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Math/Science Homework Help from Albert Einstein!
Posted on 14 December 2016 - 10:22 PM
AlbertEinstein wrote
ThatOneCombo wrote...
We begin by creating a function with a vertical asymptote of 2x+1 and y-intercept 1.
f(x) = 2x + 1 + g(x), such that f(0) = 1 = 1 + g(0) —> g(0) = 0. (1)
We also want large x to give f(x) ~ 2x + 1, so lim(x->infinity) g(x) = 0. (2)
Let's define g(x) = p(x)/q(x). From (2), we require deg q(x) > deg p(x) (3). Combining f(x) into one fraction:
f(x) = (2xq(x) + q(x) + p(x))/q(x) (4). From (3) and (4), we clearly have that the numerator of f(x) has degree deg q(x) + 1.
Now, assuming you meant three distinct zeros, one with multiplicity two, we must have that the degree of the numerator of f(x) is 2 + 1 + 1 = 4 = deg q(x) + 1 —> deg q(x) = 3.
Since g(0) = 0, we must have p(0) = 0. Thus, p(x) can be written as p(x) = x r(x), deg r(x) = 1 or 0, from (3). For simplicity, choose deg r(x) = 0 and r(x) = 1. Hence, p(x) = x.
So, f(x) = ((2x+1)q(x)+x)/q(x). Let q(x) = ax^3 + bx^2+ cx + d. Then, the numerator of f(x) is 2ax^4+ (2b+a)x^3 + (2c+b)x^2 + (2d+c+1)x + d. Let's choose the three distinct roots as j,k,l. Then, the numerator must factor as n(x-j)^2 (x-k)(x-l).
This gives a system of equations for a, b, c, d , when we choose our roots. Precisely, 2a = n, -n(2j+k+l) = 2b+a, n(kl+2jk +2jl+j^2) = 2c+b, -n(2jkl+j^2 k +j^2 l) = 2d+c+1, j^2 k l n = d.
Choosing j = 1, k = -1, l = 2, n = 2, we have a=1, b= -7/2, c= 11/4, d = -4.
So just one example would be f(x) = (2x^4-6x^3-7x^2+2x-4)/(x^3-(7/2)x^2+(11/4)x-4).
You have a lot to learn, AlbertEinstein.
kappa
Posted on 14 December 2016 - 10:32 PM
SporkHandles wrote
In your own words, what is the Pythagorean Theorem
Given a right triangle with legs of length a and b, the length of the third side c can written as c = sqrt(a^2+b^2).
The two legs and the right angle give enough information to define a unique triangle by ASA triangle congruence. It can be shown that the hypotenuse is a function of the lengths of the legs.
In some sense, it's showing a relation between the areas of squares of the side lengths of the legs.
Here are some interesting proofs:
http://jwilson.coe.uga.edu/emt668/emt668.student.folders/headangela/essay1/Pythagorean.html
Posted on 14 December 2016 - 10:51 PM
Purpkey wrote
Can you write a five paragraph essay including origin of quantum mechanics and how it evolved over time. Also mention where it is most often used.
There's a seven-paragraph one two posts above you.
I'll explain an interesting example: the hydrogen atom. Most high school chemistry classes familiarize the students with some quantum mechanical properties of atoms, such as orbitals (s, p, d, f) and quantum numbers. But these come the mathematics and nature of quantum mechanics.
Every quantum mechanical system has something known as a Hamiltonian to describe it. The Hamiltonian is basically the energy operator. It is a function the position operator and the momentum operator. In the case of a hydrogen atom, we use relative coordinates (relative to the electron and the nucleus of hydrogen) to describe the system: H = p^2 /2m -e^2/r, where r is the distance between the electron and the nucleus, and e is the charge of the electron.
Schroedinger's equation states i(h-bar) d/dt |phi> = H|phi>. OK, this will take some explaining. i is the i you all know and love: sqrt(-1). h-bar is Planck's constant divided by 2*pi. d/dt should be a partial derivative (calculus). A derivative with respect to time essentially is a rate of change. |phi> is just a way of writing the state of the system (specifically, it's a ket, which can be imagined as a vector in an infinite-dimensional Hilbert space (here), for math people). H, again, is the Hamiltonian. This equation, in essence, says that the rate of time and change of the state is governed by the energy of the system H.
There are several aspects of the system that concern us. First is the energy of the system. The energy of the system is quantized and is represented by the quantum number n. The system has orbital angular momentum, since the electron is spinning around the nucleus. We want to know as much as we can about the angular momentum, so we take two observables to describe the angular momentum: the total orbital angular momentum L and the orbital angular momentum in the z-direction (in 3D Cartesian coordinates). The quantum numbers associated with these two observables, respectively, are l and m_l (looking familiar yet?). Finally, the electron has spin-1/2, so it can be in one of two spin states: up or down. The quantum number associated with this is m_s. Hence, the states of "interest" can thus be described by four quantum numbers |n, l , m_l, m_s>. Now, I've left out a LOT of the details, but this is at least where those quantum numbers come from.
If you've ever wondered where those balloon shapes for orbitals come from in your chemistry class, look up spherical harmonics. The Schroedinger equation for this problem is solved in a coordinate system known as spherical coordinates, where you have two angles and a distance to describe any point in space. The Schroedinger equation breaks up into two differential equations (equations involving derivatives): one involving the angular parts and one describing the radial (length) part. Spherical harmonics come from the angular equation, while the rest comes from the radial equation. All those things are are the graphs of the solutions to the Schroedinger equation!
Posted on 14 December 2016 - 10:52 PM
Automatically DeletedPosted on 14 December 2016 - 10:53 PM
EhhThing wrote
Who are you?
AlbertEinstein.
Posted on 15 December 2016 - 12:42 AM
I'd consider joining if you want to write a 2 page paper on Christian Philosophy of mathematics… (I already did this, just wonder your onion)Posted on 15 December 2016 - 01:22 AM
You hurt my head.Posted on 15 December 2016 - 03:38 AM
Given f(x)=(3+x)/(x-4), what is f^-1(x) (inverse)? This isn't too tough.Posted on 15 December 2016 - 07:09 AM
Alpha527 wrote
I'd consider joining if you want to write a 2 page paper on Christian Philosophy of mathematics… (I already did this, just wonder your onion)
Here's my onion.
http://www.petpoisonhelpline.com/wp-content/uploads/2011/10/Onion.jpg
Albert wasn't a Christian, unfortunately.
Posted on 15 December 2016 - 07:14 AM
can you do my math assignment?STAGE 2 GENERAL MATHEMATICS
Assessment Type 2: Mathematical Investigation
Modelling with Transition Matrices
Introduction
There are currently 2 similar fruit and vegetable shops in one area – shop A and shop B. The initial market share of shop A is X%.
A survey of customers carrying out their weekly grocery shopping at each shop revealed that 76% of customers buying their weekly groceries at shop A intended to do their grocery shopping at shop A the following week, and 61% of customers buying their weekly groceries at shop B intended to do their weekly grocery shopping at shop B the following week.
Mathematical Investigations
A i. Decide on an initial market share value (X%) for shop A. Using this information and the shopping trend information provided above, make a prediction about the market share of shop A in the long run. Give reasons for the prediction you have made.
ii. Using matrix methods determine the market share of the two shops in the long run if the transition conditions remain the same. Does your result support your prediction?
B i. Make a prediction about what will happen to the market share of shop A in the long run if its initial market share changes (e.g. the X% increases or decreases). Give reasons for the prediction you have made.
ii. Using matrix methods investigate the impact on the long term trends of varying the initial market share for the two shops. Does your result support your prediction? Does the time it takes to reach a steady state vary with changes to the initial state matrix?
C Using matrix methods investigate the effect of one of the shops mounting a strong advertising campaign.
D A third cheaper shop (shop C) enters the market a few months later, and achieves an initial market share of no more than 15%. A new survey reveals the following trends:
12% of shop A customers will shop at shop B the following week
M% of shop A customers will shop at shop C the following week
40% of shop B customers will shop at shop B the following week
N% of shop B customers will shop at shop C the following week
14% of shop C customers will shop at shop A the following week
7% of shop C customers will shop at shop B the following week.
Decide on the initial market share of the three shops, giving reasons for the values you have chosen.
Decide on the values of M and N for the transition behaviour of customers moving from shop A and shop B to the new shop C. Give reasons for the values you have chosen.
Using matrix methods consider:
the market trends after different periods of time (weeks) and also the length of time at which the steady state is achieved with different initial market share values being used
the effect of changes to the scenario, e.g. one shop extending trading hours to encourage customers to change shopping habits. You will need to decide on the new transition behaviour for the customers of the three shops with each change in scenario investigated. (Note: You should consider at least two different ‘change’ scenarios)
Analysis/Discussion
Critically analyse your results, considering:
the information your calculations have provided
possible implications of the investigation.
Conclusion:
The conclusions should include a summary of results, comments on the appropriateness of the model used, the reasonableness of the results, and any assumptions and limitations of the investigation.
Notes to teacher:
The 2×2 transition matrix used in the initial investigations is considered routine in nature; however for the purpose of the initial investigations it is appropriate. To achieve a level of complexity 3×3 matrix systems or higher must be utilised.
The investigation report should be a maximum of 12 single-sided A4 pages if written, or the equivalent in multimodal form.
Report Format
The report may take a variety of forms, but would usually include the following:
an outline of the problem and context
the method required to find a solution, in terms of the mathematical model or strategy used
the application of the mathematical model or strategy, including:
relevant data and/or information
mathematical calculations and results using appropriate representations
discussion and interpretation of results, including consideration of the reasonableness and limitations of the results
the results and conclusions in the context of the problem.
A bibliography and appendices, as appropriate, may be used.
The format of an investigation report may be written or multimodal.
Posted on 15 December 2016 - 07:18 AM
Metarus wrote
Given f(x)=(3+x)/(x-4), what is f^-1(x) (inverse)? This isn't too tough.
For generality, let's take a,b be integers and f(x) = y = (x-a)/(x-b). Solve for x.
yx-by = x-a —> yx-x = by-a —> x = f^(-1)(x) = b(x-(a/b))/(x-1).
By substitution into f(x), f(f^(-1))(x) = x, as desired.
Thus, this is discontinuous at x = 1 and has a zero at x = (a/b). So in your case, f^(-1)(x) = (4x+3)/(x-1).
Last edited on 15 December 2016 - 07:40 AM by AlbertEinstein
Bean wrote
can you do my math assignment?
STAGE 2 GENERAL MATHEMATICS
Assessment Type 2: Mathematical Investigation
Modelling with Transition Matrices
Introduction
There are currently 2 similar fruit and vegetable shops in one area – shop A and shop B. The initial market share of shop A is X%.
A survey of customers carrying out their weekly grocery shopping at each shop revealed that 76% of customers buying their weekly groceries at shop A intended to do their grocery shopping at shop A the following week, and 61% of customers buying their weekly groceries at shop B intended to do their weekly grocery shopping at shop B the following week.
Mathematical Investigations
A i. Decide on an initial market share value (X%) for shop A. Using this information and the shopping trend information provided above, make a prediction about the market share of shop A in the long run. Give reasons for the prediction you have made.
ii. Using matrix methods determine the market share of the two shops in the long run if the transition conditions remain the same. Does your result support your prediction?
B i. Make a prediction about what will happen to the market share of shop A in the long run if its initial market share changes (e.g. the X% increases or decreases). Give reasons for the prediction you have made.
ii. Using matrix methods investigate the impact on the long term trends of varying the initial market share for the two shops. Does your result support your prediction? Does the time it takes to reach a steady state vary with changes to the initial state matrix?
C Using matrix methods investigate the effect of one of the shops mounting a strong advertising campaign.
D A third cheaper shop (shop C) enters the market a few months later, and achieves an initial market share of no more than 15%. A new survey reveals the following trends:
12% of shop A customers will shop at shop B the following week
M% of shop A customers will shop at shop C the following week
40% of shop B customers will shop at shop B the following week
N% of shop B customers will shop at shop C the following week
14% of shop C customers will shop at shop A the following week
7% of shop C customers will shop at shop B the following week.
Decide on the initial market share of the three shops, giving reasons for the values you have chosen.
Decide on the values of M and N for the transition behaviour of customers moving from shop A and shop B to the new shop C. Give reasons for the values you have chosen.
Using matrix methods consider:
the market trends after different periods of time (weeks) and also the length of time at which the steady state is achieved with different initial market share values being used
the effect of changes to the scenario, e.g. one shop extending trading hours to encourage customers to change shopping habits. You will need to decide on the new transition behaviour for the customers of the three shops with each change in scenario investigated. (Note: You should consider at least two different ‘change’ scenarios)
Analysis/Discussion
Critically analyse your results, considering:
the information your calculations have provided
possible implications of the investigation.
Conclusion:
The conclusions should include a summary of results, comments on the appropriateness of the model used, the reasonableness of the results, and any assumptions and limitations of the investigation.
Notes to teacher:
The 2×2 transition matrix used in the initial investigations is considered routine in nature; however for the purpose of the initial investigations it is appropriate. To achieve a level of complexity 3×3 matrix systems or higher must be utilised.
The investigation report should be a maximum of 12 single-sided A4 pages if written, or the equivalent in multimodal form.
Report Format
The report may take a variety of forms, but would usually include the following:
an outline of the problem and context
the method required to find a solution, in terms of the mathematical model or strategy used
the application of the mathematical model or strategy, including:
relevant data and/or information
mathematical calculations and results using appropriate representations
discussion and interpretation of results, including consideration of the reasonableness and limitations of the results
the results and conclusions in the context of the problem.
A bibliography and appendices, as appropriate, may be used.
The format of an investigation report may be written or multimodal.
STAGE 2 GENERAL MATHEMATICS
Assessment Type 2: Mathematical Investigation
Modelling with Transition Matrices
Introduction
There are currently 2 similar fruit and vegetable shops in one area – shop A and shop B. The initial market share of shop A is X%.
A survey of customers carrying out their weekly grocery shopping at each shop revealed that 76% of customers buying their weekly groceries at shop A intended to do their grocery shopping at shop A the following week, and 61% of customers buying their weekly groceries at shop B intended to do their weekly grocery shopping at shop B the following week.
Mathematical Investigations
A i. Decide on an initial market share value (X%) for shop A. Using this information and the shopping trend information provided above, make a prediction about the market share of shop A in the long run. Give reasons for the prediction you have made.
ii. Using matrix methods determine the market share of the two shops in the long run if the transition conditions remain the same. Does your result support your prediction?
B i. Make a prediction about what will happen to the market share of shop A in the long run if its initial market share changes (e.g. the X% increases or decreases). Give reasons for the prediction you have made.
ii. Using matrix methods investigate the impact on the long term trends of varying the initial market share for the two shops. Does your result support your prediction? Does the time it takes to reach a steady state vary with changes to the initial state matrix?
C Using matrix methods investigate the effect of one of the shops mounting a strong advertising campaign.
D A third cheaper shop (shop C) enters the market a few months later, and achieves an initial market share of no more than 15%. A new survey reveals the following trends:
12% of shop A customers will shop at shop B the following week
M% of shop A customers will shop at shop C the following week
40% of shop B customers will shop at shop B the following week
N% of shop B customers will shop at shop C the following week
14% of shop C customers will shop at shop A the following week
7% of shop C customers will shop at shop B the following week.
Decide on the initial market share of the three shops, giving reasons for the values you have chosen.
Decide on the values of M and N for the transition behaviour of customers moving from shop A and shop B to the new shop C. Give reasons for the values you have chosen.
Using matrix methods consider:
the market trends after different periods of time (weeks) and also the length of time at which the steady state is achieved with different initial market share values being used
the effect of changes to the scenario, e.g. one shop extending trading hours to encourage customers to change shopping habits. You will need to decide on the new transition behaviour for the customers of the three shops with each change in scenario investigated. (Note: You should consider at least two different ‘change’ scenarios)
Analysis/Discussion
Critically analyse your results, considering:
the information your calculations have provided
possible implications of the investigation.
Conclusion:
The conclusions should include a summary of results, comments on the appropriateness of the model used, the reasonableness of the results, and any assumptions and limitations of the investigation.
Notes to teacher:
The 2×2 transition matrix used in the initial investigations is considered routine in nature; however for the purpose of the initial investigations it is appropriate. To achieve a level of complexity 3×3 matrix systems or higher must be utilised.
The investigation report should be a maximum of 12 single-sided A4 pages if written, or the equivalent in multimodal form.
Report Format
The report may take a variety of forms, but would usually include the following:
an outline of the problem and context
the method required to find a solution, in terms of the mathematical model or strategy used
the application of the mathematical model or strategy, including:
relevant data and/or information
mathematical calculations and results using appropriate representations
discussion and interpretation of results, including consideration of the reasonableness and limitations of the results
the results and conclusions in the context of the problem.
A bibliography and appendices, as appropriate, may be used.
The format of an investigation report may be written or multimodal.
I won't do the whole thing, but I'll make some preliminary suggestions.
Suppose there are N people who buy from these two shops the first week, with N_A buying from shop A and N_B buying from shop B.
Then, we have (N_A)/N = X and (N_B)/N = 1-X.
Now, let's consider how this works out.
Week one: N_A people buy from shop A.
N_B people buy from shop B.
Week two: .76*N_A + .39*N_B people buy from shop A (notice that there's an influx of shoppers from shop B).
.24*N_A + .61*N_B people buy from shop B.
Before we continue, this looks perfect for a matrix representation:
[ .76 .39 ] [N_A] = [A']
[ .24 .61 ] [N_B] = [B']
Calling that first matrix T and the column vector Q, (T^(N-1))Q gives the number of people buying from each store A', B' after N weeks (N-1 necessary because week one starts at N_A, N_B). Thus, A'/N and B'/N give the market shares after N-1 weeks.
Take N to be very large to see the long run behavior.
*Disclaimer: The curriculum for your class could require you do something completely different. This is how I personally would approach the problem. Do what your teacher wants you to do.*
Posted on 15 December 2016 - 09:45 AM
Can you explain the theory of infinite pi?Can you also explain the correct way to divide by zero?
Last edited on 15 December 2016 - 10:01 AM by Utsuho
Oh man I've been looking for a guy like you.Few Questions: (No need to rush on these, I'm in no hurry and I wanna hear your most well-designed opinion on these)
- At the current rate of advancement in various technological fields (Primarily Medicine, Physics, Environmental Science and Engineering) do you think the human race will be in a safe spot for the foreseeable future (In other words, will we be able to get past the current issues of environmental damage, fossil fuels, lack of investment in the space program, etc.) I know you focus on math/science but I see what you think. Personally I believe it's very possible if we can have a permanent habitable presence on Mars by 2050, but given the current direction of the space program thanks to the Obama Administration I have my doubts.
- Do you think the Theory of Everything is possible? Broad question interpret it as you wish.
- What is your best scientific interpretation on what happens to the human mind after death? (Factoring out religious possibilities)
- This one is more basic and personal: Can you help me out with understanding Hess's Law and Bond Enthalpy? The process of handling those confuses me. I can be more specific on this if you want.
Posted on 15 December 2016 - 10:09 AM
Utsuho wrote
Oh man I've been looking for a guy like you.
Few Questions: (No need to rush on these, I'm in no hurry and I wanna hear your most well-designed opinion on these)
- At the current rate of advancement in various technological fields (Primarily Medicine, Physics, Environmental Science and Engineering) do you think the human race will be in a safe spot for the foreseeable future (In other words, will we be able to get past the current issues of environmental damage, fossil fuels, lack of investment in the space program, etc.) I know you focus on math/science but I see what you think. Personally I believe it's very possible if we can have a permanent habitable presence on Mars by 2050, but given the current direction of the space program thanks to the Obama Administration I have my doubts.
- Do you think the Theory of Everything is possible? Broad question interpret it as you wish.
- What is your best scientific interpretation on what happens to the human mind after death? (Factoring out religious possibilities)
- This one is more basic and personal: Can you help me out with understanding Hess's Law and Bond Enthalpy? The process of handling those confuses me. I can be more specific on this if you want.
Few Questions: (No need to rush on these, I'm in no hurry and I wanna hear your most well-designed opinion on these)
- At the current rate of advancement in various technological fields (Primarily Medicine, Physics, Environmental Science and Engineering) do you think the human race will be in a safe spot for the foreseeable future (In other words, will we be able to get past the current issues of environmental damage, fossil fuels, lack of investment in the space program, etc.) I know you focus on math/science but I see what you think. Personally I believe it's very possible if we can have a permanent habitable presence on Mars by 2050, but given the current direction of the space program thanks to the Obama Administration I have my doubts.
- Do you think the Theory of Everything is possible? Broad question interpret it as you wish.
- What is your best scientific interpretation on what happens to the human mind after death? (Factoring out religious possibilities)
- This one is more basic and personal: Can you help me out with understanding Hess's Law and Bond Enthalpy? The process of handling those confuses me. I can be more specific on this if you want.
Now that is leaning towards philosophy
Posted on 15 December 2016 - 10:14 AM
why is my semen bubbly?Posted on 15 December 2016 - 10:20 AM
Purpkey wrote
Utsuho wrote...
Now that is leaning towards philosophy
Einstein worked in philosophy as well if I remember correctly.
Posted on 15 December 2016 - 10:27 AM
Utsuho wrote
Purpkey wrote...
Albert Einstein (1879–1955) is well known as the most prominent physicist of the twentieth century. Less well known, though of comparable importance, are his contributions to twentieth-century philosophy of science. Einstein's own philosophy of science is an original synthesis of elements drawn from sources as diverse as neo-Kantianism, conventionalism, and logical empiricism, its distinctive feature being its novel blending of realism with a holist, underdeterminationist form of conventionalism. Of special note is the manner in which Einstein's philosophical thinking was driven by and contributed to the solution of problems first encountered in his work in physics. Equally significant are Einstein's relations with and influence on other prominent twentieth-century philosophers of science, especially Moritz Schlick and Hans Reichenbach.
Einstein worked in philosophy as well if I remember correctly.
Posted on 15 December 2016 - 10:28 AM
Utsuho wrote
Purpkey wrote...
Einstein worked in philosophy as well if I remember correctly.
Albert Einstein (1879–1955) is well known as the most prominent physicist of the twentieth century. Less well known, though of comparable importance, are his contributions to twentieth-century philosophy of science. Einstein's own philosophy of science is an original synthesis of elements drawn from sources as diverse as neo-Kantianism, conventionalism, and logical empiricism, its distinctive feature being its novel blending of realism with a holist, underdeterminationist form of conventionalism. Of special note is the manner in which Einstein's philosophical thinking was driven by and contributed to the solution of problems first encountered in his work in physics. Equally significant are Einstein's relations with and influence on other prominent twentieth-century philosophers of science, especially Moritz Schlick and Hans Reichenbach.
Last edited on 15 December 2016 - 10:34 AM by Utsuho
Purpkey wrote
Utsuho wrote...
Albert Einstein (1879–1955) is well known as the most prominent physicist of the twentieth century. Less well known, though of comparable importance, are his contributions to twentieth-century philosophy of science. Einstein's own philosophy of science is an original synthesis of elements drawn from sources as diverse as neo-Kantianism, conventionalism, and logical empiricism, its distinctive feature being its novel blending of realism with a holist, underdeterminationist form of conventionalism. Of special note is the manner in which Einstein's philosophical thinking was driven by and contributed to the solution of problems first encountered in his work in physics. Equally significant are Einstein's relations with and influence on other prominent twentieth-century philosophers of science, especially Moritz Schlick and Hans Reichenbach.
I see nothing wrong here, and anyways it's going to be up to him to answer my questions or not.
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