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[Partial Gamification]

Mike Dip, I didn't even bother to think about other ways to setup the problem; good show!

Spoiler

I will probably cover "Cecilia" and refer to you factoring cardioids at somepoint in the future

I hope that this isn't adding to any confusion; or at least if so, the questions surrounding this problem are better understood.

 

[Anth0ny]

Okay Math GAF. I need you bad. (this is the thread for Econ problems, right? lol...)

My Econ prof uploaded a sample midterm for my midterm this week. He says if you can get these questions you should be okay for the test. Only one problem...

He didn't provide solutions. Classic!

It doesn't seem that difficult, but I'm fucking lost without solutions.

Here are the questions:

Any help would be GREATLY appreciated. Thanks in advance!

 

[dinazimmerman]

Anth0ny, those aren't math problems. You need to have taken Economics 101 in order to know how to solve these. But I'll start solving them anyway. I've only done the first 2. I'm kinda rusty on this 101 stuff. I'll finish up the rest when I get home.

1.

Recall that in the long-run, P = min(LRAC(q)). We find the quantity that minimizes LRAC(q), which we denote by q*, by taking the derivative of LRAC(q) and setting it to zero:

-5 + 2q* = 0 => q* = 2.5.

q* is how much each firm produces in the long-run. We plug in q* into the expression for LRAC:

LRAC(q*) = 50 - 5q* + q*^2 = 50 - 5(2.5) + (2.5)^2 = 43.75.

Thus, P = min(LRAC(q)) = LRAC(q*) = 43.75. We now plug this into the market demand function:

Q = 1000 - 4P = 1000 - 4(43.75) = 825.

Finally, we divide Q by q* to determine the number of firms:

825/2.5 = 330.

2.

Recall that firm sets P = MC as long as P >= AVC. When P < AVC, the firm produces nothing.

The derivative of TC = 2q = MC. And AVC = q^2 / q = q.

Thus, P = 2q when P >= q, but that's true for all non-negative q so we don't have to worry about shutdown.

Q = 1000q, so we just need to solve for q and p.

To do this, you could draw the market demand curve Q = 600,000 - 100P and the market supply curve Q = 1000q = 1000(P/2), and find the intersection. Doing the algebra is simpler. Just set 600,000 - 100 P = Q = 1000(P/2), and solve for P.

600,000 - 100P = 500P
=> 600,000 = 600P
=> P = 1000
=> Q = 500,000
=> q = Q/1000 = 500.

 

[dinazimmerman]

Okay, here's 3 and 4. I'll do the rest if I have time.

3.

Again, AVC = antiderivative of SMC divided by q = 4 + q/2 < SMC, so you don't have to worry about shutdown. The firm's supply curve is equal to its marginal cost curve.

First, we solve for the equilibrium sans tax. We are given that P = 4 + q, so q = P - 4. Thus, Q = 1000q = 1000(P-4). We are also given that P = 10 - 0.002Q, so 500(P-10) = Q. We set these equal to each other:

1000(P-4)=500(P-10)
=> 2P - 8 = P - 10
=> 3P = 18
=> P = 6.
=> Q = 2000.

Now, we find the consumer surplus. This is equal to the area under the demand curve and above the price. Since this is a triangle, it's easy to calculate:

(1/2)(10-6)(2000) = 4000.

Now, we find the producer surplus. This is equal to the area under the price and above the supply curve. This is equal to:

(1/2)(6-4)(2000) = 2000.

So sans tax, total surplus is equal to 6000.

Now, with a $1 excise tax, we'll assume firms pay it. If we assume consumers pay it, we get the same results. I leave this as an exercise. Let P_s denote the price firms get and P_d equal the price consumers pay. P_s = P_d - 1. So, P_s = 4 + Q/1000 or P_d = 5 + Q/1000. The market demand curve is P_d = 10 - Q/500.

Thus, 5 + Q/1000 = 10 - Q/500 or Q = 5000/3. This implies that P_d = 20/3 and P_s = 17/3. Notice that 20/3 > 6 and 17/3 < 6.

Consumer surplus is equal to:

(1/2)(10-20/3)(5000/3) = (1/2)(10/3)(5000/3) = 25,000/9 < 4000

Producer surplus is equal to:

(1/2)(17/3-4)(5000/3) = (1/2)(5/3)(5000/3) = 25,000/18 < 2000

Tax revenue is equal to 5000/3.

Add them up to get:

(50,000 + 25,000 + 30,0000) / 18 = 5,833.33

The deadweight loss is equal to 6000 - 5,833.33 = 166.67.

4.

The perfect competition welfare was calculated in problem 3. It is equal to 6000.

We do the monopoly case now. Now, the problem doesn't say what the fixed costs are, so to complete the problem, we'll just assume the firm faces no fixed costs. If I'm making a mistake here, let me know.

Remember that the firm produces so that MR=MC.

TR = (10-Q/500)Q, so that MR = 10 - 2Q/500. We solve for Q:

10 - 2Q/500 = 4 + Q/1000
=> 10000 - 4Q = 4000 + Q
=> 6000 = 5Q
=> Q = 1200
=> P = 10 - 1200/500 = 7.6

Note that Q < 2000 and P > 6.

The firm's profit is then equal to:

7.6(1200) - 4(1200) - (1200)^2/2000 = 3600

Note that this is bigger than 2000, the producer surplus in the perfect competition case.

Finally, consumer surplus is now (1/2)(10-7.6)(1200) = 1440.

Total welfare is equal to 3600 + 1440 = 3600 = 5040.

It's less than the perfect competition welfare, as expected.

 

[Troll]

Let X_1,...,X_n be independent random variables, each having a uniform distribution over (0,1). Let M=maximum(X_1,...,X_n). The distribution function of M, F_M(.), is given by F_M(x)=x^n, 0<=x<=1. Calculate E[X] for the maximum random variable.


Also, I know the answer is E[X]=n/(n+1), I just need help with figuring out how to get to that. Thank you.

 

[Anth0ny]

Thank you so much for the help, Goya! Looks like I'm on the right track...

 

[MikeDip]

Let X_1,...,X_n be independent random variables, each having a uniform distribution over (0,1). Let M=maximum(X_1,...,X_n). The distribution function of M, F_M(.), is given by F_M(x)=x^n, 0<=x<=1. Calculate E[X] for the maximum random variable.


Also, I know the answer is E[X]=n/(n+1), I just need help with figuring out how to get to that. Thank you.

Since you have the distribution function, you can take its derivative to find the probability density function(pdf). In this case its
d(F_M) / dx = nx^(n-1)

And for expected value, its the integral from -infinity to infinity of (x times the pdf).
(And in this case since the distribution function is from 0 to 1, you can integrate from 0 to 1 since that covers everything.
so integrate (x)(nx^(n-1))
The integral ends up being (nx^(n+1)) / n+1 so from 0 to 1, this equals the answer you provided, n/(n+1).

 

[wbsmcs]

For those of you that helped me with that tree and path problem, thank you so much. It is very much appreciated!

 

[Troll]

Since you have the distribution function, you can take its derivative to find the probability density function(pdf). In this case its
d(F_M) / dx = nx^(n-1)

And for expected value, its the integral from -infinity to infinity of (x times the pdf).
(And in this case since the distribution function is from 0 to 1, you can integrate from 0 to 1 since that covers everything.
so integrate (x)(nx^(n-1))
The integral ends up being (nx^(n+1)) / n+1 so from 0 to 1, this equals the answer you provided, n/(n+1).

Thank you

 

[Mr.Fresh]

So I have financial accounting this semester. I'm stuck on this one part. If I borrowed $5000 from the bank on a note payable that means I decrease cash by $5000 and increase notes payable by $5000 right?

 

[DEAD RABBIT]

If anyone is interested, the Santa Fe Institute has begun an online introduction course into complexity theory, for free:
http://www.complexityexplorer.org

 

[SummitAve]

Working on some heat transport stuff for a fluids class, and I've seemed to have forgotten some basics of integration. Could really use a hand, especially on steps to get the 1st integration.

 

[MikeDip]

Working on some heat transport stuff for a fluids class, and I've seemed to have forgotten some basics of integration. Could really use a hand, especially on steps to get the 1st integration.

For the first integration they multiplied through by r^2 and then just did standard integration. First term, the integration just removes the d/dr. second term is q/R[r^2 - r^6/r0^3] so integration gives q/R[(r^3)/3 - r^6/6r0^3 as stated. Then remember you have to add the constant of integration c1, since this is an indefinite integral.

 

[youngwerther]

I really suck at math so I'm here again tonight.

Right now I'm stuck on this.

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

sinx= x^2 - x, (1,2)


Can I set this equal to zero?

I don't really know what they mean by showing that there is a root.
I think it means that they want me to show that between 1 and 2 there exists some number so that x^2 - 2 is equal to sinx.
Sin of x is a fucking mess though, so I'd rather show that there is some number so that x^2 - x - sinx = 0.

I don't know if I'm allowed to do that or if that even makes sense, but it seems like it would be easier.

 

[MikeDip]

I really suck at math so I'm here again tonight.

Right now I'm stuck on this.

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

sinx= x^2 - x, (1,2)


Can I set this equal to zero?

I don't really know what they mean by showing that there is a root.
I think it means that they want me to show that between 1 and 2 there exists some number so that x^2 - 2 is equal to sinx.
Sin of x is a fucking mess though, so I'd rather show that there is some number so that x^2 - x - sinx = 0.

I don't know if I'm allowed to do that or if that even makes sense, but it seems like it would be easier.

To show it has a root, you must show that sinx - x^2 + x = 0 somewhere in the interval of (1,2)

The way to do this is use the intermediate value theorem. Since we know that this function is continuous, it has no gaps.
this means that if we find out that sinx - x^2 + 0 has both a positive and negative answer in the interval, then by the intermediate value theorem we know it must pass 0(since to go from positive to negative or negative to positive it must pass zero since there are no jumps or gaps.

So just plug in the boundary conditions into the function.
sin(1) - 1^2 - 1 is roughly 0.84
sin(2) - 2^2 + 2 is roughly -1.09

So since our function starts out positive and ends up negative, we know that it must pass zero somewhere in the interval (1,2)

That's all you have to show, so we are done.

 

[youngwerther]

Ok so I was right about setting it to zero.

I'm so skittish when it comes to math that, if I've never seen someone else do it before, I'm not sure if I'm "allowed" to do that or not, even if it makes sense.

I really need to get over that, because Calculus is kind of hard when I'm thinking that way.

 

[MikeDip]

Yeah I know what you mean. Does the book you're using not have any examples? What book is it btw?

 

[youngwerther]

It only had one example, which was a standard polynomial already set to zero.

It's Stewart's Calculus, 7th ed.

 

[youngwerther]

Very basic question, but something I need some help understanding.

We're now learning about derivatives but I missed class on Monday so I'm having trouble following the formula.

This is the general

(f(a+h) - f(a))/h

I'm sure that looks familiar to many of you.

Here's one of the examples in the book.

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3,1)

Then they work through the problem.
The first step they show is this

(f(3+h) - f(3))/h

And then their next step is

((3/(3+h)) - 1)/h

(ugh these parenthesis look so nasty)

So my question, I get how they plugged 3 in for f(a), but how did they go from f(3+h) to 3/(3+h)?

 

[MikeDip]

Very basic question, but something I need some help understanding.

We're now learning about derivatives but I missed class on Monday so I'm having trouble following the formula.

This is the general

(f(a+h) - f(a))/h

I'm sure that looks familiar to many of you.

Here's one of the examples in the book.

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3,1)

Then they work through the problem.
The first step they show is this

(f(3+h) - f(3))/h

And then their next step is

((3/(3+h)) - 1)/h

(ugh these parenthesis look so nasty)

So my question, I get how they plugged 3 in for f(a), but how did they go from f(3+h) to 3/(3+h)?

You're told y = 3/x. So since f(x) = 3/x we get f(3+h) = 3/(3+h). Basically substitute 3+h for x. You did the same thing for f(3) which gave 3/3 = 1.

 

[youngwerther]

D'oh!

Right then, time to get started on this HW.
Sure I'll be back for more here in a second.

 

[Troll]

If X is a random number selected from the first 10 positive integers, what is E[X(11-X)]?

Never mind, I think I know what to do.

 

[youngwerther]

edit:

nvm

i figured it out and have erased my shame

 

[youngwerther]

Alright new one though

piece wise function

let f(x) be

-2x+b if x<2
-24/(x-b) if x is greater than or equal to 2

There are exactly two values for b which make f(x) continuous at x=2. Find the b with the greater absolute value.



Now I know how to do this when they give you a piece wise with some constant in one of the equations, but how do I set it up when my b is in both of them?

 

[Enkidu]

Alright new one though

piece wise function

let f(x) be

-2x+b if x<2
-24/(x-b) if x is greater than or equal to 2

There are exactly two values for b which make f(x) continuous at x=2. Find the b with the greater absolute value.



Now I know how to do this when they give you a piece wise with some constant in one of the equations, but how do I set it up when my b is in both of them?

If the function is continuous that means both must be equal at x=2. So simply set -2x+b=-24/(x-b), x=2 and solve for b.

 

[Partial Gamification]

If the function is continuous that means both must be equal at x=2. So simply set -2x+b=-24/(x-b), x=2 and solve for b.

I find that problem worded awkwardly. Great explanation, here's a visual, I must be tired and stupid because I was doubting the values of the roots for some reason:

 

[mattoz85]

Can someone explain real analysis to me? I'm lost.

Well, not lost, exactly, but... yeah I'm lost. We've covered the Axiom of Completeness, the Archimedean Property, Nested Interval Property, and density. Like, I can explain what all these things are intuitively in a few sentences. But writing the proofs is extremely rigorous, and just seems like an exercise in memorization. I have three sheets of paper, double sided, filled with proofs just for my first quiz tomorrow.

 

[Leezard]

Can someone explain real analysis to me? I'm lost.

Well, not lost, exactly, but... yeah I'm lost. We've covered the Axiom of Completeness, the Archimedean Property, Nested Interval Property, and density. Like, I can explain what all these things are intuitively in a few sentences. But writing the proofs is extremely rigorous, and just seems like an exercise in memorization. I have three sheets of paper, double sided, filled with proofs just for my first quiz tomorrow.

You don't memorize an entire proof. You memorize the idea of the proof and let your mathematical skills do the rest. Ask yourself what's the main idea that allows you to go from initial assumption to proof.

 

[mattoz85]

You don't memorize an entire proof. You memorize the idea of the proof and let your mathematical skills do the rest. Ask yourself what's the main idea that allows you to go from initial assumption to proof.

That's the problem though. Like I said, I know intuitively what these things all mean. I can explain density in one sentence: a set is dense in R if any element of that set is an element of the interval between any two reals. Bam, done. But constructing the proof just seems like memorizing whether it's < or <=, when to substitue (b - 1/n) for a, and stuff like that. Am I approaching this wrong? I have no problem with proofs in my number theory class, but this class just seems so much harder for some reason.

 

[velociraptor]

I have a SHL numeracy test to prepare for Deloitte. Can someone please give me resources that I can use to help prepare for it? Thank you.

 

[f0rk]

I have a SHL numeracy test to prepare for Deloitte. Can someone please give me resources that I can use to help prepare for it? Thank you.

You get practice questions before the test. They are all about reading tables and knowing what the numbers mean so that you can do some quick calculations.
I've actually been accepted for Deloitte for a grad job, what are you applying for? Let me know if you have any questions about the process later on

 

[TheFatOne]

I'm currently trying to do u substitution in Calc II, and I am just completely lost. I'm trying to find this integral.

Now I know u=x^2, and du = 2xdx, but I have no idea what I am doing after that. I have watched some videos, and looked over my notes and I am still completely lost.

Edit: I figured it out.

 

[f0rk]

Replace dx with 1/2x du and x with sqrt(u) then integrate wrt u

 

[KidA Seven]

I'm currently trying to do u substitution in Calc II, and I am just completely lost. I'm trying to find this integral.

Now I know u=x^2, and du = 2xdx, but I have no idea what I am doing after that. I have watched some videos, and looked over my notes and I am still completely lost. I know the answer is

Because you only have x and not 2x, you must add the constant 2 in order for your du to work (substituted in). Whatever constant you put on the inside, you must do the inverse on the outside. You inserted the constant 2 on the inside so the inverse of 2 is 1/2 and that goes on the outside.

So you have 1/2 outside the integral.

If you have e^u, then the integral of e^u du = e^u. It should come out to 1/2e^u. Substitute the x^2 back in for u.

 

[TheFatOne]

Replace dx with 1/2x du and x with sqrt(u) then integrate wrt u

Because you only have x and not 2x, you must add the constant 2 in order for your du to work (substituted in). Whatever you do on inside, you must do the inverse on the outside. You inserted the constant 2 on the inside so the inverse of 2 is 1/2 and that goes on the outside.

So you have 1/2 outside the integral.

If you have e^u, then the integral of e^u du = e^u. It should come out to 1/2e^u. Substitute the x^2 back in for u.

Thanks. That one step threw me off. In my notes it just skips that part into the next one. Now I know why I was so lost in class when my teacher was explaining this. Skipped that step, and assumed everyone followed what he was doing.

 

[The Lamp]

My thermo professor mentioned that the differential d(1/p) can be written by taking its derivative with respect to p...so that

d(1/p) = -(1/(p^2))*dp

how the HELL did she get that????

What makes her think she can just take a derivative of a differential like that? Some sort of whacky u substitution?

 

[Leezard]

My thermo professor mentioned that the differential d(1/p) can be written by taking its derivative with respect to be...so that

d(1/p) = -(1/(p^2))*dp

how the HELL did she get that????

What makes her think she can just take a derivative of a differential like that? Some sort of whacky u substitution?

let f = 1/p
df = (df/dp) * dp
d(1/p) = -(1/(p^2))*dp
And yes, that's how you perform differentials.

 

[The Lamp]

let f = 1/p
df = (df/dp) * dp
d(1/p) = -(1/(p^2))*dp
And yes, that's how you perform differentials.

Oh so it's basically just just Calc 2.

Been almost 2 years since Calc 2...no wonder I forgot. Thanks!

 

[Averon]

The radius and height of a circular cylinder are changing with time in such a way that the volume remains constant at 1 liter (1000 cubic centimeters). If, at a certain time, the radius is 4 centimeters and is increasing at a rate of 0.5 centimeter per second, what is the rate of change of height?

(dV/dt)=1000, r=4, and (dr/dt)=0.5. dh/dt=?

Volume of a cylinder is (pi)(r^2)(h)

dV/dt = 2r(pi)h(dr/dt) + (pi)(r^2)(dh/dt)

Find h.

1000 = (pi)(4^2)h
1000 = 16(pi)(h)

125/2pi = h


Find dh/dt

1000 = 2(4)(125/2pi)(0.5)(pi) + 16(pi)(dh/dt)

1000 = 250 + 16pi(dh/dt)

750 = 16pi(dh/dt)

375/8pi = dh/dt

The answer in the back of the book says it's -125/8pi. What am I doing wrong?

 

[Enkidu]

(dV/dt)=1000, r=4, and (dr/dt)=0.5. dh/dt=?

Volume of a cylinder is (pi)(r^2)(h)

dV/dt = 2r(pi)h(dr/dt) + (pi)(r^2)(dh/dt)

Find h.

1000 = (pi)(4^2)h
1000 = 16(pi)(h)

125/2pi = h


Find dh/dt

1000 = 2(4)(125/2pi)(0.5)(pi) + 16(pi)(dh/dt)

1000 = 250 + 16pi(dh/dt)

750 = 16pi(dh/dt)

375/8pi = dh/dt

The answer in the back of the book says it's -125/8pi. What am I doing wrong?

First of all, dV/dt is not 1000, it's 0. The part where you go wrong is when you calculate dV/dt.

V' = 2*pi*r'*h+pi*r^2*h'=0 => h' = -(2*pi*r'*h)/(pi*r^2)=-(2*r'*h)/r =
[r=4, r'=0.5, h=125/(2*pi)] = -(2*0.5)/4 * 125/(2*pi) = -125/(8*pi)

 

[Vaporak]

Can someone explain real analysis to me? I'm lost.

Well, not lost, exactly, but... yeah I'm lost. We've covered the Axiom of Completeness, the Archimedean Property, Nested Interval Property, and density. Like, I can explain what all these things are intuitively in a few sentences. But writing the proofs is extremely rigorous, and just seems like an exercise in memorization. I have three sheets of paper, double sided, filled with proofs just for my first quiz tomorrow.

Yeah, don't try to memorize tons of proofs for a real analysis class. It won't work well. Memorize definitions and get familiar with a very large variety of proofs, and then let your intuition do the rest. Hopefully you've been building up your proof intuition, otherwise this class might hit you like a slack of bricks.

edit:

That's the problem though. Like I said, I know intuitively what these things all mean. I can explain density in one sentence: a set is dense in R if any element of that set is an element of the interval between any two reals. Bam, done. But constructing the proof just seems like memorizing whether it's < or <=, when to substitue (b - 1/n) for a, and stuff like that. Am I approaching this wrong? I have no problem with proofs in my number theory class, but this class just seems so much harder for some reason.

That's not what density is iirc. A set S is dense in X if every point of X is either an element of S or is a limit point of S.

 

[BlueMagic]

A friend of mine asked me for help and I can't solve this. This is statistics (and it's been a while since I did that course), but still:

We know that a random variable with an unknown distribution has a probability of 20% of being within a distance minor to 40 around the mean. Calculate the value of the mean deviation.

Original problem was in Spanish (only thing I'm not sure about is 'mean', but a quick google tells me it is).
There must be something I'm missing, it doesn't look difficult at all but I can't get the grasp of it.

 

[oxrock]

Turning to my math GAF brethren for assistance yet again, don't fail me now!

Find the degree measure for pi/21 rad. Express your answer in exact form and also in approximate form to four sig figs.

My work 180(pi/21)/pi ---> 180/21(pi)/pi ---> 180/21?
If so is approximate form to 4 sig fig's should be : 8.571

Part of a special graded homework assignment so just really want to make sure I nail down some easy points and this is the only question I was hesitant about. Thanks in advance.

 

[Partial Gamification]

A friend of mine asked me for help and I can't solve this. This is statistics (and it's been a while since I did that course), but still:

We know that a random variable with an unknown distribution has a probability of 20% of being within a distance minor to 40 around the mean. Calculate the value of the mean deviation.

Original problem was in Spanish (only thing I'm not sure about is 'mean', but a quick google tells me it is).
There must be something I'm missing, it doesn't look difficult at all but I can't get the grasp of it.

I know there is a lot of different terminology used in stats, globally, and I'm no probability/stats expert but "a distance minor to 40..." has me confused.

Turning to my math GAF brethren for assistance yet again, don't fail me now!

Find the degree measure for pi/21 rad. Express your answer in exact form and also in approximate form to four sig figs.

My work 180(pi/21)/pi ---> 180/21(pi)/pi ---> 180/21?
If so is approximate form to 4 sig fig's should be : 8.571

Part of a special graded homework assignment so just really want to make sure I nail down some easy points and this is the only question I was hesitant about. Thanks in advance.

Your values and technique are both good, you could reduce the fraction to 60/7 but its a matter of taste.

 

[BlueMagic]

I know there is a lot of different terminology used in stats, globally, and I'm no probability/stats expert but "a distance minor to 40..." has me confused.

I guess technically I wanted to express: P((mean-40)<x<(mean+40))=0.2

 

[Partial Gamification]

I guess technically I wanted to express: P((mean-40)<x<(mean+40))=0.2

Okay that makes sense to me, I recognize that. Hoinestly, I find this stuff somewhat counter-intuitive sometimes; so, hopefully someone else can chime in. I know where to look but I'm slow,

Spoiler

and a little stupid

.

Edit: is it a matter of setting up the density function?
the limits of integration are from the inequality set equal to 0.2? I'm going to do that real quick and someone can verify or show my mistake.

 

[Exuro]

Alright, I'm preparing for a calc 3 test on friday and theres a problem I'm not quite sure how to solve.

I need to find the distance between point (1,2,3) and vector r(t) = <2,2,0> + t<1,-3,5>

All of the questions in the book only deal with planes and vectors which I can just use a scalar projection using a random point on the plane to make a second vector. Not sure what to do with this problem.

 

[Partial Gamification]

Alright, I'm preparing for a calc 3 test on friday and theres a problem I'm not quite sure how to solve.

I need to find the distance between point (1,2,3) and vector r(t) = <2,2,0> + t<1,-3,5>

All of the questions in the book only deal with planes and vectors which I can just use a scalar projection using a random point on the plane to make a second vector. Not sure what to do with this problem.

here is the setup, or a setup: edit: the triangle should have vertex r(0) NOT r(theta), mspaint failure

and Blue Magic, I need to rethink my proposal:

edit: oops, it is definite, drop the C, but doesn't give much

edit: okay, I understand the difficulty of this. I was making/eating dinner and was too back and forth to pick up on what is being asked. Someone will surely pop in, its been too ling for me with this topic. I need help math gaf.

 

[BlueMagic]

and Blue Magic, I need to rethink my proposal:

edit: oops, it is definite, drop the C, but doesn't give much

edit: okay, I understand the difficulty of this. I was making/eating dinner and was too back and forth to pick up on what is being asked. Someone will surely pop in, its been too ling for me with this topic. I need help math gaf.

Yeah, I set it up that way too but of course, it took me nowhere.

 

[Exuro]

here is the setup, or a setup: edit: the triangle should have vertex r(0) NOT r(theta), mspaint failure

Hmm give me a sec...

Alright I think I get it. This looks really familiar to finding the distance from a point to a plane, only it uses the dot product.