Any Smart Math People

[kermitology]

Originally Posted by keenan87

so thats not the right answer?

He's still pretty much right. The limitation on the equation exists for angles at which the tangent is zero. But angles at which tan is infinite does not invalidate the equation.

[keenan87]

Originally Posted by Phanuthier

I'm doing my masters in integrated circuit design. Basically the math you are doing, I make circuits to do that. Except I try and do it really really fast. And I get to debug all the errors using what you are asking here (statistics of white noise in circuits... mean... deviation... if I'm lucky and the noise is Gaussian distributed)

The 2 questions... if you post it, I can give you recommendations and help you along the way. I don't mind taking a look to see if you are on the right path, but I just don't believe in giving someone an answer; I'd rather they propose what their solution is, and if you are wrong, then I tell you where you are wrong and which direction you need to go.

1. Solve sin2y=cos4y for y, where 0<y<360. Hint (cos4y=cos(2y+2y))

2.Also just wondering guys, this question was worth a lot and I just want to make sure if I am on the right track.

In Saskatchewan, the sun rises at 09:17 on December 21 and at 04:35 on June 22. Because there is no daylight savings time in Saskatchewan, the time the sun rises on any other day can be predicted from a sinusodial graph with a period of 365 days.

Write a sinusoidal equation that realtes the time the Sun rises to the day of the year.

I got
y=2.35cos(2pi/365)(x-173)+6.933

is this the right way?

3.To play a game, a die is rolled to see who plays first. Four players are goig to play the game. What is the probability that atleast two people roll the same number? Express your answer to the nearesr tenth of a percent.

4.There are 12 feathered shuttlecocks and 9 plastic ones in a bag. If two shuttles are pulled from the bag without replacement, determine the probability:
a)1 plastic and then 1 feathered
---would we go (12P1 X9P1)/21P2?

b)1 plastic and 1 feathered
---would I go (12C1 X 9C1)/21C2

C)Atleast 1 plastic
----would I go ((12C1 X 9C1) + (12C0 X 9C2))/21C2


The first question is something I totally dont understand...and would love for you to tell me where to start (if you understand it. Along with the 4 people rolling a die, all the other ones, I am just wondering if you can tell me if I am on the right track.

[keenan87]

Originally Posted by kermitology

He's still pretty much right. The limitation on the equation exists for angles at which the tangent is zero. But angles at which tan is infinite does not invalidate the equation.

O ok thanks a lot

[Phanuthier]

Originally Posted by FlamesPuck12

I'm planning to do Software Engineering, so I'm assuming that the career path for it isn't too limited. I'm thinking about finishing my degree, 5 years with coop program, then working for a year or two and go into a law school. I'm not too sure about how that works, but if you have some words of advice about it, I'd love to hear it. (I mean law schools)

Ah yes, software. Engineers who end up in law do really well for themselves, if you have both strong in both math and english skills: Thats in real high demand, most people are usually good at one or the other (the ex I talked about above fits into that, scored real high in her LSAT and already has a company that wants to sponser her law degree when she finishes her masters).

If you do law after engg, you are likely going to be doing something in patent law. That pays big bucks, more then 99% of people here make.

Software... I dunno. I'm a little skeptical about the software market, just because it is so easy to outsource to India, et al to do. Having to know way too many people from India right now, and the fact that setup costs for a SoftE / SoftE business is so low, I can't see there being a strong market demand for young SoftE's out there. Of coarse, right now I'm looking wrong and there are a lot of SoftE's getting jobs. Long term? Like I said, I'm not confident. But hey, if you are doing law after, no biggie.

(Sorry to any SoftE's I might offend with that remark)

[STeeLy]

Originally Posted by kermitology

Tan can be infinity. 1/(infinity) is zero, so the equation is still valid.

I guess that's the one part I forgot. But aside from that, is it right?

From another way though. cot (x) = cos (x)/sin (x). Sin (0) = 0, sin (pi) = 0 and sin (2pi) = 0.

And again, cot (x) cannot be undefined. so then from this point of view, x cannot be n(pi))?

Is that right kermit?

[keenan87]

Originally Posted by STeeLy

I guess that's the one part I forgot. But aside from that, is it right?

From another way though. cot (x) = cos (x)/sin (x). Sin (0) = 0, sin (pi) = 0 and sin (2pi) = 0.

And again, cot (x) cannot be undefined. so then from this point of view, x cannot be n(pi))?

Is that right kermit?

Yo man, is the answer cannot = pi/2 or just pi? shouldnt it be just pi?

Steely, do you know how to solve the last trig questions?
1. Solve sin2y=cos4y for y, where 0<y<360. Hint (cos4y=cos(2y+2y))

2.In Saskatchewan, the sun rises at 09:17 on December 21 and at 04:35 on June 22. Because there is no daylight savings time in Saskatchewan, the time the sun rises on any other day can be predicted from a sinusodial graph with a period of 365 days.

Write a sinusoidal equation that realtes the time the Sun rises to the day of the year.

I got
y=2.35cos(2pi/365)(x-173)+6.933

[kermitology]

Originally Posted by STeeLy

I guess that's the one part I forgot. But aside from that, is it right?

From another way though. cot (x) = cos (x)/sin (x). Sin (0) = 0, sin (pi) = 0 and sin (2pi) = 0.

And again, cot (x) cannot be undefined. so then from this point of view, x =/= n(pi)?

Is that right kermit?

Yeah, the cot is the limiting factor. It cannot be undefined. At Pi/2 and 3*Pi/2 the equation is still true as Sin(Pi/2) is 1 and csc(Pi/2) is also 1, while at 3*Pi/2 they're both -1.

Gah! I don't like dealing with these trig functions unless they're involved in Euler's identity.

[kermitology]

Originally Posted by keenan87

Yo man, is the answer cannot = pi/2 or just pi? shouldnt it be just pi?

Pi and 0 invalidate the equation. Sin of Pi and Sin of 0 are 0 and dividing by zero makes a universe blow up.

[STeeLy]

Originally Posted by keenan87

Yo man, is the answer cannot = pi/2 or just pi? shouldnt it be just pi?

the answer is cannot = n(pi) where n is any integer, Just n(pi).

Originally Posted by keenan87

Steely, do you know how to solve the last trig questions?
1. Solve sin2y=cos4y for y, where 0<y<360. Hint (cos4y=cos(2y+2y))

I'm working on this one

[keenan87]

Originally Posted by kermitology

Pi and 0 invalidate the equation. Sin of Pi and Sin of 0 are 0 and dividing by zero makes a universe blow up.

haha ok

[kermitology]

Originally Posted by STeeLy

the answer is cannot = n(pi) where n is any integer, Just n(pi).



I'm working on this one

Just to note.. Any integer multiple of Pi is the same as Pi or 0.

[STeeLy]

Originally Posted by kermitology

Just to note.. Any integer multiple of Pi is the same as Pi or 0.

yeah, but that's the way I was taught. The restriction I think will be on the angle and not on the function (the cot). So unless it's within a certain range, I was always taught to write n(pi) with n as any integer.

[onetwo_threefour]

Originally Posted by FlamesPuck12

This is Math 30P (Grade 12 Math).
They're only asking for the relationship between the mean and standard deviation in a normal distribution.

The question says: Explain what Janice has to do before sending in her results to head office

Not solve, but explain the relationship between the mean and standard deviation.

Algebraically adjusting the mean and standard deviation isn't part of Math 30 Pure curriculum. (I don't even know if you can adjust mean and standard deviation when the data points aren't given)

Umm no, the question asks what she needs to do before submitting the results and I just confirmed an earlier person's assertion that she needs to standardize the scores. The hint is right there in the question, it specifically asks for a mean of 100 and a standard deviation of 10. Pretty convenient hey? Now it's been an awful long time since I took math 30, and my last stats course was a 4th year statistical analysis course in my psych. degree that approached these questions through manipulation of matrices (i.e. factor analysis) rather than algebraic formulae, but I believe that the correct answer to the question would be something along the lines of:

"She needs to standardize the scores by computing the z-scores through using the following formula:
z= (x-xbar)/sigma

She will need to subtract the mean (xbar=106.5) from each raw score (x) and divide the result by the standard deviation (sigma=8.4) to obtain a z-score for each actual test score. The z-scores are a normal distribution with a mean of zero and a standard deviation of 1, so in order to convert to a distribution with a mean of 100 and standard deviation of 10 the z-score for each test score must be standardized by multiplying by 10 and adding one hundred. This is a simple algebraic manipulation of the z-score formula.

x= (z*sigma)+xbar

Basically by using the above method you can convert any set of data points to a different mean and standard deviation."

The point of my post was that you don't throw away data points. The above is the description of the correct method, and that's the answer to the question posed. It doesn't matter if he has the data points, because the above is the description of the correct method if you do, which the question presupposes.

I'm pretty sure I took z-scores in my very first statistics course in high-school....

And now you made me spell out the whole answer to prove I knew what I was talking about even though I really didn't want to hand the whole answer to the OP. I can only hope that you're right and this is a more advanced method than you are supposed to know, so it won't amount to me helping the OP cheat, but I'm thinking that that is probably exactly what the question is asking for.

[STeeLy]

Originally Posted by keenan87

Steely, do you know how to solve the last trig questions?
1. Solve sin2y=cos4y for y, where 0<y<360. Hint (cos4y=cos(2y+2y))

sin2y = cos4y

Using your hint, you get:
sin2y = cos(2y+2y)

Using the trigonometric identity, you get:
sin2y = cos2ycos2y - sin2ysin2y

Rearrange the equation:
sin2y+sin^2(2y) = cos^2(2y)

Another trig identity 1=cos^2(x) + sin^2(x):
sin2y+sin^2(2y) = 1 - sin^2(2y)

Factor out the sin2y
2sin^2(2y)+sin2y = 1

from here, you can deduce that the sin2y can be negative since sin^2(2y) will still become positive. So you have:
sin2y=-1
sin^-1(-1) = 2y = 270 degrees
y = 135 degrees.

2sin^2(270) = 2(-1)^2 = 2
sin(270) = -1.

2+(-1) = 1

I can't think of any other way to do this... unless you need mathematical proof, then I don't know how to do it.

[metallicat]

*whooooosh*

That's the sound I hear with all of this stuff flying over my head.

[keenan87]

Originally Posted by STeeLy

sin2y = cos4y

Using your hint, you get:
sin2y = cos(2y+2y)

Using the trigonometric identity, you get:
sin2y = cos2ycos2y - sin2ysin2y

Rearrange the equation:
sin2y+sin^2(2y) = cos^2(2y)

Another trig identity 1=cos^2(x) + sin^2(x):
sin2y+sin^2(2y) = 1 - sin^2(2y)

Factor out the sin2y
2sin^2(2y)+sin2y = 1

from here, you can deduce that the sin2y can be negative since sin^2(2y) will still become positive. So you have:
sin2y=-1
sin^-1(-1) = 2y = 270 degrees
y = 135 degrees.

2sin^2(270) = 2(-1)^2 = 2
sin(270) = -1.

2+(-1) = 1

I can't think of any other way to do this... unless you need mathematical proof, then I don't know how to do it.

Thanks man, its better then anything I would think of.

[STeeLy]

Originally Posted by keenan87

Thanks man, its better then anything I would think of.

I guess you can try something like this:
2sin^2(2y)+sin2y = 1

From here, set sin2y=x, so how you have:
2x^2+x=1

Rearrange:
2x^2+x-1 = 0

Factor out, you get:
(-2x+1)(-x-1) = 0

-2x+1 = 0
2x = 1
x = 1/2
If x = sin2y = 1/2
2y = 45 degrees
y=22.5 degrees.

Put that y into the 2sin^2(2y)+sin(2y), your answer is 1, which fits 2sin^2(2y)+sin2y = 1

You also have -x-1 = 0
you have x = -1
sin2y = -1
2y = 270 degrees
y = 135 degrees

Put that why into 2sin^2(2y)+sin(2y), your answer is also 1, which again, fits the bill for 2sin^2(2y)+sin2y = 1

[Phaneuf]

Question: I've finished Grade 11 Math (Math 20 P) and got in the low 80's and looking at this stuff I have no clue what the hell most of this stuff means. Should I be worried, or will I just be learning that much more next year?

[Phanuthier]

woah i totally forgot about this thread when the game started. i'll see if i can look at this when i'm done debugging.

Phaneuf - don't worry if this stuff looks like jargon. It'll make sense when you get to it. Low 80's, not a big deal, just try and get some good skills down and let the marks follow (rather then aim for the marks, and hope you get the education with it too)

[FlamesPuck12]

onetwo_threefour: That's way above Math 30 Pure curriculum. Stats in Math 30P is basically calculating simple probabilities using Binomial distribution (and that's with the help of Binompdf and Binomcdf functions on TI 89) and calculating areas under the bell curve using either the z-score table or InvNorm function on TI 89. I completed Math 30 Pure last semester and I've never learned anything you posted above, that must be college/university level statistics.

From the way the question was worded, as a grade 12 student, I would assume that it would be just asking about how one can manipulate the mean and the standard deviation. Throwing out or adding data points may not be a valid method for stats but in grade 12 math, I'm pretty sure they're just testing you if you know what a mean or standard deviation is.