EVILNess needs algebra help hopefully for the last time

EVILNess · 04-22-2011, 09:01 PM

It's time for finals, and I am doing these practice tests like crazy for my final on the 28th. I have gotten 40+ of the possible questions right multiple times, but a few are hit or miss to say the least. If a question shows up on the actual final it will look identical except have different numbers.

Long story short I need someone to work some algebra for me so I can compare what I am doing to what is correct.

Any help is much appreciated and I promise I will never ask again. Mainly because I will be done and will never have to do math in an academic setting ever again!

TDK · 04-22-2011, 09:47 PM

Well ln(e^9) is just 9.

ln (natural log) is the same as log base e of the value. So log base e of e^9 is 9 because e^9 = e^9

ln and e pretty much always cancel out. So like, if you have something like

5 = e^x

Solving for x, you would take ln of both sides.

ln5 = ln(e^x) = x

x = ln5

and vice versa.

5 = lnx solving for x, take e to the power of both sides

e^5 = e^(lnx) = x

x = e ^ 5

Eltargrim · 04-22-2011, 10:59 PM

Question 2:

|y-7.8| <= 1.5
y - 7.8 = +- 1.5
y = +-1.5 + 7.8
y = [6.3, 9.3]

Toastburner B · 04-22-2011, 11:56 PM

I did that wrong. The formula I was using was for dilutions, not mixing of two solutions. Sorry, my bad.

I can help with question one, I think.

I had to do similar problems with my studies. My teacher taught us a very simple formula for it:

Concentration1 X Volume 1 = Concentration 2 X Volume 2 (C1XV1 = C2XV2)

So, in the case of this problem you know the concentration and volume you have for one, but only the concentration for the other, so

EDIT: I plugged in the wrong numbers. See my next post for the right numbers.

9 X V1 = 60 X 7

Simplified down to

9(V1) = 420

Just solve for V1:

V1 = 420/9

V1 = 42.67 mL

Just round it out to what decimal place you need.

TDK · 04-23-2011, 09:19 AM

Quote:

Originally Posted by Toastburner B

I did that wrong. The formula I was using was for dilutions, not mixing of two solutions. Sorry, my bad.

If you do the problem in terms of the 2% solution, it would be a dilution problem. :I

Eltargrim · 04-23-2011, 11:08 AM

Quote:

Originally Posted by TDK

If you do the problem in terms of the 2% solution, it would be a dilution problem. :I

Not of the kind that his formula would work for :P

And Smarty, someone needs to teach the undergrads how to do it. Once.

Krylo · 04-23-2011, 12:05 AM

The answer to all of them is five.

Except the last one.

That is C.

EVILNess · 04-23-2011, 12:26 AM

Thank you everyone. Much appreciated!

Except Krylo. Fuck that guy.

Eltargrim · 04-23-2011, 03:00 AM

Question 1:

Let x = volume of 9% solution
Let y = volume of 7% solution = 60 mL + x

All units are hereby neglected for typing convenience

2*60 + 9*x = 7*y
120 + 9x = 7(x + 60)
120 + 9x = 420 + 7x
-300 = -2x
300 = 2x
x = 150

The pharmacist should add 150 mL of the 9% solution

Question 4:

S_n = (n/2) * (a_1 + a_n)
S_18 = (18/2) * (a_1 + a_18)
252 = 9*(a_1 + 31)
252/9 - 31 = a_1
a_1 = -3

a_18 = a_1 + (18-1)*d
31 = -3 + 17d
34 = 17d
d = 2

Professor Smarmiarty · 04-23-2011, 04:31 AM

Last question solved by elimination:
20x-4+3y+9=120
20x+3y=115

3x+3-2x+2y=18
x+2y=15

20x+3y=115
x+2y=15

40x+6y=230
3x+6y=45
37x=185
X=5

5+2y=15
2y=10
Y=5
So answer A with X=5 y=5

But the answers make no sene to me. Either I did something really wrong or they hoping other people do something really wrong.

04-22-2011, 10:59 PM	#3
Eltargrim Fifty-Talents Haversham Join Date: Mar 2006 Location: FABULOUS Posts: 1,904	Question 2: \|y-7.8\| <= 1.5 y - 7.8 = +- 1.5 y = +-1.5 + 7.8 y = [6.3, 9.3] __________________ <Insert witticism here; get credit; ???; profit!>

04-22-2011, 11:56 PM	#4
Toastburner B Toasty has left the building Join Date: Jun 2004 Location: Hiding...because I don't want to die. Posts: 3,936	I did that wrong. The formula I was using was for dilutions, not mixing of two solutions. Sorry, my bad. I can help with question one, I think. I had to do similar problems with my studies. My teacher taught us a very simple formula for it: Concentration1 X Volume 1 = Concentration 2 X Volume 2 (C1XV1 = C2XV2) So, in the case of this problem you know the concentration and volume you have for one, but only the concentration for the other, so EDIT: I plugged in the wrong numbers. See my next post for the right numbers. 9 X V1 = 60 X 7 Simplified down to 9(V1) = 420 Just solve for V1: V1 = 420/9 V1 = 42.67 mL Just round it out to what decimal place you need. __________________ I came, I saw, I got team-killed. A lot. Last edited by Toastburner B; 04-23-2011 at 01:25 AM.

04-23-2011, 12:05 AM	#7
Krylo The Straightest Shota Join Date: Nov 2003 Location: It's a secret to everybody. Posts: 17,789	This is how I took all of my tests. My report cards were amazing. The answer to all of them is five. Except the last one. That is C. __________________ I am very tired.

04-23-2011, 03:00 AM	#9
Eltargrim Fifty-Talents Haversham Join Date: Mar 2006 Location: FABULOUS Posts: 1,904	Question 1: Let x = volume of 9% solution Let y = volume of 7% solution = 60 mL + x All units are hereby neglected for typing convenience 260 + 9x = 7y 120 + 9x = 7(x + 60) 120 + 9x = 420 + 7x -300 = -2x 300 = 2x x = 150 The pharmacist should add 150 mL of the 9% solution Question 4: S_n = (n/2) (a_1 + a_n) S_18 = (18/2) * (a_1 + a_18) 252 = 9(a_1 + 31) 252/9 - 31 = a_1 a_1 = -3 a_18 = a_1 + (18-1)d 31 = -3 + 17d 34 = 17d d = 2 __________________ <Insert witticism here; get credit; ???; profit!> Last edited by Eltargrim; 04-23-2011 at 03:04 AM.

04-22-2011, 09:47 PM	#2
TDK Sent to the cornfield Join Date: Jan 2008 Location: Reality Posts: 2,914	Well ln(e^9) is just 9. ln (natural log) is the same as log base e of the value. So log base e of e^9 is 9 because e^9 = e^9 ln and e pretty much always cancel out. So like, if you have something like 5 = e^x Solving for x, you would take ln of both sides. ln5 = ln(e^x) = x x = ln5 and vice versa. 5 = lnx solving for x, take e to the power of both sides e^5 = e^(lnx) = x x = e ^ 5

04-23-2011, 04:31 AM	#10
Professor Smarmiarty Sent to the cornfield Join Date: Mar 2007 Location: K-space Posts: 9,758	Last question solved by elimination: 20x-4+3y+9=120 20x+3y=115 3x+3-2x+2y=18 x+2y=15 20x+3y=115 x+2y=15 40x+6y=230 3x+6y=45 37x=185 X=5 5+2y=15 2y=10 Y=5 So answer A with X=5 y=5 But the answers make no sene to me. Either I did something really wrong or they hoping other people do something really wrong.