No, you are supposed to make the numerator into the diffrential of the denominator by adding/subtracting and multiplying/dividing terms, then proceed from there. (i.e. you need to make the numerator into a multiple of 2x+3, following which the fraction is in the form f'(x)/f(x) )
-
Hey Guest. Check out your NeoGAF Wrapped 2025 results here!
The Math Help Thread
- Thread starter -COOLIO-
- Start date
- Status
No, you are supposed to make the numerator into the diffrential of the denominator by adding/subtracting and multiplying/dividing terms, then proceed from there. (i.e. you need to make the numerator into a multiple of 2x+3, following which the fraction is in the form f'(x)/f(x) )
BlueLiquid
Member
First of all, yeah, wow, that's a mess of an integral to do by hand.
What they did was x + 6 = x + 12/2 = x + 3/2 + 9/2, so
(x+6)/(x^2 + 3x + 9) = (x + 3/2)/(x^2+3x+9) + 9/2/(x^2+3x+9)
On the (x + 3/2)/(x^2+3x+9) on the right, you can now perform a "u" substitution with u = x^2+3x+9. The second one is more involved. You need to complete the square on the denominator which gives you an expression of the form 1/(u^2 + a^2), with u = x^2 + 3/2 and a = 3Sqrt(3)/2 which is where the messy arctan stuff is coming from.
What they did was x + 6 = x + 12/2 = x + 3/2 + 9/2, so
(x+6)/(x^2 + 3x + 9) = (x + 3/2)/(x^2+3x+9) + 9/2/(x^2+3x+9)
On the (x + 3/2)/(x^2+3x+9) on the right, you can now perform a "u" substitution with u = x^2+3x+9. The second one is more involved. You need to complete the square on the denominator which gives you an expression of the form 1/(u^2 + a^2), with u = x^2 + 3/2 and a = 3Sqrt(3)/2 which is where the messy arctan stuff is coming from.
cpp_is_king
Member
Yea that answer looks correct, just seemed more likely that you had copied it down wrong, because usually "problem" integrals work out nicely and it was pretty "close" to working out with a nice u substitution.
triplestation
Member
thanks for explaining!
id still have no clue what to do if i didnt see this
most of it makes sense now except for the part that involves completing the square.. this problem is not something we learned at all so for it to be on my homework is kinda nuts
if it shows up on an exam im doomed lol
Well, you learnt it now, so you will be well prepared.
These 2 methods are actually fairly common. I'd suggest you practice similar type of questions until you can do it easily.
BlueLiquid
Member
So this integral came up in my last exam half-way into solving an ODE by variation of parameters.
Wtf, how did he expect us to solve that?
That doesn't have an elementary antiderivative so I really don't know.
triplestation
Member
Biggest-Geek-Ever
Member
It's not uncommon in an intro ODE course to throw in problems where you leave your answer with an unevaluated integral. Probably the most common example is ∫ e^(-x^2) dx.
So this integral came up in my last exam half-way into solving an ODE by variation of parameters.
Wtf, how did he expect us to solve that?
With your problem, you can apply integrate once by letting u = x^2, dv = e^x cos(e^x) dx, du = 2x dx, and v = sin(e^x). So
∫ x^2 e^x cos(e^x) dx = x^2 sin(e^x) -2 ∫ x sin(e^x) dx
Unfortunately, integration by parts fails here, since choosing u = x will result in us having to find the antiderivative of sin(e^x) (which is NOT elementary. It actually become the sine integral after a substitution), and choosing u = sin(e^x) just leads us back to where we started.
It may be possible to express this answer in the form of an infinite series that is meaningful, but I highly doubt that's what the instructor expected. So I would say the RHS of that equality is as far as you can go.
So, normally i don't ask for help but somehow i am "stucked" with this subtask.
I've got this function:
on z=0
which looks like this (parabola)
the "chamber" goes linear until the depth of z=-16 where it hits the minimum of 0.
which looks like a half "elipse cone". I need to calculate the 3-D domain of it.
don't have a problem integrating the parabola.
but somehow i don't know, how to "add" the information of the depth into it (i kinda know, that i do need a double integral). Someone got an idea?
I've got this function:
on z=0
which looks like this (parabola)
the "chamber" goes linear until the depth of z=-16 where it hits the minimum of 0.
which looks like a half "elipse cone". I need to calculate the 3-D domain of it.
don't have a problem integrating the parabola.
but somehow i don't know, how to "add" the information of the depth into it (i kinda know, that i do need a double integral). Someone got an idea?
eot
Banned
So this integral came up in my last exam half-way into solving an ODE by variation of parameters.
Wtf, how did he expect us to solve that?
If I ended up with an integral like that on an exam I'd assume that I made a mistake somewhere along the way.
FortuneFaded
Member
So, normally i don't ask for help but somehow i am "stucked" with this subtask.
I've got this function:
on z=0
which looks like this (parabola)
the "chamber" goes linear until the depth of z=-16 where it hits the minimum of 0.
which looks like a half "elipse cone". I need to calculate the 3-D domain of it.
don't have a problem integrating the parabola.
but somehow i don't know, how to "add" the information of the depth into it (i kinda know, that i do need a double integral). Someone got an idea?
I have two ideas, but haven't tested them out.
1. Linearity implies self-similarity.
Parametrize the parabola in terms of z, so that it is similar to y = -x^2/8 + 16 at z = 0 and so that it "vanishes" at z = -16. Then, do a double integral to find the volume. Note, the parabola vanishes in the sense that it is below the x-axis.
You can verify if your parametrization is correct by checking the x- and y-intercepts. Since the intercepts are (+/- sqrt(128), 0) and (0, 16) for z = 0 and the parabola vanishes at z = -16, the intercepts at z = -8 (i.e. half-way) should be (+/- sqrt(128)/2, 0) and (0, 8).
2. Linearity implies a quadratic relation for area.
Think of basic shapes like squares or triangles. You know that if you multiply all the sides by x, the area gets multiplied by x^2.
Since you know the area under the parabola at z = 0, you could add all the areas from z = -16 to z = 0 (i.e. an integral).
MisterLuffy
Member
I need help with homework using R studio. Can I pm someone the problem and show you what I have?
Stumpokapow
listen to the mad man
post it in here, use pastebin to copy/paste your code if it's too long to post
MisterLuffy
Member
I just need help on part a and b. I'm not getting any output and want to see if I'm doing this problem right. I'm still not sure if I have to use the 4 distributions or pick either one to answer part a and b. And lets say if I have to use 4 of them, I'm not sure if I have to implement them in the for loop or outside of it.
http://pastie.org/private/yn5bj6sccdvhxfumuh5kcg
Stumpokapow
listen to the mad man
You're being asked to basically simulate the properties of these distributions that you know analytically to be true.
First note: Not sure why poisson distribution is being parameterized with mu=2 when poisson distributions are usually charactered by the parameter lambda, which is also the mean (expected value) of the random variable. Not aware of what mu would mean in this context. But I'll assume mu here means lambda. That seems non-standard to me. Anyway.
The help you need is programming help, not math help. Nothing tough is going on statistically here. Just think through your code. What does each line mean? What am I trying to do here? You should probably brush up on what a for loop does, what it's iterating over, how vectors of data are stored in R, what rep does, etc.
Here is some of your code, with comments added by me.
Do you see what's going wrong in this snippet?
Here's some code that generates the data you want. You can do the analysis of the data yourself.
First note: Not sure why poisson distribution is being parameterized with mu=2 when poisson distributions are usually charactered by the parameter lambda, which is also the mean (expected value) of the random variable. Not aware of what mu would mean in this context. But I'll assume mu here means lambda. That seems non-standard to me. Anyway.
The help you need is programming help, not math help. Nothing tough is going on statistically here. Just think through your code. What does each line mean? What am I trying to do here? You should probably brush up on what a for loop does, what it's iterating over, how vectors of data are stored in R, what rep does, etc.
Here is some of your code, with comments added by me.
Code:
n=5
mu=(0+5)/2 # okay, so mu = 2.5? Why are we storing 2.5 in this? Is this the analytic solution for the mean of a
# uniform random variable? Why is it being used as the parameter input for a poisson distribution below?
X = 500 # X is now a scalar of the number 500
X = rep(1,500) # X is now a vector with 500 1s <-- why did we previously define X to be the scalar 500?
for(i in X) # Run i a series of times, each time loading another value from the vector X.
{
# What do you think would happen if you ran print(i) here? What would it print? Try it out.
X[i] = mean(runif(n,0,5)) # This stores the mean of n draws from a uniform range 0-5 into the index i of the vector X
# What value is stored in i right now? So what is being overwritten in your vector each time?
rpois(n,mu) # This generates n values from a poisson distribution with lambda=mu (mu=2.5) and stores them nowhere--
# because you're inside a loop, R does not return these values and they are totally ignored
}Do you see what's going wrong in this snippet?
Here's some code that generates the data you want. You can do the analysis of the data yourself.
Code:
# The function c() in R concatenates scalars or vectors into a vector and takes as many argument as you want.
for(i in c(5,50)) # First run all code in this loop with i = 5; then with i=50
{
# Create empty vectors of numeric data to store each of our 500 sample means
unifData = numeric(500)
binData = numeric(500)
expData = numeric(500)
poisData = numeric(500)
# Recall that : is the range operator in R, so 1:500 will give you vector range of integers from 1 to 500
for(j in 1:500) # Run the code in this loop 500 times, starting with j=1 and moving 1 by 1 to j=500
{
unifData[j] = mean(runif(i,0,5)) # sample mean of i draws from uniform dist [0,5] is stored in index j of the vector
binData[j] = mean(rbinom(i,15,0.2)) # sample mean i draws from binom dist, n=15, p=0.2 is stored in index j of the vector
expData[j] = mean(rexp(i,5)) # sample mean of i draws from exp dist, lambda=5, is stored in index j of the vector
poisData[j] = mean(rpois(i,2)) # sample mean of i draws from pois dist, (mu? again, typically lambda)=2, is stored in index j of the vector
}
# Okay, so now each of my vectors contains a series of 500 sample means
print(paste("With i =",i," the results I get are:"))
print(paste("Mean of unifData: ",mean(unifData)))
print(paste("Mean of binfData: ",mean(binData)))
print(paste("Mean of expData: ",mean(expData)))
print(paste("Mean of poisData: ",mean(poisData)))
# Probably put your code to calculate variances of the samples here
}I'm not sure if I am doing this counting problem correctly. I have a string of English letters of length n. I have to create a recurrence relation that counts the number of strings of length n that if it contains both an x and a y, then all the x's must come before the y's. This includes strings that don't contain an x or don't contain a y or neither an x or y. I'm not really looking for the answer, but I was curious if somebody could point out if I am wrong and where the issue is with my idea.
I think:
a
= 25 * a(n-1) + 25^(n-1)
I am worried that I am double-counting some strings though.
I think:
a
= 25 * a(n-1) + 25^(n-1)I am worried that I am double-counting some strings though.
Stumpokapow
listen to the mad man
I'm not sure if I am doing this counting problem correctly. I have a string of English letters of length n. I have to create a recurrence relation that counts the number of strings of length n that if it contains both an x and a y, then all the x's must come before the y's. This includes strings that don't contain an x or don't contain a y or neither an x or y. I'm not really looking for the answer, but I was curious if somebody could point out if I am wrong and where the issue is with my idea.
I think:
a
I am worried that I am double-counting some strings though.
Edit: I originally misread the problem bigtime. This is an updated answer
You should always check answers by manual verification when there exists some case you can manually verify.
Consider the simple case where n=2, solve what your recurrence relation is telling you
a(2) = 25*a(1) + 25
a(1) = 25*a(0) + 1
a(0) = ???
???
Okay, a reasonable base case is a(1) = 26, since we can trivially see that any string of length n=1 satisfies your requirement.
a(2) = 25*26 + 25 = 675. Are there 675 strings of length 2 excluding the substring YX? The only string of length n=2 with YX in it is YX, so there are 675 remaining substrings that work. So far so good.
a(3) = 25*675 + 625 = 17,500
Okay, let's solve a(3) empirically:
26^3 = 17,576
Invalid strings have the form:
YX_ <-- 26 possible strings including YXX
Y_X <-- 26 possible strings including YXX and YYX
_YX <-- 26 possible strings including YYX
a(3) = 26^3 - (26+26+26-2) = 17,500
So far so good.
I think you caught that the string can be a string like abc or axb or ayb, but not ayx. It could also be xby. The y does not have to come immediately before the x, it just must be before the x if there is an x and y.
Also, my base case is that a(0) = 1.
Stumpokapow
listen to the mad man
I completely misread the problem and though it was a count of strings containing both X and Y in that order. I missed that AAA was valid or AAX or AAY. I updated my analysis and your recurrence relation seems correct to me. My apologies if my initial post was confusing.
I don't think this won't work, because while it correctly seeds a(1), it is not the case that there is a zero-length string that meets your requirements, is there? Like, how many zero-length strings are there? How many zero-length strings contain Q? How many zero-length strings don't contain J? These are nonsense questions, right? So a(0) would have to be 0 if it's anything.
Your base case would have to be a(1) = 26, no? Or the double base case a(0) = 0, a(1) = 26. Double base cases are okay--the function f
where n is the nth fibonacci number can be defined recursively but requires two base cases. This is the prototypical example we use for recursion generally, actually 
The empty string. There is exactly 1 string of length 0 that follows the given rule, and that string is "".I completely misread the problem and though it was a count of strings containing both X and Y in that order. I missed that AAA was valid or AAX or AAY. I updated my analysis and your recurrence relation seems correct to me.
I don't think this won't work, because while it correctly seeds a(1), it is not the case that there is a zero-length string that meets your requirements, is there? Like, how many zero-length strings are there? How many zero-length strings contain Q? How many zero-length strings don't contain J? These are nonsense questions, right? So a(0) would have to be 0 if it's anything.
Your base case would have to be a(1) = 26, no? Or the double base case a(0) = 0, a(1) = 26. Double base cases are okay--the function f
Glad to see that my idea works so far, but I guess I am worried that perhaps it falls apart at a(4) or a(5). I guess I should go back and figure out how the recursion is happening exactly. I feel like I've guessed something that works at a(2), and also works for a(3), but I didn't really build it in a recursive way.
Stumpokapow
listen to the mad man
Heh, this seems to be a philosophical disagreement.
Beyond that, you are correct. I just verified it by constructing the recursion myself.
Background and establishing our strategy:
Let c
be the number of strings of length n. c is trivially 26^n, correct? We could also define c recursively as: 26 * c(n-1) -- i.e. any string of length n-1 prepended by any letter. We could also partition the recursive definition as such: 25 * c(n-1) + 1 * c(n-1) -- i.e. any string of length n-1 prepended by any letter except Y plus any string of length n-1 prepended by Y--the definition of a partition in either probability of combinatorics implies that the partition sums to the entire space of interest and that the elements of the partition are mutually exclusive. So it is clear that there is no double-counting here.Problem:
Let b
be the number of strings of length n excluding the letter X: trivially 25^n.Let a
be those strings that meet your requirement. a includes two cases:- Every string of length n-1 that meets your requirement prepended by any letter except Y. 25 * a(n-1)
- Every string of length n-1 that do not contain an X, prepended by the letter Y. 1 * b(n-1)
There is obviously no double-counting as we know without even examining anything else that the first character of strings from each part of the partition differ--by definition the second part of the partition starts with Y and the first does not.
a
= 25*a(n-1) + b(n-1)a
= 25*a(n-1) + 25^(n-1)No double-counting, you're correct. This will hold.
Edit: Just did a pass for argumentative and numeric clarity. Done editing this post.
spelltropy
Member
So i'm trying to revise for this statistics module and am looking at an example of "Dutch books". I'm a little confused how the Stakes column has been arrived at. The premise of the problem is you have £100 available to bet, and this is the outcome in the example:
Any ideas on how the stake column is arrived at?
(also thanks a lot kgtrep and Therion for your help a few days ago, sorry for not replying earlier!)
Any ideas on how the stake column is arrived at?
(also thanks a lot kgtrep and Therion for your help a few days ago, sorry for not replying earlier!)
Stumpokapow
listen to the mad man
So i'm trying to revise for this statistics module and am looking at an example of "Dutch books". I'm a little confused how the Stakes column has been arrived at. The premise of the problem is you have £100 available to bet, and this is the outcome in the example:
Any ideas on how the stake column is arrived at?
(also thanks a lot kgtrep and Therion for your help a few days ago, sorry for not replying earlier!)
First, observe that the S/P (how much you'd get paid out if you win) is the same for each bet. What does the bookie pay? Well he pays the left number in the odds field times your bet. And he gives you back your original bet. (i.e. a 1:1 bet gives you 1*your bet + your bet). Hence the bookie pays (Stake * (Odds+1))--1 to account for you getting your original bet back.
i.e. as we see in the S/P
14.38*8 = 115.04
19.17*6 = 115.02
9.58*12 = 114.96
7.19*16 = 115.04
Recall your total bet adds to 100 (bets on horses on the same odds should be the same bets so we treat those bets as duplicates of the earlier bet):
X1+X2+X3+X4+X3+X2+X4+X5 = 100
Simplify:
X1+2*X2+2*X3+2*X4+X5 = 100
Bet payout should be the same irrespective of the horse that wins--as it is in the S/P column, ignore the rounding errors:
8*X1 = 6*X2
X2 = 4/3 * X1
8*X1 = 12*X3
X3 = 2/3 * X1
8*X1 = 11 * X4
X4 = 8/11 * X1
8*X1 = 16 * X5
X5 = 1/2 * X1
Substitute in multiples of X1 for all other variables:
X1 + 2*(4/3 *X1) + 2*(2/3*X1) + 2*(8/11*X1) + (1/2*X1) = 100
X1 = 14.37908...
You should know how to substitute X1 back into X2, X3, X4, X5 to derive those. This could also be done with linear algebra.
MisterLuffy
Member
Thank you so much. I would have never thought of doing this way.
To update the folks here, I'm almost finished with my slides on infinity. I learned a lot since last week, and recommend the book "To Infinity and Beyond" by Maor if you want to learn more about infinity.
Here's a really nice proof that the number of real numbers between 0 and 1 equals the number of all real numbers. I think we are usually taught to use the arctangent function to show this, and think that this is far more intuitive.
Here's a really nice proof that the number of real numbers between 0 and 1 equals the number of all real numbers. I think we are usually taught to use the arctangent function to show this, and think that this is far more intuitive.
mariachi507
Member
Calc 2
I'm having issues with a couple of problems relating to Hydrostatic Pressure/Force. Any help would be appreciated.
I believe my professor is using calculus to pursue a passion of writing bad science fiction.
1. An unidentified space craft dives 1332 ft to the bottom of Lake Minnetonka. The cockpit window is the shape of a circle with a radius of 3 ft, which is at an angle of 45 degrees from the vertical and is centered 4 ft from the bottom of the space craft. What is the pressure against this window?
2. In the spacecraft, the two Vulcanewoks decide to flip a coin, which is a square measuring 3 gronbecks by 3 gronbecks (1 gronbeck = .2987 in). An equilateral triangle with sides measuring 1 gronbeck has been cut out of the coin. Think of a square with an equilateral triangle cut out in the bottom right corner. Unable to flip the coin the Vulcanewoks decide instead to balance it with a stick. At what point of coin must the stick be to balance the coin?
I can't believe that second question is real, it's also a bonus question while the first one is a regular one. Once again, any help is appreciated.
I'm having issues with a couple of problems relating to Hydrostatic Pressure/Force. Any help would be appreciated.
I believe my professor is using calculus to pursue a passion of writing bad science fiction.
1. An unidentified space craft dives 1332 ft to the bottom of Lake Minnetonka. The cockpit window is the shape of a circle with a radius of 3 ft, which is at an angle of 45 degrees from the vertical and is centered 4 ft from the bottom of the space craft. What is the pressure against this window?
2. In the spacecraft, the two Vulcanewoks decide to flip a coin, which is a square measuring 3 gronbecks by 3 gronbecks (1 gronbeck = .2987 in). An equilateral triangle with sides measuring 1 gronbeck has been cut out of the coin. Think of a square with an equilateral triangle cut out in the bottom right corner. Unable to flip the coin the Vulcanewoks decide instead to balance it with a stick. At what point of coin must the stick be to balance the coin?
I can't believe that second question is real, it's also a bonus question while the first one is a regular one. Once again, any help is appreciated.
triplestation
Member
i dont know any tan angle that returns infinity, im not crazy right?
RIGHT?
triplestation
Member
i would think the answer would either be pi/2 or -pi/2
but aren't the angles limited to be between pi/2 and -pi/2 for arctan?
It's a limit. As b gets larger and larger, arctan(b^3/3) will get closer and closer to pi/2 from the left.
arctan(infinity) doesn't make sense, but this limit does.
triplestation
Member
thanks, it makes a bit more sense now ><
Stumpokapow
listen to the mad man
The visuals are great too. Sparse but very pretty,
Stumpokapow
listen to the mad man
I think pretty much anyone is OK with pretty much anyone asking anything, although I have no idea if we have any physical chemists here that would answer
dr3upmushroom
Banned
On differential equations (ch 9.1 Steward), I'm on the first question and already confused... I have to verify that y=-tcost-t is a solution of the initial-value problem,
t(dy/dt)=y + (t^2)sint
So what I have written down in my notes is IVP=DE+IC
I've been struggling with Calc II this semester and feel like I've actually regressed in my understanding of Calculus.
t(dy/dt)=y + (t^2)sint
So what I have written down in my notes is IVP=DE+IC
I've been struggling with Calc II this semester and feel like I've actually regressed in my understanding of Calculus.
Calc 2
I'm having issues with a couple of problems relating to Hydrostatic Pressure/Force. Any help would be appreciated.
I believe my professor is using calculus to pursue a passion of writing bad science fiction.
1. An unidentified space craft dives 1332 ft to the bottom of Lake Minnetonka. The cockpit window is the shape of a circle with a radius of 3 ft, which is at an angle of 45 degrees from the vertical and is centered 4 ft from the bottom of the space craft. What is the pressure against this window?
2. In the spacecraft, the two Vulcanewoks decide to flip a coin, which is a square measuring 3 gronbecks by 3 gronbecks (1 gronbeck = .2987 in). An equilateral triangle with sides measuring 1 gronbeck has been cut out of the coin. Think of a square with an equilateral triangle cut out in the bottom right corner. Unable to flip the coin the Vulcanewoks decide instead to balance it with a stick. At what point of coin must the stick be to balance the coin?
I can't believe that second question is real, it's also a bonus question while the first one is a regular one. Once again, any help is appreciated.
Just a general note: always come up with a drawing for the problem before you do much else.
For problem 1, the pressure at a point in water is determined only by the depth you at (i.e., the distance from the surface). With the circle at a pi/4 angle, you need to find an expression for slices of the circle at the same depth, and then integrate along those slices.
For problem 2, whenever you are trying to find the center-of-mass of an object with a complicated geometry, it is always best to see if you can think of the object in terms of simpler objects where the center-of-mass is obvious. You can relate the center-of-mass of the square with an equilateral triangle cut-out to the CM of a complete square and the CM of the triangle (at the location of the cutout) separately. Assuming the mass distribution is uniform this shouldn't require any integration really.
Hope some of that gives you ideas of where to start.
The definition of a solution to a Differential Equation is that when inserted into the Differential Equation is maintains the equality - i.e., the RHS equals the LHS of the equation.
t(dy/dt)=y + (t^2)sint is your DE. that equation from your notes isn't an equation of any sort but looks like your professor's shorthand way of defining an inital value problem. I would recommend taking more detailed notes though
triplestation
Member
so i just found out that e^2x can be written as (e^x)^2 and its bothering me because it feels like it makes no sense
is this just with e?
is this just with e?
Omega Ultimus
Member
Just in case you're still stuck, here's what's key to solving this problem (and others like it):
You have dy/dt, the derivative of y with respect to t [dy/dt = f'(t)], and y, a function of t. Do you see a/the connection?
Read and memorize this.
Epsilon-delta
Banned
I would do it this way:
take the derivative of y, which is dy/dt
y = -tcost-t
dy/dt = -cost + tsint -1
Now plug in the expressions for dy/dt and y into the original equation:
t(-cost + tsint -1) = -tcost-t + (t^2)sint
Distribute LHS:
-tcost + (t^2)sint-t = -tcost-t +(t^2)sint
Subtract (t^2)sint from both sides to get:
-tcost-t = -tcost-t -> verified
I think pretty much anyone is OK with pretty much anyone asking anything, although I have no idea if we have any physical chemists here that would answer
True haha. I guess i'll give it a try.
Sodium Chloride has an enthalpy of solution of dHsoln = 4.25 kj/mol. 10.0 g of NaCl is dissolved in 100.0 g H2O at 298 K. Determine the following:
a.) The final temperature of the solution
b.) contributions from enthalpy and entropy to the solubility of NaCl in water.
c.) Calculate dGmix for NaCl at the final temperature
Assume the heat capacity of the solution is equal to the heat capacity of water.
Given:
S[NaCl(s)] = 72.13 j/molk
S[NaCl(aq)] =115.5 j/molk
Cp[H2O(l)] = 75.291 j/molk
MW (NaCl) = 58.44 g/mol
Any help or hints would be greatly appreciated!
InvertedComposer
Banned
Is there a key to being good at calculus diff/inte?
As in how do you study? Traditionally I always used flashcards for the great majority of classes but clearly it's not applicable in math. So how does one go about it? o.o
Probably more of a "how the heck do you even do this and master it" type of question than actual math. Sorry ( " . . )
As in how do you study? Traditionally I always used flashcards for the great majority of classes but clearly it's not applicable in math. So how does one go about it? o.o
Probably more of a "how the heck do you even do this and master it" type of question than actual math. Sorry ( " . . )
When I took calculus, the best way I could really study for tests was just keep doing problems. Experiencing different ways to solve a problem is really the best way you can prepare in my experience. Also understanding what the equation is trying to tell you, and what it gives you helps with word problems (and especially those discs and sphere problems lol)
Find "shortcuts". Like, how could I make my methods faster but still being right. Just by doing that helps you analyze and fully understand each concepts, because you force yourself to understand why a particular concept works. It might lead you to multiple routes but it's OK. Just explore.
For example, using derivatives to find highest/lowest points/peaks of a function. Why does setting up the derivative of a function to zero give me those peaks? Asking yourself those things help you understand them fully, and when you understand them fully, you can easily solve for any kind of problem, given that you don't get stuck on a mindset.
Hope that makes sense lol
Thanks, I'm looking forward to presenting it on Monday!
I didn't use your 0.9... = 1 example, but because you had brought it up, I got to understand better how interweaving two decimal numbers to show that |R| = |R^2| works.
mariachi507
Member
Thanks for the assistance.
spelltropy
Member
- Status