equations...I'd probably think it's 2s>w....am I wrong? but then how would I solve? S is on the Y-axis, and w is on the x-axis...so would this be like 2y>x? Would I then need to divide both sides by 2 to get y=1/2x?

Another quick question:
Donna has to read a 325 page novel for her literature class. She can read 40 pages each day. Let An be the number of pages that are left to be read after n days.
a. write an explicit formula for An.
b. How many pages are left to be read after 2 days?

my solutions (am I wrong or right)
a. An=325 - 40n
b. 245 pages.

YET another question...

Tony spent $32 for C used CD's at $8 each and B used books at $4 each. He bought at least 1 of each.
a. What equation relates C, B, and the total amount spent?
b. Graph the solutions on the axes at the right.
c. How many ways are there to spend $32 on C CD's and B books?
^(this one I completely don't get...)


Thanks for any help/input.
 
On the sleeping-versus-working exercise, I don't see how they're expecting you to graph "all" solutions, since there are infinitely many. Or maybe they're wanting you to graph a system of linear inequalities...?

You've got:

. . . . .s > 2w

. . . . .s + w < 24

Graph the system of linear inequalities, and shade the feasibility region, I suppose, keeping in mind that s > 0 and w > 0.

On the "reading the novel" exercise, your formula for (a) looks good, and the answer for (b) is easily checked:

. . . . .0 days: 325 pages left
. . . . .1 day: 325 - 40 = 285 pages left
. . . . .2 days: 285 - 40 = 245 pages left

Eliz.
 
WTF? said:
Carlita decides she wants to devote at least twice as many hours per day sleeping as she does working. Graph all the possible combinations of sleeping (s) and working time (w). I'd probably think it's 2s>w
Click to expand...
You have it backwards. s > 2*w

Hopefully, one can see that 0 ≤ s + 2*w ≤ 24
 
stapel said:
On the sleeping-versus-working exercise, I don't see how they're expecting you to graph "all" solutions, since there are infinitely many. Or maybe they're wanting you to graph a system of linear inequalities...?

You've got:

. . . . .s > 2w

. . . . .s + w < 24

Graph the system of linear inequalities, and shade the feasibility region, I suppose, keeping in mind that s > 0 and w > 0.

On the "reading the novel" exercise, your formula for (a) looks good, and the answer for (b) is easily checked:

. . . . .0 days: 325 pages left
. . . . .1 day: 325 - 40 = 285 pages left
. . . . .2 days: 285 - 40 = 245 pages left

Eliz.
Click to expand...

Does this mean that the x and y intercepts are both 24?

So I shade...below the half plane on a straight line, right?
 
You have two lines if you treat the inequlities as equations for the moment. If s is on the y-axis and w is on the x-axis, rewrite the inequalities as

\(\displaystyle s \geq 2w \, [ 1 ]\)
\(\displaystyle s \leq 24 - w \, [ 2 ]\)

Don't forget to use dotted lines because they are \(\displaystyle \geq\) and \(\displaystyle \leq\) (not > and <).

The second does indeed have x and y intercepts at x=24 and y=24, respectively.

Now, shade "above" the first dotted line, and "below" the second.
 
thanks..

hey guys, what if they give me something like "graph "2y=4x" or "2x=4y"

how would I go about doing this?
 
\(\displaystyle 2y = 4x \, \Leftrightarrow \, y = 2x\)

\(\displaystyle 2x = 4y \, \Leftrightarrow \, y = (1/2)x\)

After you familiar with \(\displaystyle y = mx + c\)?
 
Unco said:
\(\displaystyle 2y = 4x \, \Leftrightarrow \, y = 2x\)

\(\displaystyle 2x = 4y \, \Leftrightarrow \, y = (1/2)x\)

After you familiar with \(\displaystyle y = mx + c\)?
Click to expand...

Well, I thought the 2x=4y would be a vertical line.

wouldn't I divide both sides by 2 to isolate x? therefore x=2y? but then how do I graph this?
 
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