Let's make a homework help thread!

I'm trying to turn a laplace transform into an equation using heaviside functions.

So, we have f(s) = (e^-s)/(s^2)-2(e^-2s)/(s^2)+4(e^-5s)/s-3(e^-8s)/(s^2)

I know that each e^as is going to be a different segment of the step function, and I know that the +4 term is the only term that's not going to be continuous because it has an s in the denominator instead of an s^2.

However whenever I try to do this and graph it doesn't turn out right.

I have on one hand f(t)=tH(t-1)-2tH(t-2)+4H(t-5)-3tH(t-8) or

f(t)=(t-1)H(t-1)-2(t-2)H(t-2)+4H(t-5)-3(t-8)H(t-8)

I'm not entirely sure which to use, but whenever I try to make piecewise functions of either of them the first two terms are not continuous, which I know they should be. Help?

Um. I need to figure out which of these series converge. And how do I figure that out?

All of them have this prefix. Sigma infinity, n=1

• 1. (4/3)^n
• 2. (cos(n Pi))/n
• 3. 1/n

I know for sure 3 doesn't converge.

1 is just a geometric series, so you have to check that the value of r (from the a*r^n-1) is less than 1.

Not really sure how to explain 2 without giving it all away, but what are the possible values of cos(n*pi)? Remember how cosine is sinusoidal, so it'll repeat its values...Try writing the first few out (e.g. cos(pi), cos(2pi), cos(3pi), etc..), if that previous sentence was confusing. From here, hopefully your textbook mentioned the alternating series test?

Ah, I see. Thank you.

For the second one, hmm, getting -1, 1, and -1 here. And yeah, it does mention the alternating series test. Will work on it later, but thank you.

edited 28th Mar '12 9:09:58 PM by Marioguy128

Normally I'm good at math homework, but it turns out I'm really shitty at word problems and the only one of my friends who knows how to do this is not one I want to ask.

I know that the answer is 195 min, but I have no idea how to get there.

Let t be the number of 15-minute time intervals. At t=0, you have 20 bacteria. At t=1, you have 40, or 20*2¹. At t=2, 80, or 20*2². In general, you have the number of bacteria at 20*2^t. So you're looking for the value of t where 20*2^t=163840.

From there, it's either logarithms (if you have a calculator handy), or getting the powers of 2 by hand.

edited 11th Apr '12 4:30:55 AM by KylerThatch

Thanks! My brain must have been really shot, because once I retried the problem, I got it in, like, a minute XD

edited 12th Apr '12 8:18:27 PM by czhang

Ergh, I can never win in my neverending battle with chemistry. Two problems I'm having and I get the feeling I'm using the wrong methods/constants.

For 1) If 23.2g of PCl ₅ decompose, what is the volume of Cl ₂ produced at STP? I'm assuming stoichiometry is at play here so am I doing the right thing?

23.3g PCl5 x 1mol PCl5/207.9g PCL5 x 5mol Cl2/2mol PCl5 x 22.4L Cl2/1M Cl2

The answer is supposed to be 2.49L Cl₂

For 2) In the reaction between nitrogen gas and hydrogen gas to form ammonia (NH₃), how many grams of nitrogen are required to react with 1500 mL of hydrogen if the pressure is 101.3 kPa and the temperature 0C? I set it up as:

1500mL H2 x 1M H2/1000mL H2 x 2mol N2/3mol H2 x 28.0g N2/1mol N2

The answer is supposed to be .63gN₂

As usual, much appreciation for anyone that can help.

edited 12th Apr '12 8:40:03 PM by Rivux

Hint: using the superscript and subscript coding makes your equations much easier to read. CTRL+C and V if you don't have time to write it out.

23.3g P Cl 5 x 1mol P Cl 5/207.9g PCL 5 This gives us total mols of reactant, so far so good.

Ans x 5mol Cl2/2mol P Cl 5 This gives us total number of mols of result products, still good.

Ans x 22.4L Cl2/1M Cl2 This is multiplying total number of mols of gas by the volumetric constant, all good if your numbers are good.

2) So the gas is at STP, right or was that 27 C? Bah, I assume it is because that makes the problem easier.

1500mL H2 x 1M H2/1000mL H2 I'm pretty sure this is wrong. You should be using the same gas constant as above since all gases have the same Vol/mol constant. However, this gives you total molage based on volume, which is correct.

Ans x 2mol N2/3mol H2 These numbers are running together for me, add more spaces please.

Edit: thinking on it, you don't really need to find the exact number of mols H2 to convert. You have 3 hydrogens to one nitrogen, so we know how many mL of nitrogen you have, and you can just back track to the number of grams you have by jumping to mols.

edited 13th Apr '12 4:14:04 AM by Deboss

Did the above post make sense?

I'm sorry, but I couldn't comprehend that. (I'm only in College Prep Chemistry with a B-!)

We went over it in class yesterday, though, so there's that.

1 was correct.

2 should have been something like .5L of N2 divided by 22.5 L/mol multiplied by mass of N2 molecule.

I'm taking a class in public speaking this term (on account of it is a quality that is scarce and in high demand for engineers!), and we're being required to give three major speeches between now and the end of the class - one expository, one persuasive (i.e. attempt to persuade an hostile audience of the view you describe), and one 'protest' (i.e. attempt to persuade a favourable audience to take action). Tricky, because all three are required to share a topic, which should be a problematic/controversial issue with multiple possible approaches.

I've narrowed my topics down to 'inflicted insight' and 'social stigma against sufferers of mental illness'. Which one should I use? (And, for the second, what's a tangible issue to focus on?)

For the second, you could perhaps use Alzheimer's or depression?

It's not so much a matter of 'focus on a specific condition' as 'focus on a specific, measurable problem to bring to my audience's attention'. Like the misuse of psychiatric terms like 'psycho' or 'retard' as pejoratives in a way that constitutes hate speech, or increased medical insurance rates for sufferers of mental illness.

Well, we're wrapping up the semester for Calc II. We have our last exam on Friday, and all I have to get on it is Taylor series and trig substitution to get a perfect cumulative grade. The Taylor series are no problem, but trig sub has consistently eluded me all semester. Anyone have any tips/advice?

If you see a square root with (1 - stuff²) inside it, you should recognize that as some kind of circle, so think of sin²+cos²=1. Set stuff = sin u or cos u to knock out the root, convert the dx and any other x's accordingly, and see what's left.

If you have (1 + stuff²) in the root, you usually want to let stuff = sinh u so you can exploit cosh²-sinh²=1. Be ready to solve whatever's left via conversion to something else, because hyperbolics suck that way.

In either case, make sure you convert everything back to the original variable at the end.

edited 18th Apr '12 9:32:53 PM by Pykrete

Hey, uh, anybody know how to make the X or Y axis in Microsoft Excel or Word 2010 start from zero? 'cause I have to input rather small numbers, and the axes keep shifting so that all the values are spaced evenly across the graph, which is not what I want. All the info I can find online only work for much older versions of Excel or Word and can't be used anymore.

If you can select the axis, right-click and select 'Format Axis'. There should be an option to 'select intercept', which you want to set to zero.

Just did it, it works for the y-axis, but not for the x-axis.

Edit: Solved it, just had to add an extra bit in the info columns themselves where 0 = 0. Derp.

edited 22nd Apr '12 8:16:53 AM by Exploder

I have a question that should be easy. How do you find the area of a triangle using apothem/radius?

Well, that gives you a right triangle and two sides. Just use the pythagorean equation to derive the base of the main triangle and use the apothem as the height.

sorry let me rephrase that. How do you find the area of a triangle using ONLY the apothem/radius?

Just to clarify, you are given a measurement for the apothem and a measurement for the radius?

Because that was what I was assuming when I made my last post.

No, actually, there are 2 problems, one gives only the apothem,the other gives only radius. I should have specified that.

edited 22nd Apr '12 10:33:20 AM by Somedude1337