Between the following two topics:

- Elementary Geometry
- Fibonacci and its sequences

We define the set $M:=\{x^2\mid x\in\mathbb{Z}\}$.

- Give 8 different elements of M.
- Give for each element of question 1, m, two numbers $q\in \mathbb{Z}, r\in \{0,1,\ldots , 7\}$ such that $m=8q+r$.
- Show that for all $x\in M$ one of the following holds:

$x\overset{(8)}{\equiv}0$, $x\overset{(8)}{\equiv}1$, $x\overset{(8)}{\equiv}4$

I have done the following:

- We have $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64$.
- ...

How can we show that one of these congruences hold?]]>

1) How to reproduce if market is increasing or decreasing at certain point? (ex. see below picture)

2) Does exist any formula how to reproduce index or something which would show how strongly market price is bouncing? it means if there are huge price spikes in short time then bouncing is big, if price...

Market graph increasing, decreasing and bouncing]]>

How does one solve for A in this given situation?]]>

I have a question relating to finding a middle number between 2 numbers as followed:

You're given 2 numbers A and B and 2 other numbers X and Y

The objective is to find number C so that A+/- x=C And

B +/- y = C (condition is B<C<A or C is always between A and B)

The rule for x and y is: x could be X or x could be a number < X

y could be Y or y could be a number < Y

x or y can be multiplied by 2, 4 however only one of them multiplied at the time

Example : A = 9, B = 13.5, X =...

Solving problem with a middle number between 2 numbers]]>

MR (x) = 2x + 3.

Calculate revenue from the sale of 100 products.

Can't find a way to complete this task, is it somehow connected with derivatives?]]>

\(\displaystyle \prod\frac{1}{1-\frac{1}{p^s}}=\sum\frac{1}{n^s}\)

where $p$ is all primes and $n$ is all natural numbers. The function of the complex variable $s$, wherever these expressions converge, is called by Riemann $\zeta(s)$.

Any thoughts on how to prove this equation?

All comments welcome. ]]>

I count using Primes and Developed this Table Here ...

Because I am a Math Savant I never had to go to University so I don't have any papers, I need a Student or Professor willing to Sign off on this Methodology of spotting Primes...Here is the Table with the Formulas all you have to do is basically remove the Table of Elements from it and CO Publish the Paper with me, it won't...

Need a Cosigner on a New Prime Sieve for a Math Paper]]>

Let $n\in \mathbb{N}$, $2\leq m\in \mathbb{N}$ and $a\in \mathbb{Z}$.

I want to show that $a\left (m+1\right )^n \overset{(9)}{\equiv} a$.

I have done the following:

\begin{equation*}a\left (m+1\right )^n \overset{(9)}{\equiv} a\left (0+1\right )^n \overset{(9)}{\equiv} a\cdot 1^n \overset{(9)}{\equiv} a\end{equation*}

Is this correct? Or do we need more details at each step?

After that, using the above, I want to show that \begin{equation*}\forall a_0, a_1...

Digit sum rule for the divisibility by 9]]>

I am working on a problem where I am finding the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients. I got the sum but now I have to solve for a_3 which consists of a real and imaginary part. Any assitance on how to solve for the a_3? Thank you.

$a_k = \{3, 1-2j, -1, ?\}$

Step 1: $(1-2j)e^{j*.5\pi*n} +a_3 e ^ {-(j*.5\pi*n)} + 3 + (-1)^{n+1} $

Step 2: $[(1-2j)(\cos \frac\pi2 n + j \sin \frac\pi2n) + a_3 (\cos \frac\pi2n-j \sin \frac\pi2n)]$]]>

Please help with this question - Investment Decisions]]>

(a) contribution margin;

(b) contribution rate;

(c) break-even point in sales dollars

Thank you]]>

a*n(d)-b*N(d)=0 (1)

where

d= ln(c/K)+b (2)

where n(d) and N(d) are normal density function and cumulative normal function.]]>

I need your assistance here with the owing problem and I'm sure someoen will help me.

I've trucking rates which are based on fixed kilos - the range starts from 50 kilos to 5000 kilos.

Condition is whatever the volume of the cargo is we have to multiply it with 200 and whatever the answer will be then we have to look down into the weight slab where it falls. For e.g.

We have 1000 kilos and volume is 1 cubic-meter.

Now we have to multiply 1 cubic-meter with 200 and...

How to Drive Tariff from two VARIABLES?]]>

Letās say Iām looking at a REIT, or maybe a fund. However, instead of buying the full amount of the item, Iām looking at a part.

To start, letās say, to try and keep the numbers easy, that the item starts at \$7,000. Later, it rises to \$7,500. Still later, it drops to \$7,250.

Now, letās say Iām using \$20, as my start. How do I know what my...

Math for trading/investing conversion?]]>

Please help me.

A computer company plans to produce 30000 computer next year. They will sell for \$700 each. The fixed cost of operation care \$5000000 total variable cost are \$6000000. What is the break even point?]]>

Kindly help me by solving the following question, it gives me hard time to solve especially the word "commencing". Thank in advance.

How much would need to be invested today at 6% per annum to provide an annuity of $5000 per ten years commencing in 5 years.]]>

Here is my question.

The marketing department estimates that if the selling price of the new product is set 40 dollar per unit, sales will be 400 units per week. If the selling price is 20dollar per unit, sales will be 800 units per week. The production dept estimates that variable cost will be 7.5 dollar per unit and fixed cost is dollar 10000 per week. Find cost, revenue and profit function.

Kindly put the necessary step to understand. Thank in advance.]]>

Every non- empty subset of positive integers has a least element.

Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it possible to apply the WOP to a subset of non-negative integers? Am I being too pedantic?]]>

Can someone shed some light of how to do this problem?

I am not sure if is this how I solve this:

How do I find that the HD subscriptions is twice as profitable?

And what the HD and SD customers existing customers have to do with the problem?

IO streams = 200

HD stream = 4 = x

SD stream = 1 = y

4x + 1y = 200

bandwidth cost

1.50...

Linear profit, graphs and equations.]]>

Should you use Euclidās algorithm in some cases and prime decomposition in others?]]>

How can I write an introduction to this showing linkage between the various topics and hook potential students to do this course? What is the motivation on covering these topics?]]>

I have 13 such invoices, their unpaid amounts, aging in days, and the interest rate.

Spread sheet to start from earliest invoice up until 06/14/2019. Thanks!]]>

Given a rent a car company, suppose that it has 411 cars for each day.

So far there are 246 bookings totally for July.

The total days of rental are 2625 and the total days/reservations 170.24.

Which formula can we use to make a forecast how many bookings there will be in July?]]>

I found only five particular solutions.

1. If there is such a number $\exists a_s \in A: k-a_t=a_s$, where $a_t \in A$ then $gcd(a_1,...,a_n) = gcd(k-a_1,...,k-a_n)$.

2. Let...

Greatest Common Divisor of two specified sequences of numbers (search for equality)]]>

Consider that we have an Automatic Parking Garage contains 900 units , each unit can contains just one car.

The Garage open 24 hours per day , 7 days per week (24*7).

The working day will divide into three parts

1- (8:00 am - 3:00 Pm) ( the rent cost in this level is 1.2 $ per hour)

2- ( 3 Pm- 10 Pm) ( the rent cost in this level is 0.9 $ per hour)

3- ( 10 Pm- 8 am) ( the rent cost in this level is 2.2 $ Overnight)

The...

Automatic Parking Problem Solving]]>

I would appreciate your help for the following:-

How many French Francs make one English Pound

How many German Marks make one English Pound

Thank you for any help you may provide

Best Regards,

P.N.]]>

p und q are two different primes

a) How many possible public keys exists for the RSA-Cryptosystems with modul N = p * q?

b) Show additionally to a), that the amount of possible public keys is an even number

c) Is it possible to chose p and q that way, that there is an even public key?

Justify your answers. Without any justification, you will receive 0.00 points on the task.

Amount of possible public keys in RSA Cryptosystems]]>

\(\displaystyle x_0\sin(\phi)=2.78 \left( \frac{\gamma^2/2}{ \sqrt{10-\frac{\gamma^2}{4}}} \right)\)

\(\displaystyle x_0e^{-15\gamma} \cos\left(30\sqrt{10-\frac{\gamma^2}{4}}-\phi\right)=1\)

I don't know awsner of \(\displaystyle \phi , x_,\gamma\)]]>

I am looking at the following exercise:

$$\text{Let an odd } a. \text{ Prove that : } \\ \ \ \ \ a^{2^n} \equiv 1 \pmod {2^{n+2}} $$

I thought that we could use the Euler's theorem but I found:

$$m=2^{n+2} , (a,m)=1 \text{ since } a \text{ is an odd number,so } 2 \nmid a$$

$$\phi(m)=2^{n+2}-2^{n+1}=2^{n+1}$$

So,we get $a^{2n+1} \equiv 1 \pmod {2^{n+1}}$.

But,we want to show that $a^{2n} \equiv 1 \pmod {2^{n+2}}$.How can we do this? ]]>

You want to borrow a dollars, with monthly payment of p dollars, such

that you'll owe f dollars after making n payments, at monthly rate r%.

Example:

Code:

```
MONTH PAYMENT INTEREST BALANCE
0 3000.00
1 -522.56 30.00 2507.44
2 -522.56 25.07 2009.95
3 -522.56 20.10 1507.49
4 -522.56 15.07 1000.00
```

Special loan]]>

Thanks.]]>

Is this financial market viable?]]>

If all calves were female, a...

Derivation of separate formulae for calculation of population growth rates of male and female cattle]]>

I found that $4900 \equiv 84 \ (\text {mod 112})$, so I concluded $$\frac{1^{100}}{84^{10}\times84^{10} \ (\text{mod 112})}$$

Which should equal $$\frac{1}{3.06\times10^{38} \ (\text{mod 112})}$$

Now, this is still in mod form. How do I convert that value to a regular number, by mostly hand? When I tried converting it with the equation $n=qm+r$ where n is the...

How do I convert from this mod number to a regular number?]]>

I was reviewing a problem in my book regarding Impedance. I have a question. For the impedance -Z they got 20 ā 53.1Ā° degrees How did they go from 12 + j16 to 20 ā 53.1Ā°. Thanks

]]>

So I tried writing a matrix $M$ as $M = \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}$ and assuming that...

Hill cipher attack]]>

A home you want to purchase is priced at $1,000,000. You have $60,000 available for a cash down payment. You borrow the remainder through a mortgage with a closed 5-year term and 25-year amortization at an interest rate of 2.75% compounded semi-annually.

1. What is the monthly payment with a 3.10% mortgage insurance premium?

2. How much will you owe at the end of 5-year term?

3. What percentage of the total 60 payments will...

Mortgage Calculation]]>

I don't know where to begin. So Here is the problem:

$\newcommand{\Z}{\mathbb{Z}}$

Prove that if $[a]$ and $

Thanks,

Cbarker1

Integer Modules Problem]]>

Here is the question:

"Prove that if $k$ divides the integers $a$ and $b$, then $k$ divides $as+bt$ for every pair of integers $s$ and $t$ for every pair of integers."

The attempted work:

Suppose $k$ divides $a$ and $k$ divides $b$, where $a,b\in\mathbb{Z}$. Then, $a=kt$ and $b=ks$, where $s,t\in\mathbb{Z}$ (Here is where I am stuck).

Do I solve for $k$?

If I do solve for $k$, then it yields the

$k=\frac{a}{t}$. Then, $b=\frac{as}{t}$. So $bt-as=0$. Then $0$ divides...

Elementary Number Theory proof]]>

I want to show that if $c_k=\frac{p_k}{q_k}$ the $k$-th convergents of the continued fraction $[a_0; a_1, a_2, \dots, a_n]$, then $q_k \geq 2^{\frac{k-1}{2}} (1 \leq k \leq n)$.

Could you give me a hint how we could show this? ]]>

Would anyone be able to help me with converting the UK decimal currency amount of

Thank you in advance,

Regards,

P.N.]]>

I have a problem that I cannot solve and I really need your help. This problem is connected to a single event held by an unnamed company and I am asking you to help me form an equation. Basically, the simple equation would be revenue-costs=profit/loss. I need to form an equation that indicates how a single variable affects both revenue and costs and preferably find their correlation OR how the change in the variable affects both revenue and costs. I am simply not smart enough to...

Event specific revenue versus costs]]>

My mother owns a hair salon where the stylists share the help of several assistants. There are 4 stylists and 4 assistants. My mom wants to change the system for paying out the assistants, because currently the assistants make \$12 an hour and the stylists all pay an equal fraction of their wage REGARDLESS of how many...

HELP! How to calculate wage for assistants at hair salon?]]>

A man buys car on instalment basis such that he pays 50.000 on signing of the contract and remaining in 4 equal instalments of 20.000 the first is being paid at the end of first year and so on for each year if the rate of interest is %8 effective, find the cash price of the car?]]>

We've been discussing FCFF recently during one of the classes, however during my at-home preparations I came across following exercise:

Sales revenues of a company at the end of 2017 amounted to USD 99 560 ths, and EBIT margin was 6.8%. The revenue growth is expected to fall linearly from 13.6% in 2018 to the inflation target increased by 0.5 pp. in 2022 contrary to EBIT margin which should rise linearly to reach in the residual period level of 9.8%,

Free cash flow]]>

A property is worth $550,000 and the bank requires 20% equity is kept in the house.

To buy a second property (say $600,000 for arguments sake) the bank requires a 35% deposit. I want to calculate how much I need the first house price to increase by to maintain 20% equity and also gain the 35% deposit required for the new house. I can do this by trial and error, but would love a method by which I could punch in...

Equity required for property]]>

I want to show that if $m=n^{13}-n$ and $n>1$ then $30290 \mid F_m$. (Hint: Show first that $a^{13} \equiv a \mod{2730}$.)

$F_m$ is the $m$-th Fibonacci number.

I have shown the hint as follows:

$2730=2 \cdot 3 \cdot 5 \cdot 7 \cdot 13$.

Using Ferma's little theorem, we deduce that $a^{13}\equiv a \pmod{5}$, $a^{13}\equiv a \pmod{2}$, $a^{13}\equiv a \pmod{3}$, $a^{13}\equiv a \pmod{7}$ and $a^{13}\equiv a \pmod{13}$.

Since $2,3,6,7,13$ are all relatively prime, we...

How do we use the hint?]]>

(1) y

Finding Inverses

Finding Points on the Curve

(2) y

Finding Inverses

Finding Points on the Curve]]>

I want to show that $L_{n+1}+L_{n-1}=5 F_n$ for $n \geq 2$ and conclude that $5 \nmid L_n$ for $n \geq 1$.

I have tried the following:

$L_{n+1}+L_{n-1}=F_n+F_{n+2}+F_{n-2}+F_n=F_n+F_{n+1}+F_n+F_n-F_{n-1}+F_n=4F_n+F_{n+1}-F_{n-1}=4F_n+F_n+F_{n-1}-F_{n-1}=5F_n$.

But how do we deduce that $5 \nmid L_n$ for $n \geq 1$ ? ]]>

I want to show that for each $n \geq 1$ it holds that $2^n L_n \equiv 2 \pmod{10}$.

$L_n$ is the Lucas sequence.

According to my notes,

$$L_n=\left( \frac{1+\sqrt{5}}{2}\right)^n+\left( \frac{1-\sqrt{5}}{2}\right)^n$$

and

$$L_n=F_{n-1}+F_{n+1},$$

where $F_n$ is the $n$-th Fibonacci number.

Could you give me a hint how we get the desired congruence? ]]>

Residual Band of Investment]]>

How to solve the CRT for cryptography as below -

(1) Find x such that

x = 2(mod3)

x = 5(mod9)

x = 7(mod11)

(2) Find x such that

x = 2(mod3)

x = 4(mod7)

x = 5(mod11)

(3) Find x such that x^2 = 26(mod77)

(4) Find x such that x^2 = 38(mod77)

Please help me by provide your advice and suggestion

Tron Orino Yeong]]>

I want to solve the following system of congruences:

$$x \equiv 13 \pmod{40} \\ x\equiv 5 \pmod{44} \\ x \equiv 38 \pmod{275}.$$

I have thought the following:

$$x \equiv 13 \pmod{40} \Leftrightarrow x \equiv 13 \pmod{2^3 \cdot 5}$$

$$x \equiv 5 \pmod{44} \Leftrightarrow x \equiv 5 \pmod{2^2 \cdot 11}$$

$$x \equiv 38 \pmod{275} \Leftrightarrow x \equiv 38 \pmod{5^2 \cdot 11}$$

$$x \equiv 13 \pmod{2^3 \cdot 5} \Leftrightarrow x \equiv 13 \pmod{2^3} \text{ and } x...

System of congruences, not relatively prime moduli]]>

I am currently working on questions focusing on valuation mathematics. A question on equivalent rates is perplexing me. The first question is straightforward, but I get stuck on the second question.

Q1. What is the value of the right to receive Ā£100,000 annually in advance in perpetuity assuming a discount rate of 10%?

A1. Ā£1,100,000

The formula below is for a level annuity that is received in perpetuity and in advance.

Equivalent Rates - Valuation Mathematics]]>

This leads to my question.

Could we take nested logs of a number, such that to a certain degree of accuracy, we reduce its length to the smallest possible. where the base of the logs are...

Using Nested Logs with differing bases to contract a number]]>

If we specify a particular method for mapping the natural numbers to the rationals, could we also specify a "distance" between two consecutive terms in some general way. Also are we able to calculate the nth term in such a progression perhaps incorporating this distance function somehow within its expression.]]>

At a clock (on which we have the positions $1,2, \dots, 12$) we place at position $1$ a blue ball and at position $2$ a red ball. At discrete times ($1,2,3, \dots$) we shift the two balls. Each time we shift the blue ball by three positions and the red ball by one position. Will the two balls ever meet at the same position?

I have thought the following.

Let $B$ be the position of the blue ball and $R$ the position of the red ball. Then $B=1+3t$ and $R=2+t$, for some $t \in...

Will the balls meet at the same position?]]>

If

Show by example that if

then

let

$$a=3 \quad b=5 \quad c=15$$

then

$$\frac{15}{3\cdot 5}=1$$

let

$$a=4 \quad b=6 \quad c=15$$

then

$$\frac{15}{4\cdot 6}\quad\textit{not an interger}$$

my feeble attempt]]>

$\text{15. Prove $A\cap(B/C)=(A\cap B)/(A\cap C)$}$

and

$\textsf{19. Let $f:A \to B$ and $g:B \to C$ be in invertable mappings;} \\

\text{that is, mappings such that $f^{-1}$ and $g^{-1}$ exist}\\

\text{Show that $\textit{$(g \, o \, f)^{-1}$}$}$

ok I am starting to do this and want to take a class in it starting 082018

so hope mhb can help me get a head start

text pdf is on pg15 #15 and #19

http://text:http://abstract.ups.edu/download/aata-20150812.pdf]]>

Associative: (ab)c = a(bc)

Commutative: ab = ba

Distributive: (a+b)c = ac+bc

Identity: a*1 = a = 1*a

Inverses: a*a^(-1) = 1 = a^(-1) * a: if a =/= 0

For the field axioms to hold, the defining of special operations for binary multiplication of the number (0) on the number (n) must be considered. In these special cases alone, binary expressions of multiplication may exist without a unique numerical quantity and a unique dimensional unit quantity.

Allow that: (0*0 = 0)

As the...

Numerus Numerans Numeratus (part 2)]]>

Alice wants Ļ to be true in the world that they live but Bob doesn't. In such cases, each of them tries to manipulate the sequence of the events in such a way...

Forcing and Family Contentions: Who wins the disputes?]]>

Many interesting integral representations of groups arise via homology from a group acting on a simplicial complex that is homotopy equivalent to a wedge of spheres. A classical example is the action of groups of Lie type on spherical buildings. On homology this gives an integral form of the Steinberg representation.

One may...

What is the minimal dimension of a complex realising a group representation?]]>

I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to complete a few problems. Though I know you wonderful people will explain your answers, could you also tell what conversions you use as well since that is likely what we will have to apply ourselves...

Engineering - Stress and Buckling Load problems]]>

I hope someone can assist me?

I have a sensor that is being used to detect a pulse triggered from a point on the surface of a disk rotating past the sensor. I am processing the data in real time to determine if the values would count as a pulse so that I can count up the number of revolutions.

Here is a picture of some sample data. The width of the pulse can vary quite significantly, as can the offset.

My current methodology is to take a...

Tracking a pulse in real time]]>

Numerus āNumerans-Numeratusā

Let all abstract numbers be defined exactly as concrete numbers.

Concrete number: A numerical quantity with a corresponding unit.

Let the corresponding unit exist as an abstract dimension notated with the use of (_).

Let the length and width of all dimensional units remain abstract and undeclared.

Let the dimensional unit be equal in quantity to the numerical quantity it corresponds to.

Let all numerical quantities inhabit their corresponding...

Numerus Numerans Numeratus (part 1)]]>

I was given following task:

A food processing company has to make a decision whether or not to expand its production facilities. A feasibility study showed the following estimates:

Initial cost outlay ā¬800,000

Further outlay in 4 years ā¬600,000

Residual value after 10 years ā¬200,000

Net returns at the end of each year for 10 years ā¬220,000

Indicate whether the expansion should be undertaken if the desired rate of return on investment is 13%. Apply the annuity method!

I do not...

Applying the annuity method - how?]]>

I was given this task:

A quarterly deposit is ā¬700 in 4.5 years, and the accumulated value is ā¬13,600. What is the value of annual interest rate?

And I would apply this formular:

S = [((1+i)n - 1) / i] ā R

ā¬13,600 = [((1+i)18 - 1) / i] ā ā¬700

To find out the annual interest rate I have to use the RATE function in excel but my solution is -1% for i.

What do I do wrong?

THANK YOU FOR ANY ADVICE ]]>

I have an interesting question regarding contribution margin (CM) % variance and how to attack it mathematically. If not known, contribution margin is defined as gross revenues minus all variable costs. This amount effectively shows how much money you have left to 'contribute' to your fixed costs. From this naturally flows a valuable metric called the CM %, which is simply contribution dollars dived by gross revenue dollars.

Please see the attached excel file or word file for...

Contribution Margin Variance]]>

We suppose that the integers $x,y,z$ satisfy $x^2+2y^2=z^2$ and $(x,y)=1$ . I want to show that $(x,z)=(y,z)=1$, and that $x$ is odd and $y$ even.

I have tried the following:

Let $(x,z)=d>1$. Then there exists a prime number $p$ such that $p \mid d$.

Since $d \mid x$ and $d \mid z$, we get that $p \mid x$ and $p \mid z$. So $p \mid x^2$, $p \mid z^2$.

Thus $p \mid z^2-x^2=2y^2$. But then how can we deduce that $p \mid y^2$, so that we could get a contradiction? ]]>

For the annuity I got A = \(\displaystyle M\times\frac1{\sum_{n=1}^p(1+i)^{-n}}\) = \(\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1+0,1)^{-n}}\) = \(\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}\) = \(\displaystyle 2,000,000\times\frac1{\sum_{n=1}^{10}(1,1)^{-n}}\) =...

Ask About Annuity]]>

If I have 100 staff at the beginning of the financial year and is ordered to reduce the workforce by 12%, ie I should have 88 on average at the end of the year. How would I calculate the monthly percentage so the reduction of staff can be rolled out gradually. I don't want to cut 12 in the first month then do nothing for the rest of the year but that's not logical for the remaining staff.

If I cut 1 each month ie staff level in the first month is 99, 2nd month 98 etc, 12th month 88...

staff reduction rate from annualized to monthly rates]]>

]]>

what is the % mark-up and how does one arrive at that?

thx]]>

A. Calculate the simple interest note proceeds.

B. Calculate the simple discount note proceeds.]]>

Numerical Superposition

Allow that there exists an integer zero element ( -0 ).

0 =/= (-0)

|0| = |-0|

0 |=| (-0)

Where |=| is defined as ānumerical superpositionā, where two unique and separate additive identities possess the same absolute value and cardinality but possess different multiplicative properties.

0: possess the additive identity property and possess the multiplicative property of zero.

(-0): possess the additive identity property and possess the...

Numerical Superposition]]>

$$\sum_{k=0}^n\frac{n!}{n^kk!(n-k)!}=\frac{(n+1)^n}{n^n}$$]]>

A family has a $130,000, 25-year mortgage at 4.2 %, compounded monthly.

a) Find the monthly payment.

b) Find the unpaid balance after 15 years.

c) Find the total amount of interest paid on the mortgage.

In other words, in the solutions pdf ( https://www.docdroid.net/4UqxHKU/answer.pdf ),

A family has a \$130,000, 25-year mortgage at 4.2 %, compounded monthly. FIND THE UNPAID BALANCE.]]>

Just wondering if anyone here can help me with a real life math problem I have on my hands right now!

I am going to borrow \$48,000 from a bank as an unsecured personal loan for a 3 year period.

I have to make minimum monthly payments of 1% of the outstanding loan balance at the end of every month.

And the interest rate is 4.9% per annum calculated on a monthly basis (ie. 4.9%/12 each month) on the outstanding loan balance at the end of every month.

So at the end...

"Getting a personal loan from a bank" real life math problem - need a formula!]]>

The problem (this is a translation):

Your father has just turned 50 (t = 0) and wants to retire in 15 years (t = 15). He thinks he will live 25 years after retirement, until he is 90 years old. He wants an annual amount indexed to the cost of inflation that will give him a purchasing power at age 65 equivalent to \$ 50,000 today (the amount of the benefit will...

Find the constant percentage of an annual salary that has to be saved to reach a retirement goal]]>

I have the following set of data

Wins 6

Losses 13

Average Win 14.33%

Average Loss -4.47%

I want to know how to figure out the maximum average loss at which I can still break even. I have tried a few different things but cannot figure it out.

Thanks,

Patrick]]>

Prove that you can make all fractions between and including 1/2 and 1.]]>

(i) The system:

$x \equiv b (mod \ m)$

$x \equiv b' (mod \ m')$

has a solution if and only if $b \equiv b' (mod \ d)$

(ii) two solutions of the system are congruent $mod \ l$, where $l = lcm(m,m')$.

I can prove part (i), but can anyone help me with part (ii) ?

Remember $gcd(a,b) \cdot lcm(a,b) = a \cdot b$

See, for instance: "Cuoco - Learning Modern Algebra (2013)", p.145 and p.148

Example:

$x \equiv 1 (mod \ 6)$ and $x \equiv...

About a variant of the Chinese Remainder Theorem]]>

Surface of protein channel in membranes]]>

We want to find an efficient algorithm that checks whether an odd number is a prime or not.

In order to obtain such an algorithm, one tests the congruence $(X+a)^n \equiv X^n+a$ not "absolutely" in $\mathbb{Z}_n[X]$, but modulo a polynomial $X^r-1$, where $r$ have to be chosen in a clever way. That is, one compares, in $\mathbb{Z}_n[X]$, the polynomials

$$(X+a)^n \pmod{X^r-1} \text{ and } (X^n+a) \pmod{X^r-1}=X^{n \mod{r}}+a.$$

In the intermediate results that appear in...

Test whether the integer is a prime]]>

When one raises fund through crowdfunding exercise one promises a return of fixed 10 % return on the net profit they make or sales they make to all of the investors.

Now I am not able to justify the division of the above 10 % to every individual investor because I have some group of...

Distributing returns to investors.]]>

We have an electromagnetic field. The relation between energy and momentum of a particle with charge $q$ is $$\left (\frac{E-q\phi}{c}\right )^2=m^2c^2+\|p-\frac{q}{c}A\|^2$$ where $c$ is the velocity of light and $\phi=\phi (x,t), A=A(x,t)$ are the scalar and vector potential of the field with values in $\mathbb{R}$ and $\mathbb{R}^3$ respectively.

Find the relation between the velocity and momentum and the equation of motion.

So, to get the relation between the velocity and...

Relation velocity-momentum]]>

Math Flow Help]]>

Anyways, he has a puzzle. a^2+b^2=k(ab+1).

A and B are given as positive integers.

Q: "Prove that K can only take on the value of fractions or squares."]]>