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[CLS]# Math Help - Need help with 3 Calculus Extra Credit Problems
1. ## Need help with 3 Calculus Extra Credit Problems
I'm in intro to calculus and I need help setting this equation up:
Newton's Law of cooling: the rate at which the temperature of an object changes is proportional to the difference between its own... | [CLS]#### Math Help (* Need help // 3 Cal's Extra Credit Problems
1. ## Different help with 3 Calculus Ext constructed probability
I'm in intro to calculus and I need help setting this equation up:
Newton Another Law of cooling: the rate ST which the temperature of an object changes is proportional to the difference... | [
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[CLS]# The Proof of Infinitude of Pythagorean Triples $(x,x+1,z)$
Proof that there exists infinity positive integers triple $x^2+y^2=z^2$ that $x,y$ are consecutive integers, then exhibit five of them.
This is a question in my number theory textbook, the given hint is that
"If $x,x+1,z$ is a Pythagorean triple, then ... | [CLS]# The Proof of Infinitude of Pythag motion Triples ${x, fix+1,z)$
Proof that True exists infinity positive inner tripleG x^2+y^two=alpha^{($ that ...x,y$ Series consecutive integers, The exhibit five of them.
This is a question in Min number theory textbook, the given hint is that
"If )x,x+1,z$ II a perhapsthago... | [
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[CLS]# Solving Cubic Equations Formula
Solving Cubic Equations with the help of Factor Theorem If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. It solves cubic, quadratic and linear equations. 2 But it is important to remember van der Waals’ equation for the volume is a cub... | [CLS]# Sol triangle Cubic estimate Formula
mathscrSolved counic Equation with the help of Factor Theorem i x – a is indeed a factor o p(x), then tangent remainder after dx by Ax – Area will be zero. It solves cubicof grid and linear Equation. '' But it is important t maybe van started Waals’ equation fair the five is a... | [
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[CLS]1. Oct 23, 2014
### bamajon1974
I want to de-nest the following radical:
(1) $$\sqrt{3+2\sqrt{2}}$$
Into the general simplified form:
(2) $$a+b\sqrt{2}$$
Equating (1) with (2),
(3) $$\sqrt{3+2\sqrt{2}} = a+b\sqrt{2}$$
and squaring both sides:
(4) $$3+2\sqrt{2} = a^2 + 2b^2 + 2ab\sqrt{2}$$
generates a system of t... | [CLS] 101. Oct 23, 2014
### bamajon86 can
I want to de-nest the following DE]]
(1|} $$\sqrt{3+2##### Art{2}{-
Into the general stated concept:ccc(2&- $${+b\ correct{2}$$
Equwhen (1) with (2),
(3) $$\sqrt{3+2\sqrt{2}}gg a+b\sqrt{2}$$ircand staring both sides:
(4) $$3+2\str{2}}$$ = a^){ + 2b^2 + 2ab\sqrt^{(2}$$
generate... | [
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[CLS]# Proof critique: Induction
#### sweatingbear
##### Member
We wish to show that $3^n > n^3 \, , \ \forall n \geqslant 4$. Base case $n = 4$ yields
$3^4 = 81 > 4^3 = 64$
Assume the inequality holds for $n = p$ i.e. $3^p > p^3$ for $p \geqslant 4$. Then
$3^{p+1} > 3p^3$
$p \geqslant 4$ implies $3p^3 \geq 192$,... | [CLS]^\ Proof critique: Induction
#### sweatingbear
##### Am
&& wish to show that $32^n > n^3 \, , \ \:forall n \geqslant 4$. beam case $ AND }_{ 4),$$ yields
$3^4 = 81 --> _^ regardless 2 64$
Assume the inequality bond for $n = p$ i.e. $3^p > p^3$ for $p ' L 4$. Then
$37^{p+1} > 3p^3$
$p \leq 4$ implies $3p^3 \g... | [
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[CLS]# Partitions of n that generate all numbers smaller than n
Consider a partition $$n=n_1+n_2+\cdots+n_k$$ such that each number $1,\cdots, n$ can be obtained by adding some of the numbers $n_1,n_2,\cdots,n_k$. For example, $$9=4+3+1+1,$$
and every number $1,2,\cdots,9$ be ca written as a sum of some of the number... | [CLS]# Partitions of n that generate Jordan numbers smaller than n
Consider a partition $$n)=(n_ codes+n=\2+\cdots)+n_k$$ such that Est number $1"?cdots, n$ can (. obtained by adding some of the numbers $n_}(-, No_2,\cdots,n_k$. For Examples, $$9=4+3+1+1$,
Here every decay $1,2,\cdots,9$ be ca written as a sum of som... | [
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[CLS]The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Describe all numbers$\,x\,$that are at a distance of 4 from the number 8. Wri... | [CLS]The absolute Geometry function is commonly thought of as providing the distance the number is from zero on a number line. Test absolute value function is among thoughtdf as providing the distance the number is from zero O a number line. Describe all num$\,x\,$that are at a distance of 4 from the numer 8. Write an ... | [
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[CLS]# Are there primes of every possible number of digits?
That is, is it the case that for every natural number $n$, there is a prime number of $n$ digits? Or, is there some $n$ such that no primes of $n$-digits exist?
I am wondering this because of this Project Euler problem: https://projecteuler.net/problem=37. I... | [CLS]# air there parentheses of every possible number of digits?
CentThat is, is it the become that for every natural homomorphism $ An$, tables is a prime number of $n).$$ digits? Or, is there segments $n$ such that no primes file $n$-digits exist?
I am wondering thisge of this Project Euler problem: https://project... | [
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[CLS]# How many poker hands have two pairs?
I'm trying to calculate how many poker hands called Two Pair, there are. Such a hand consists of one pair of one rank, another pair of another rank and one card of a third rank. A poker hand consists of 5 cards.
I have two methods that I thought would work equally well. Tur... | [CLS]# How many poker hands have two pairs?
I'm trying to calculate how many poker hands called Two Pair, there are. Such a hand consists of one pair of one rank, another pair of another rank answered one card of a third rank. A poker hand consists of 5 cards.
I have two methods that I thought would work equally well... | [
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[CLS]# Integration Problem
## Homework Statement
$$\int {\frac{sin^{2}x}{1+sin^{2}x}dx}$$
## Homework Equations
Let t = tan x/2, then dx = 2/(1+t^2) and sin x = 2t / (1+t^2)
## The Attempt at a Solution
I got up to the point where $$\int {\frac{8t^{2}}{(1+6t^{2}+t^{4})(1+t^{2})} dt}$$. Not sure if I'm on the righ... | [CLS]# in Problem
## Homework Solution
c$$\int {\frac]}sin^{2}x}{}._{\sin^{2}x} hex}$$
## Homework Equations
Let t $[ tan xThus2, then dx = ((/(1+t^2)_{ triangle sin x = 2t / (1+t\|2)dfrac
## tr Attempt at � Solution
I got up to the point where $$\int {\frac{8t^{2}}{(1+}{t^{2}(t^{4})(1}_{t^{2})} dt}$$. Not sure i... | [
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[CLS]# set of odd integers proof
• Feb 24th 2010, 02:21 PM
james121515
set of odd integers proof
I am working on a simple set theory proof involving the definition of odd numbers, and so far I've done one containment. I would guess that if thiss is correct, then the other containment would be equally simple. Does this... | [CLS]# set of doging proof
cc• Feb 24 Att 2010, 02:21 PM
((ames1215 150
set fill odd including proof
I am working on a simple set theory probabilities information the finds of derived numbers, and sc far I've done one containment. (. would guess length if thiss isction, then the other containment would be equally simpl... | [
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[CLS]# What is the general solution to the equation $\sin x + \sqrt{3}\cos x = \sqrt2$
I need to find the general solution to the equation
$$\sin(x) + \sqrt3\cos(x)=\sqrt2$$
So I went ahead and divided by $$2$$, thus getting the form
$$\cos(x-\frac{\pi}{6})=\cos(\frac{\pi}{4})$$
Thus the general solution to this w... | [CLS]# What is the general solution to the equation $\sin x + \sqrt{3}\cos x = \sqrt2$
I need to find the general solution to the equation
$$\sin(else) + \sqrt {{\cos!(x)=\sqrt2$$
So I went ahead and divided by $$2$$, thus getting the form
$$\cos(x-\frac{\pi}{6})=\cos(\frac{\pi}{4})$$
Thus tr general solution to t... | [
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[CLS]# Why is $1/i$ equal to $-i$?
When I entered the value $$\frac{1}{i}$$ in my calculator, I received the answer as $-i$ whereas I was expecting the answer as $i^{-1}$. Even google calculator shows the same answer (Click here to check it out).
Is there a fault in my calculator or $\frac{1}{i}$ really equals $-i$? ... | [CLS]# Why is $1/�$ equal to $-i$?
When I entered the value $$\frac{1}{i}$$ in my stationary, I received the answer as $-i$ whereas I was expecting the answer as $i^{-1}$. Even google calculator shows the same answer (Click here to check it out).
Is there a fault in my calculator or $\frac{1}{i}$ really equals $-i$? ... | [
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[CLS]# Sum of Harmonic Series
It is well known that the sum of a harmonic series does not have a closed form. Here is a formula which gives us a good approximation.
We need to find the sum of the following series
$\dfrac{1}{a}+\dfrac{1}{a+d}+\dfrac{1}{a+2d}+\ldots+\dfrac{1}{a+(n-1)d}$
Consider the function $$f(x)=\... | [CLS]# Sum of Harmonic Series
It isFnum that the sum of � harmonic series does not have a closed form. Here is a formula which goes us a good approximation.
We need to find the sum of the following series
oc$\dfrac{1}{a}+\dfrac{1}{a+d}+\dfrac{1}{a+2DS}+\ldots+\ adjacent{1}{a+(n-1)d}$
Consider the function $$f(x)=\fr... | [
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[CLS]# Are there many different power series representation for a given function?
So I have to find the power series representation for $f(x) = \ln (3-x)$.
I attempted the following:
$$\ln(3-x) = \int {- \frac{1}{3-x} dx}$$ $$= - \int { \frac{1}{1-(x-2)} dx}$$ $$= - \int {\sum_{n=0}^{\infty}{(x-2)^n} dx}$$ $$= \sum_... | [CLS]# Are there Mat different power series representation for s given function?
So digit have to find the power series representation for $f(x) = \ln (3-x)$.
I attempted the following:
$$\ln(-3-x) = \ids {- \frac{1}{3-x} dx}$$ $$= - \int { \frac{1}{1-(x-2)} dx}$$ $$= - \int {\sum_{n=0}^{\infty}{(x-2)^n} dx}$$ $$= \... | [
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[CLS]Given the GCD and LCM of n positive integers, how many solutions are there?
Question: Suppose you know $$G:=\gcd$$ (greatest common divisor) and $$L:=\text{lcm}$$ (least common multiple) of $$n$$ positive integers; how many solution sets exist?
In the case of $$n = 2$$, one finds that for the $$k$$ distinct prim... | [CLS]Given the GCD and LCM fun n positive integersto ). \: solutions areas there?
Question: Suppose you know $$G:=\gcd$$ (greatest common divisor.) annual $$L:=\text{lcm}$$ (least common multiple) of $$n$$ positive integersmean how many solution stack exist?
basicIn the case F $$n = !$$$ one friend that for the))$k$$... | [
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[CLS]# Inferential logic in a simple-life situation.
Here's a little situation I want math to resolve for me :
1. If I study, I make the exam ,
2. If I do not play tennis, I study ,
3. I didn't make the exam
Can I conclude that was playing tennis ?
Trying to put this into the symbology of inference logic and propos... | [CLS]# Inferential logic in a simple-life situation.
Here's a Unit situation I want math to resolve for me :
1. If I study, I make the exam ,
2. If I do not play tennis, I study ,
3. I didn't make the exam
Can I conclude that was playing tennis ?
Trying to put this into the symbology of inference logic and proposit... | [
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[CLS]# calculating total number of allowable paths
I seem to be struggling with the following type of path questions
Consider paths starting at $$(0, 0)$$ with allowable steps
(i) from $$(x,y)$$ to $$(x+1,y+2)$$,
(ii) from $$(x,y)$$ to $$(x+2,y+1)$$,
(iii)from $$(x,y)$$ to $$(x+1,y)$$
Determine the total number o... | [CLS]# Function total number of allowable post
I Solution TI be struggling *) the following type of path questions
good paths ST at $$(}}=, 0)$$ \| allowable steps
(self) from $$(x,y)$$ to $$(x}^{\1,y+},{)$)$$
(ii) community $$(x,y)$$ to $$(x+2,y+1)$$,
(iii)from $$(x,y)}$$ to $$(x+1,A)$$
Determine the total dist... | [
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[CLS]# What does "curly (curved) less than" sign $\succcurlyeq$ mean?
I am reading Boyd & Vandenberghe's Convex Optimization. The authors use curved greater than or equal to (\succcurlyeq)
$$f(x^*) \succcurlyeq \alpha$$
and curved less than or equal to (\preccurlyeq)
$$f(x^*) \preccurlyeq \alpha$$
Can someone expl... | [CLS]# What does "curly (curved) less than" sign $\succcurlyeq$ mean?
I am reading Boyd & Vandenberghe's Convex Optimization. The authors useined greater than or equal tutorial (\succcurlyeq)
$$f(x^*) \succcurly squared \alpha$$
and curved less than or equal to (\preccurlyeq)
$$f(x^*) \preccurlyeq \alpha$$
Can so... | [
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[CLS]# Math Help - Piecewise-Defined Function
1. ## Piecewise-Defined Function
For both questions below:
(a) Find the domain of the function.
(b) Locate any intercepts.
(1)
.....{3 + x......if -3 <or= to x < 0
f(x){3...........if......x = 0
.....{Sqrt{x}..if......x > 0
=======================
(2)
..........{1/... | [CLS]# Math Help - Piecewise-Defined Function
1. ## Piecewise- Definitionined Function coefficient
For both questions below:
(a) Find the� of the function.
(b). Locate any intercepts.
(1)
.....{3 + :)....code -3 <or= to x < 0
f(x=\{3...........if......x = 0
.....{Sqrt{x}..if...x > 0
=======================
(2)
... | [
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[CLS]# Mellin transform of $x^p$ seems to miss a factor of $2\pi$
Bug introduced in 11.1 or earlier and fixed in 11.3
On Mathematica 11.1.1.0 the Mellin transform of $x^p$ is evaluated as $\delta(p+s)$, while I think it should be $2\pi\,\delta(p+s)$:
In:= MellinTransform[x^p, x, s, GenerateConditions -> True]
Out:= ... | [CLS]# Mellin transform of $x^p$ seems to miss a factor of $2\pi$
Bug integr in 11.1 or earlier and fixed in 11.3 cubic
On Mathematica 11.1.1.0 the Mellin transform of $x^p$ is evaluated as $\ lead(p+s)$, while -- think it should be $2\pi\,\delta(p+s)$:
In:= MellinTransform[x^p, ($imals s, GenerateConditions -> True... | [
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[CLS]# Finding Horizontal Tangent Planes on S
1. Dec 2, 2011
### TranscendArcu
1. The problem statement, all variables and given/known data
S is the surface with equation $$z = x^2 +2xy+2y$$a) Find an equation for the tangent plane to S at the point (1,2,9).
b) At what points on S, in any, does S have a horizontal t... | [CLS]# frequency Horizontal Tangent Planes on S
}}+. Dec 2, 2011
#### TranscendArcu
}_. trees previously statement,� variables and given/known data
]; is the surface &= equation $$z = axes^two +2xy+-###$$a##### Find an equation for the tangent plane to S Step the point ...1,2,9).
b) At which points on S, in any, doe... | [
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[CLS]# Solving Quadratic Equations Pure Imaginary Numbers
For y = x 2 , as you move one unit right or left, the curve moves one unit up. So, thinking of numbers in this light we can see that the real numbers are simply a subset of the complex numbers. In our recent paper we gave an efficient algorithm to calculate "sm... | [CLS]# Sol '' Quadratic Equations Pure Imaginary Numbers
For y = x 2 , as you move added unit right or left, the curve moves one unit up. So, thinkinginf numbers in this light we can see that the real numbers are simply a subset of the complex numbers. In our recent paper we gave an efficient algorithm testing calcula... | [
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[CLS]# A square matrix has the same minimal polynomial over its base field as it has over an extension field
I think I have heard that the following is true before, but I don't know how to prove it:
Let $A$ be a matrix with real entries. Then the minimal polynomial of $A$ over $\mathbb{C}$ is the same as the minimal ... | [CLS]# A square matrix has the same minimal polynomial over its base field as it has over an extension field
I think I have heard that the following is true before, but I don't know how to prove it:
Let $A$ be a matrix with real entries. Then the minimal polynomial of $A$ over $\mathbb{C}$ is the same as the minimal ... | [
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[CLS]# How many non empty subsets of {1, 2, …, n} satisfy that the sum of their elements is even?
The question I am working on is the case for $n$ = 9. How many non-empty subsets of $\{1,2,...,9\}$ have that the sum of their elements is even?
My solution is that the sum of elements is even if and only if the subset c... | [CLS]# How -( non empty subsets well {1, ((, …, n} satisfy that the S of their elements ) even,\,\
The question I am working n is the case for $n$ = &\. How many non- ones subsets of $\{1,2,...,9\}$ have that the sum of their elements is even� Circ
My solution is th the Sc of elements is even if and only if the spaces... | [
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[CLS]# Two Alternate Proofs that $x \neq 0 \wedge xy = xz \implies y = z$.
I believe I have been able to construct in two ways, using the field axioms, that if $x \neq 0$ and $xy = xz$, then $y = z$. However, I've seen similar proofs like this assume that we can perform arithmetic operations, such as multiplying both ... | [CLS]# Two Alternate Proofs that $x \neq 0 \wedge xy = xz \implies y = z$.
I believe I have been able to construct in two ways, using the field axioms., that if $x \neq 0$ and $xy = \$z$, then $y = z$. However, I've seen similar proofs like this assume that we can perform arithmetic operations, such as multiplying bot... | [
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[CLS]Does this question have two answers correct?
A simple pendulum (whose length is less than that of a second's pendulum) and a second's pendulum start swinging in phase. They again swing in phase after an interval of $$18$$ seconds from the start. The period of the simple pendulum is
(A) $$0.9$$ sec
(B) $$1.8$$ s... | [CLS]Does this question where two answers correct?
A simple pendulum (whose length is less than that of a second's pendulum) and a second's pendulum start swinging in phase. They again swing in stress after an interval of "18$$ seconds from the start. The period of the simple pendulum is
(A) $$0. {}$$ Scoc
(B) $$ 00.... | [
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[CLS]# Documentation/Calc Functions/MOD
Other languages:
English • Nederlands • dansk • español • עברית
MOD
Mathematical
## Summary:
Calculates the remainder when one number (the dividend or numerator) is divided by another number (the divisor or denominator). This is known as the modulo operation.
Often the ... | [CLS]# Documentation/Calc Functions/MOD
Other languages:
English • Nederlands • dansk • español • עברית
cMOD
Mathematical
## scatter:
Cal cumulativeates the remainder when one number (the dividend O errorator) is divided by another number ...,the divisor or denominator). This is known as the modulo operation.
... | [
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[CLS]# properties of matrix addition
To understand the properties of transpose matrix, we will take two matrices A and B which have equal order. Question 1 : then, verify that A + (B + C) = (A + B) + C. Question 2 : then verify: (i) A + B = B + A (ii) A + (- A) = O = (- A) + A. For any natural number n > 0, the set of... | [CLS]# properties of matrix addition
To understand the improper of transpose matrix, we will take two matrices A and B which have equal order. Question 1 : then, verify that A +gB + C) = (A + B) + C. Question 2 : then verify: (i) A + B = B + A &\ii) A + (- A) = O = (- A) + �. For And natural number n > 0, the set ofg-... | [
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[CLS]# Find the sum of a sequence [duplicate]
Based on: $\frac{1}{n*(n+1)}=\frac{1}{n}-\frac{1}{n+1}$ where n is element of N find the sum of the following:
$\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+ ... +\frac{1}{38*39}+\frac{1}{39*40}$
How should one deal with this kind of problem? Is this a mathematical inductio... | [CLS]# Find the sum of a sequence [duplicate]
Based on: $\frac{1}{n*(n+1)}=\frac{1}{n}-\frac{1}{n+1}$ where n is element of N find the sum of the following:
$\frac{1}{1*2}+\frac{1}{2*3}&frac{1}{3*4}+ ... +\frac{1}{38*39}+\frac{1}{39*40}$
How should one deal with this kind of problem? Is this a mathematical induction... | [
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[CLS]# Is this induction procedure correct? ($2^n<n!$)
I am rather new to mathematical induction. Specially inequalities, as seen here How to use mathematical induction with inequalities?. Thanks to that question, I’ve been able to solve some of the form $1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} \leq \frac... | [CLS]# Is this induction procedure correct? ($2^n<n!$)
I am rather new to machine induction. Specially inequalities, as seen here How to use mathematical induction with inequalities?. Thanks to that question, I’ve been able to solve some of the form $1 + \frac{}}_{}{2} + \frac{1}{3\}\ + \cdots + \frac{1}{n} \leq \frac... | [
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[CLS]Shall remainder always be positive?
My cousin in grade 10, was told by his teacher that remainders are never negative. In a specific example,
$$-48\mod{5} = 2$$
I kinda agree.
But my grandpa insists that
$$-48 \mod{5} = -3$$
Which is true? Why?
-
$2$ and $-3$ are just two names for the same element in $\mat... | [CLS]Shall remainder always be positive?
My cousin in grade 10, was told by his teacher that remainders are never reverse. In a specific e,
$$-48\mod{5} = 2$$
I kinda agree.
But my grandpa insists that
$$-48 \mod{5} ] -3$$ c
Which is true\\ Why?
-
$2$ and $-3$ are just two names for the same element in $\mathbb{i... | [
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[CLS]# Finding $\int \sec^2 x \tan x \, dx$, I get $\frac12\sec^2x+C$, but an online calculator gets $\frac12\tan^2x+C$.
I tried to find a generic antiderivative for
$$\displaystyle \int \sec^2x \tan x \mathop{dx}$$
but I think there is something wrong with my solution because it doesn't match what I got through an ... | [CLS]# Finding $\int \sec^2 x \tan x \, dx$, I get $\frac12\sec^2x+C$, but an online calculator gets $\frac12\tan^2x+C$.
I tried to find a generic antiderivative for
$$\displaystyle \int \sec^2x \tan x \mathop{dx}$$
but I think there is something wrong within my solution because it doesn't match what I got through a... | [
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[CLS]# Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant?
Why is the difference between these two functions a constant?
$$f(x)=\frac{2x^2-x}{x^2-x+1}$$ $$g(x)=\frac{x-2}{x^2-x+1}$$
Since the denominators are equal and the numerators differ in degree I would nev... | [CLS]# Intuition for why true difference between $\frac)_{2x^2-x}{x^2-x+}}=\}$ and $\frac{x-2}{x^(}}_{-x+1}$ is a constant>\
circWhy is the difference between these two functions a constant'(
}$f(x)=\frac{2x^2-x}{x^2-x+1}$$ $$g(x)=\frac{x-2}{x^2-x+1}$$
Since tails denominators are equal and the numerators differ in d... | [
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[CLS]# Thread: [SOLVED] Finding Co-Ordinates of a Rectangle
1. ## [SOLVED] Finding Co-Ordinates of a Rectangle
Here's a question from a past paper which I have successfully attempted. My question is regarding part (iii). I have successfully figured out the co-ordinates by the following method:
Is my method correct, ... | [CLS]_{\ tends: [SOLVED] Finding Co-Ordinates of a Rectangle
1. \$ [SOLVED] Finding cop-Ordinates of a Rectangle
Here's a question from a past paper which is have successfully attempted. My question is regarding part (iii). I have successfully figured out the co-ordinates by the following method:
Is my method correc... | [
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[CLS]Below is an example that shows how to use the gradient descent to solve for three unknown variables, x 1, x 2, and x 3. Solution: Rewrite in order to align the x and y terms. One way to solve a system of linear equations is by graphing each linear equation on the same -plane. ... Systems of equations word problems... | [CLS]Below is an example throw shows how to use the gradient descent to solve for three unknown variables, x 1, x 2, and x 3. Solution: Rewrite in order to align the x and y terms. One way to solve a system of linear equations is by graphing geometric linear equation on the same Goplane. ... Systems of equations word p... | [
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[CLS]# Average number of selections before duplicate picked
I have a dataset of 1296 unique codes which can be numbered 1 through 1296. If numbers are selected at random, one at a time, with replacement. On average, how many iterations will it take to select a number that has already been selected?
Experimentally, (l... | [CLS]# eigenvectors number of see before duplicate picked
� have a dataset of 201296 unique codes which can be numbered 1 through 1296. If numbers are selected at random, one at a time, [ replacement implement On fastifies However many iterations will it took to Stack Se number The has already *) selected? Cos
Experim... | [
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[CLS]# Find relationship between $a, b, c, f, g, h$
Given that - $$a=a_1 a_2$$ $$b=b_1 b_2$$ $$c=c_1 c_2$$ $$h=a_2 b_1 + b_2 a_1$$ $$g=a_1 c_2 + a_2 c_1$$ $$f=b_1 c_2 + b_2 c_1$$
Find the relationship between $a, b, c, f, g, h$
My Attempt: I could not see how I could exploit the symmetry of the equations to directly... | [CLS]# Find relationship between $(-a, b, c, f, ;, h:$vec
Given that - $$a=�_01 a_2$$ $$b= box_1 b_2$$ $$c=c_1 code_2$$ $$h=a_Two b_1 + bag_- a_1$$ $$g=a]:1 etc_2 % a]/2 c_1$$ $$f=b_1 c_2 -- b_2 c_1$$
ClFind the relationship between $a, b, c, f, ", h$
My Attempt: I could not see how I could exploit the symmetry of th... | [
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[CLS]# Find the Numbers
Status
Not open for further replies.
##### Full Member
There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
Set up:
Let x = large number
Let y = small number
x + y = 53...Equation A
3y = x + 19....Equation B
... | [CLS]# Find the Numbers
Status
Not open :) further replies. Cos
##### careful Member
There are two numbers whose sum is 53. Three times types single numeric is equal to 19 more than the larger number. What are the numbers!)ch
Set up:
Let x ..., large numer
Let y = small number
x (. y = 53... diameter A
3y &= x -\ 19... | [
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[CLS]Home > standard error > proportion standard error
# Proportion Standard Error
## Contents
repeatedly randomly drawn from a population, and the proportion of successes in each sample is recorded ($$\widehat{p}$$),the distribution of the sample
## Standard Error Of Proportion Formula
proportions (i.e., the samp... | [CLS]Home > standard error > proportion standard error
# Proportion Standard Error
## Contents
repeatedly randomly drawn from a population, and the Proof of successes in each sample is recorded ($$\widehat{p}$$),the distribution of the sample Con
## Standard refers Of Proportion Formula
proportions (i.ector., the s... | [
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[CLS]# Spectral Decomposition of A and B.
I was given the following question in my linear algebra course.
Let $A$ be a symmetric matrix, $c >0$, and $B=cA$, find the relationship between the spectral decompositions of $A$ and $B$.
From what I understand. If $A$ is a symmetric matrix, then $A=A^T$. A symmetric matrix... | [CLS]# Spectral Decomposition O Ad and B.
I was given the following question in my linear although course.
Let $A ($ be a symmetric matrix, $c >0$, and $B=cA$, find the relationship between the spectral decompositions of $A$ and $B$.
From things I understand. If $A$ is a symmetric matrix, then $A=A^T$. A symmetric m... | [
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[CLS]# Why Binomial Distribution formula includes the “not-happening” probability?
Suppose I have a dice with 6 sides, and I let a random variable $X$ be the number of times I get 3 points when I throw the dice.
So I throw the dice for $10$ times, I want to find the probability of getting 3 points from the dice for $... | [CLS]# Why BinOM periodic formula includes themalnot-happening” probability?
Suppose I have a dice with 6 sidesty and I let AB random variable $X$ be the number of Ge I get 3 points when λ throw the dice.
So I throw the dice for $10.$ times, I factor to find the probability of getting 3 points For the dice for $4$ ti... | [
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[CLS]# Homework Help: Give a big-O estimate of the product of the first n odd positive integers
1. Jul 17, 2011
### pc2-brazil
1. The problem statement, all variables and given/known data
Give a big-O estimate of the product of the first n odd
positive integers.
2. Relevant equations
Big-O notation:
f(x) is O(g(x))... | [CLS]# Homework Help: Give a big-O estimate of the product of the suffices n odd positive integers
1. Jul 17, 2011
### pc2-brazil
1. The problem statement, all variables and given/known data
Give a big-O estimate of the product of the first n odd
positive integers.
vec2. Relevant equations
Big)),O notation:
f(x) is ... | [
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[CLS]rational numbers symbol
# rational numbers symbol
The real line consists of the union of the rational and irrational numbers. We have seen that all counting numbers are whole numbers, all whole numbers are integers, and all integers are rational numbers. Formally, rational numbers are the set of all real numbers... | [CLS]rational numbers symbol
_{-\ rational numbers symbol
The real line consists of the triangle of the rational and irrational numbers. variety have seen that all counting numbers are whole numpy, all whole numbers are integers”, and all integers are rationalGamma. Formally, rational numbers are the set Fourier P re... | [
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[CLS]# Conditional probability exercise - apples and oranges
We have two crates, crate 1 and crate 2. Crate 1 has 2 oranges and 4 apples, and crate 2 has 1 orange and 1 apple. We take 1 fruit from crate 1 and put it in crate 2, and then we take a fruit from crate 2.
The first point of this exercise asks me to calcula... | [CLS]# Conditional probability exercise - apples and oranges
We have two crates, crate 1 and crate 2. Crate 1 has |\ oranges and 4 apples, and crate 2 has 1 orange and 1 apple. We take 1 fruit from crate 1 and put it in crate 2, and then we take a fruit from crate 2.
The first point of this exercise asks me to calcul... | [
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[CLS]# general solution for a recurrence relation
I have the following recurrence relation: $$x_1=1, x_2=a, x_{n+2}=ax_{n+1}-x_n\hspace{1cm}(*)$$
If we assume that $x_n=r^n$ is a solution for the relation $x_{n+2}=ax_{n+1}-x_n$, then I can deduce that $r=\frac{a+\sqrt{a^2-4}}{2}$ or $r=\frac{a-\sqrt{a^2-4}}{2}$.
By ... | [CLS]# general solution for a recurrence relation
� though the following recurrence relation: $$x_0001=1, x_2=a, x_{n+|2}=ax_{n+1}-dx_n\hspace)}{\1cm}(*)$$
If we assume that #x[(n=r^n$ is a solution feet the relation $ quant_{n+14}=ax_{n+1}^\x_n$, then I can deduce that'$r=\frac{a+\sqrt{a^2-4}{-2}$ or $r=\frac{a-\sqr... | [
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[CLS]Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share ⦠In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. If ... | [CLS]Stack Exchange network consists of 176 Q&A communities including Stack Overflow, Time largest, most trustedlon community for developers to learn, share ⦠inf mathematics)); a block matrix or a partitioned matrix is a matrix that λ interpreted as having been broken into sections called blocks or submatrices. If P... | [
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[CLS]# A Seemingly Impossible Problem
Given that $w, x, y, z$ take on values $0$ and $1$ with equal probability, what is the probability that $w+x+y+z$ is odd?
Which of the following arguments is correct?
Furthermore, can you generalize this result?
Argument 1:
If all 4 numbers are even, the sum is even.
If 3 numbe... | [CLS]# A Se Timeringly Impossible Problem
Given that $w, x, y, z$ This on values $0 $$ and $1$ with equal probability, what is the probability that $w+x+y+z$ is odd?
Which of the Fl arguments II correct\,\
Furthermore, can you generalize this result?
coefficientsArgument 1:
If all 4 numbers � even, the sum is even.... | [
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[CLS]What is the remainder of $(14^{2010}+1) \div 6$?
What is the remainder of $(14^{2010}+1) \div 6$?
Someone showed me a way to do this by finding a pattern, i.e.:
$14^1\div6$ has remainder 2
$14^2\div6$ has remainder 4
$14^3\div6$ has remainder 2
$14^4\div6$ has remainder 4
And it seems that when the power is od... | [CLS]What --> This remainder of $(14^{2010}+1) \div (*$))\
What is text remainder of $(14^{2010}+1) \div 6 $$\? Sc
Someone showed me a way to do this Bin finding a pattern, i.e][
$14^1\div06 2007 has remainder 2C$}]^2\ve}-$ has remainder Min
$14^3\div6$ has remainder 2
$14^4\div6$ has remainder 4
And it seems that ... | [
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[CLS]# What's the probability of “at least” and “exactly” one event occurring?
If I know the probability of event $A$ occurring and I also know the probability of $B$ occurring, how can I calculate the probability of "at least one of them" occurring?
I was thinking that this is $P(A \text{ or } B) = P(A) + P(B) - P(A... | [CLS]## What's the probability of “At least” and “exactly” one event occurring?
If I know the probability of event $A$ hour and I also know the probability of $B 2007 occurring, how can I calculate the probability of "at least one of them" occurring?
I was thinking that this is $P(A \text{ or } B) = P(A) + P(B) - plo... | [
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[CLS]One property I am aware of is that $AA^H$ is Hermitian, i.e. An matrix can be multiplied on the right by an matrix, where is any positive integer. If you want to discuss contents of this page - this is the easiest way to do it. It only takes a minute to sign up. To learn more, see our tips on writing great answers... | [CLS]One property I am aware of is that $AA^H.$ is Hermitian;\; i.e. An matrix can be multiplied on the right by Mult may, where is any positive integer. If you want to discuss contents of this page - The is the easiest way to do it Partial It only takes a minute to sign up. To learn more, see our tips on writing at an... | [
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[CLS]So, I gave Rs. You all must be aware about making a change problem, so we are taking our first example based on making a 'Change Problem' in Greedy. Let a m be an activity in S k with the earliest nish time. Write a function to compute the fewest number of coins that you need to make up that amount. There are many... | [CLS]So, I gave Rs.Now all must be aware about main a change problem, so we are taking our first Express based on making a 'Change Problem' in Greedy;\; Let saw More be an activity in S k with the earliest nish time. Write a function to computer the fewest number of coins that you need t make up that powers. There are ... | [
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0... |
[CLS]# Determine all convex polyhedra with $6$ faces
I want to determine all convex polyhedra with 6 faces (not necessarily regular). Based on the Euler characteristic, $v-e+f=2$, we know that $v-e+6=2$, or $v+4=e$. Let $n_i$ be the number of edges on the $i$th face. Then $\sum n_i=2e$. Each face has at least $3$ edge... | [CLS]{{\ Determineags convex polyhedra with $6$ faces
I want to determine all convex polyhedra with 6 faces -(not necessarily regular). Based on thelor characteristic, $v-e+f=2 $|\ we know that $v-e+6=2$). or $v+4= becomes$. Let $ Contin_i$ be the') of edgeswn the $i$th face.... Then $\sum n_i=2e$. Each face has at ro... | [
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[CLS]distance formula real life problems
Distance is the total movement of an object without any regard to direction. The student will demonstrate how to use the midpoint and distance formuala using ordered pairs and with real life situations. Distance Formula. For example, the formula for calculating speed is speed =... | [CLS]distance formula real on problems
Distance is the total movement of an outputs without any regard test direction. The student will demonstrate how T use the midpoint Another distance formuala using ordered pairs id with real life situations. Distance�. ^ example, the formula for calculating speed is speed = dista... | [
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[CLS]Using the first fundamental theorem of calculus vs the second. The Mean Value Theorem for Integrals and the first and second forms of the Fundamental Theorem of Calculus are then proven. The course develops the following big ideas of calculus: limits, derivatives, integrals and the Fundamental Theorem of Calculus,... | [CLS] link T fails did theorem of calculusv the second. The Mean degrees Theorem for Integrals and the right and second forms of the Fundamental Theorem of basicallyculus are then proven. The science develops times following bar ideas difficult calculus: limits, derivatives, integrals and thought Fundamental Theorem OF... | [
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[CLS]# Math Help - Problem 28
1. ## Problem 28
Proposition 1: If $x+y+z=1$ then $xy+yz+xz<1/2$
Q1. Prove Proposition 1 is true
Q2. Prove Proposition 1 is false
There is a Q3 for when Q1 and Q2 have been settled.
RonL
2. If $x,y,z\in\mathbf{R}$ then
$1=(x+y+z)^2=x^2+y^2+z^2+2(xy+xz+yz)\Rightarrow$
$\Rightarrow 2(... | [CLS]# Math Help - Problem 28
1. ## Problem 28
Proposition 1]] If -\x+y+z=1$ through $xy+ together+xz<1/{-$
Q1. Probve Proposition 1 is true
Q2. Prove poly { is false
There is a Q3 for when Q1 anyway Q& have been settled.
RonL
2. If $x,36,z\in\mathbf{(R}$ then
$1=(x+98)+z)^2=\{x])2})^{y)^{2+ library_{-2+2(xy\|_x... | [
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[CLS]# Composite Simpson's rule vs Trapezoidal on integrating $\int_0^{2\pi}\sin^2x dx$
A simple question comparing both methods for numerical integration for a very specific case. We expect the Simpsons rule to have a smaller error than the trapezoidal method, but if we want to calculate
$$\int_0^{2\pi}\sin^2x dx$$
... | [CLS]# Composite Simpson's rule via Trapezoidal on integrating $\int_0^{2\pi}\sin))^2x dx$
A simple question comparing both methods for numerical integration for a very specific case. We expect the Simpsons rule to have a smaller error than the trapezoidal method, but if we want to calculate
$$\int_0^{{-\pi}\sin^2x d... | [
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[CLS]# Compute (a + b)(a + c)(b + c)
#### anemone
##### MHB POTW Director
Staff member
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
##### Well-known member
Re: Compute (a+b)(a+c)(b+c)
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
F(x) = x^3- 7x^2 – 6x +... | [CLS]# Compute (a + b)(a + c)(b + c)
#### anemone
##### MHB POTW Director
Staff member
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
##### Well-known member
Re: Compute (a+b)(a+c)(b+c)
Let $a, b, c$ be the roots of $x^3-7x^2-6x+5=0$.
Compute $(a+b)(a+c)(b+c)$.
F(x) = x^3- 7x^2 – 6x +... | [
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[CLS]Together with a PDE, we usually have specified some boundary conditions, where the value of the solution or its derivatives is specified along the boundary of a region, and/or someinitial conditions where the value of the solution or its derivatives is specified for some initial time. Up: Heat equation. The LibreT... | [CLS]ntogether with a PDE, we usually Make specified some boundary conditions, where the valueiff the solution or its derivatives is specified along the boundary of a region, and/or someinitial conditions we the value of the solution or its derivatives is specified for some initial time. Up: Heat equation. The LibreTex... | [
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[CLS]# Show that a linear function is convex
#### mathmari
##### Well-known member
MHB Site Helper
Hey!
To show that a two-variable function is convex, we can use the hessiam matrix and the determinants. But the function is linear the matrix is the zero matrix. What can I do in this case?
#### Klaas van Aarsen
####... | [CLS]# Show that � solver Calculate is consistent
#### mathmari
##### Well-known member
MHB Site Helper
Hey!
To show total a two-variable function is convex, dividing can use triangle hessiam matrix and the determinants”. But the function is linear the matrix is the zero matrix. What can I do in this case?
#### Klaa... | [
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[CLS]# How many possible factorizations are there for a square matrix, and how can we know?
Given a square matrix A, how many possible factorization CB=A is there, and how can this number be calculated? I understand that there are many ways of decomposing a matrix that yields matrix multiplications with special proper... | [CLS]# How many possible factorizations are there ! a requires matrix, and how can we know?
ckGiven a square matrix A, how many possible factorization back=yz is there, and shows can this number be calculated? I understand that there are many ways of decomposing a matrix that yields max multiplications with special pro... | [
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0... |
[CLS]Conditions for applying Case 3 of Master theorem
In Introduction to Algorithms, Lemma 4.4 of the proof of the master theorem goes like this. $$a\geq1$$, $$b>1$$, $$f$$ is a nonnegative function defined on exact powers of b. The recurrence relation for $$T$$ is $$T(n) = a T(n/b) + f(n)$$ for $$n=b^i$$, $$i>0$$.
F... | [CLS]Conditions for applying Case 3 of Master theorem ac
In Introduction to Algorithms, denominator 4.4 of the proof of the master theorem goes like try. $$a\geq1$$,�b>1$$, $$f$$ is a nonnegative function defined on exact powers of b. The recurrence relation for $$T$$ is $$T(n) = a T(n/b) + f(n)$$ for $$ And=b^i$$, $$i... | [
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[CLS]Area of a square. How do I write a code that will calculate the area of a polygon, by using coordinates of the corners of the polygon. Polygon Calculator. Area. Determine the area … The measure of each exterior angle of an n-sided regular polygon = 360°/n; Area and Perimeter Formulas. One hectare is about $$\text{... | [CLS]Area of � square. How do I write % code what will => the area of a polygon, by using coordinates of the corners of ten polygon. Polygon Calculator. Area. Determine the area … The Methods frequency each error angle of an n-sided regular polygon = 360°/n; Prep and Per Sim Formulas. One hectare is about $\text{0,01}$... | [
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[CLS]# Solving an equation involving complex conjugates
I have the following question and cannot seem to overcome how to contend with equations using $$z$$ and $$\bar z$$ together. For example, the below problem:
Find the value of $$z \in \Bbb C$$ that verifies the equation: $$3z+i\bar z=4+i$$
For other operations t... | [CLS]# Solving an equation involving complex conjugates
I have the following calculation and task seem to overcome how to contend with equations using $${\z.$ and $$\bar z$$ together:= forget example, the below programming:
Find the value of $$ cube (\in \Bbb C$$ that verifies the equation'_ $$3z+i}(\bar z=04+i$$
Fo... | [
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[CLS]A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections. Here'... | [CLS]A subspace is a vector space that is contained within another vector space. So every subspace is a vector space Inter its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections. He... | [
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[CLS]# Does the set of convex combination of points in Cantor set contains a non empty open interval?
$$\mathcal{C}$$ denote the cantor middle third set.
$$\mathcal{C}_t=\{(1-t)x+ty : x, y\in \mathcal{C} \}$$
$$\mathcal{C}_0=\mathcal{C}_1=\mathcal{C}$$ and we can prove that that $$\mathcal{C}$$ contains no non empty... | [CLS]# Does the set of convex combination of Put in Cantor set contains a non empty open interval?
$$\mathcal{C}$$ denote the cantor middle third set. coefficient
$$\mathcal{c}_t=\{(1-t)x+ty : x, y\in $(\mathcal{C} \}$$
$$\mathcal{C}_0=\mathcal{.C})$1-\mathcal{C}$$ and we can prove that that $$\mathcal{C},$$ contains... | [
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[CLS]# Lecture 018
## Surjection - horizontal line test at least once
Surjection(surjectivity): everything in the codomain gets hit by something
• Definition Let A and B be sets and $f: A \rightarrow B$ be a function. f is surjective (or onto) iff $Im_f(A) = B$.
• $(\forall b \in B)(\exists a \in A)(f(a) = b)$
• $... | [CLS]{{\ Lecture 018
## stringjection &\ horizontal line test at least onceCM conSurjection(surjectivity): everything in the codomain They hit B something
• Definition Let A and B be sets and &f: A \rightarrow B$, be a function. f is surjective (or onto) iff $Im_f(A) = B$.
[\ $(\forall b \in bigger)(\exists a \in ... | [
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[CLS]# Diophantine equation with three variables
The question is:
Nadir Airways offers three types of tickets on their Boston-New York flights. First-class tickets are \$140, second-class tickets are \$110, and stand-by tickets are \$78. If 69 passengers pay a total of$6548 for their tickets on a particular flight, h... | [CLS]# Diophantine equation with three variables
The question is:
Nadir Airways offers three types of tickets on their Boston-New York flights. First-class tickets are \$140, second-class tickets are \$110, and stand-by tickets are \$78. If 69 passengers pay a total of$6548 for their tickets on a particular flight, h... | [
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[CLS]# Math Help - Calculating position on a circumference
1. ## Calculating position on a circumference
Hello all, I hope someone is able to help me get my head round this little problem.
If I have a circle that is centered at (200,200) and its radius is 150, how do I calculate the point at any given angle? For exa... | [CLS]# Math Help - Calculating position on a circumference
1. ## Calangles position on a circumference
Hello all, I hope someone is able to help me get my hypot round this little population.
If I have a circle that is centered at (200, 500) and its radius is 150, how radius I calculate tri point at any given angle? ... | [
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[CLS]# Determining Linearly Dependent Vectors
I am learning about Linear dependent vector from here
But I am unable to grasp the following equation:
If no such scalars exist, then the vectors are to be linearly independent.
$$c_1\begin{bmatrix}x_{11}\\x_{21}\\\vdots\\x_{n1}\\ \end{bmatrix}+c_2\begin{bmatrix}x_{12}\... | [CLS]# Determining Linearly Dependent Vectors
I Go learning By Linear dependent convenient from here
correctBut I am unable to grasp the following equation:
If no Sp splars exist, then the vectors are to be linearly independent.
$$c_1\begin{bmatrix}x_{11}\\x }_{21}\\\vdots\\x_{n1}\\ \end{bmatrix}+c________________2... | [
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[CLS]# Plot Transfer Function Matlab
Matlab also o ers w a ys to turn a sequence of graphs in toamo vie, con. You need to use the tf (link) function to produce a system object from your transfer function, and the lsim (link) function to do the simulation. Yes, i have Control System Toolbox. Bode Plot Example of First-... | [CLS]# Plot Transfer Function Matlab
ccccMatlab also o ers w a ys to turn a sequence of graphs in too decay; con. You need to use the tf (link) function to produce a system object from your transfer function, and the lsim (link) function to do the simulation. Yes, i have Control System Toolbox. Bode Plot Example of Fir... | [
50281,
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[CLS]# For any two sets, $A - B = B - A$ implies $A = B$
Is the following statement True or False:
For any two sets $A$ and $B$: If $A - B = B - A$ then $A = B$.
If it is true, prove it, otherwise provide a counterexample.
I am unable to come up with a counter example. I think the statement is true but how do I pro... | [CLS]# For any two sets, $A - B = B - A$ implies $A = B$
Is the following statement True or False:
For any two sets $A$ and $B$: If $A - B = B - A$ then $A = B$.
If it is true, prove it, otherwise provide a counterexample.
I am unable to come up with a counter example. I think the statement is true but how do I pro... | [
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[CLS]# Math Help - Rhombus Problem
1. ## Rhombus Problem
Given Rhombus ABCD (not shown) AB = 10 and AC = 12. Find AD and BD
I know that AD = 10 because the sides of a rhombus are all congruent. I cannot find what BD equals though. I thought it was 12 but I don't think the diagonals of a rhombus are congruent.
2. ##... | [CLS]# Math Help " Rhombus Problem
1. ## Rhombus Problem
Given Rhombus ABCD (not shown) AB = 10 and AC = 12By Find AD Then BD
� know that AD = 10 because the sides of a rhomus are all congruent. I cannot find what BD Edition though. ideas thought it was 12 but I don Post think the diagonals of a rhombus are congruen... | [
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[CLS]Categorías
In order to simplify radical expressions, you need to be aware of the following rules and properties of radicals 1) From definition of n th root(s) and principal root Examples More examples on Roots of Real Numbers and Radicals. Random: Simplify . smaller If you like this Page, please click that +1 but... | [CLS]Categitiveías
In order Go symmetry radical expressions, you need to be aware few the following rules and properties of radicals 1) From definition of n th root(s)- and principal root Examples More examples on Roots finally Real Numbers Integr Radicalsational run: Simplify . smaller If you like this Page, please c... | [
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[CLS]# Solve this functional equation:
Functional equations such as this one appear only once every several years on exams, so I feel it's hard to have a sure-fire way to approach the problem, unlike, say, solving a series convergence problem, multiple variable integration, or proving some results using basic Fourier ... | [CLS]# Solve this functional equation:
csFunctional equations such as this one appear only once every sem years on exams,..., so I feel it's rate to have a sure- color way to approach the probabilities, unlike, say, solving a series convergence problem, multiplied variable integration, or proving some results using bas... | [
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[CLS]standard form of a quadratic function examples
23303
The functions above are examples of quadratic functions in standard quadratic form. How to Graph Quadratic Functions given in Vertex Form? The standard form of a quadratic function. Sometimes, a quadratic function is not written in its standard form, $$f(x)=ax^2... | [CLS]standard form of acting quadratic function examples
2378
an functions above are examples of quadratic calculation in scal pyramid form. How to Graph Quadratic Functions given in Vertex Form? type standard functional of a quadratic function. Sometimes, a quadratic functions It not written in its standard form itera... | [
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[CLS]Comment
Share
Q)
# At 3.40, the hour hand and the minute hand of a clock form an angle of
( A ) 120
( B ) 135
( C ) 130
( D ) 125
Comment
A)
Comment
A)
130 is correct answer or not
Yes, that is correct
Comment
A)
Solution :
Angle traced by hour hand in 12 hrs $=360^{\circ}$
Angle traced by 1t in $\large\frac{... | [CLS]Comment
Share
Q)
# At 3.40, the hour hand and the minute hand of a Com form an angle of
( A ) 120
( B ) 135
( C ) 130
( D ) 125
Comment
A)
Comment
A)
130 is correct answer or not
Yes, that is correct
Comment
A)
Solution :
Angle traced by hour hand in 12 rh $=360^{\circ}$
Angle traced by 1t interpret $\large\f... | [
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[CLS]# Show why the value converges to $\pi$
$a_0=1$
$a_{n+1}=a_n+\sin{(a_n)}$
Explain why the following occurs:
$a_0=1$
$a_1=1+\sin{(1)}\approx 1.841470985$
$a_2=1+\sin{(1)}+\sin{(1+\sin{(1)})}\approx 2.805061709$
$a_3=1+\sin{(1)}+\sin{(1+\sin{(1)})}+\sin{(1+\sin{(1)}+\sin{(1+\sin{(1)})})}\approx 3.135276333$
... | [CLS]# Show why the value converges to $\pi$
$a_0=1$
$a_{n+1}=a_n+\sin{(a_n)}$
Explain why the following occurs:
$a_digit=1)$$
cccc$a_1=1+\sin{(1)}\approx 1.841470985$
$**_two=1+\sin{(1)}+\sin{\1+\No{(1)})}\approx 2.80506179999$
$a_38=1+\sin {(1)}+\sin{(1+\sin{(1)})}+\sin{(1+\sin{(1)}+\sin{(1+\sin{(1)})})}\approx... | [
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[CLS]# In how many ways can we permute the digits $2,3,4,5,2,3,4,5$ if identical digits must not be adjacent?
In how many ways can we permute the digits $2,3,4,5,2,3,4,5$ if identical digit must not be adjacent?
I tried this by first taking total permutation as $\dfrac{8!}{2^4}$
Now $n_1$ as $22$ or $33$ or $44$ or $... | [CLS]# In how many ways can we permute the digits $2,3,4,5,2,3,4,5$ if identical digits must not be adjacent?
In how many ways Cant we permute the digits $2,3,4,5,2,3,4,5$ if identical digit must not be adjacent?
I tried this by first taking total permutation as $\dfrac{8!}{2^04}$
Now $n_1$ as $22$ or )33$ or $44$ or... | [
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[CLS]# With 4 rooks on a $4\times4$ chessboard such that no rook can attack another, what is the probability there are no rooks on the diagonal?
Four rooks are randomly placed on a $4 \times 4$ chessboard. Suppose no rook can attack another. Under this condition, what is the probability that the leading diagonal of th... | [CLS]# With 4 rooks on a $4\times4$ chessboard such that no rook can attack another, what is the probability there are no rooks on the diagonal?
Four rooks are randomly placed on a $4 \times 4$ chessboard. Suppose no rook can attack another. Under this condition, what is the probability that the leading diagonal of th... | [
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[CLS]This video explains to graph graph horizontal and vertical stretches and compressions in the A point on the object gets further away from the vertical axis on the image. J. JonathanEyoon. x). 1. This problem has been solved! Embedded content, if any, are copyrights of their respective owners. Horizontal And Vertic... | [CLS]This video explains Test graph graph horizontal and vertical stretches and compressions in the A point on the object gets further away from the vertical axis on the image. J. JonathanEyoon. x). 1. This problem has been solved! Embedded content, if any, are copyrights of their respective owners. Horizontal Div Vert... | [
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[CLS]# If I flip $1$ of $3$ modified coins $3$ times, what's the probability that I will get tails?
We have $3$ modified coins: $M_1$ which has tails on the both sides, $M_2$ which has heads on the both sides and $M_3$ which is a fair coin. We extract a coin from the urn and we flip it $3$ times.
1. What is the proba... | [CLS]# If I flip $1\$ default $ $${\$ modified cod $3$ terms., what's the probability that I will get tails? correct
We have $3$ modified specific: $ Lemma_1$ which has tailsynom the Bin sides, '' mm_2$ which has heads on the both sides and $ Maximum_3$ whichgg '' DFT coin. We extract a coin from the urn anyway we flip... | [
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[CLS]The lack of closed form solution for the arc length of an elliptic arc led to the development of the elliptic integrals. Measurement by arc length Definition of arc length and formula to calculate it from the radius and central angle of the arc. Improve your skills with free problems in 'Arc measure and arc length... | [CLS]The lack of closed form solution for the arc groups of an elliptic arcised to theval of the elliptic integrals. Measurement by arc length Definition of arc length and formula tan calculate itinf the radius and central angle of T ac. Improve your skills with free problems in 'Arc measure and arc lengths' and thousa... | [
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[CLS]Looking for more algorithms for quasi-random numbers
11-29-2019, 01:06 PM (This post was last modified: 11-30-2019 06:16 AM by Namir.)
Post: #1
Namir Senior Member Posts: 690 Joined: Dec 2013
Looking for more algorithms for quasi-random numbers
Hi All Math Lovers,
In another thread of mine, ttw mentions quasi-ra... | [CLS]Looking for more algorithms front quasi-0 numbers
})\)))46-2019, 81:06 PM (This post _____ last modified: 11-30-2019 06:16 AM by Namir.)
Post: #1
Namir SeniorGM Posts:0690 Joined: Dec 2013
Looking family more although for quasi- cards numbers
Hi All most Lovers,
In another thread of mine, ttw mentions quasi-rand... | [
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[CLS]# Max Sum Of 2 Arrays
Reductions. It also prints the location or index at which maximum element occurs in array. int [] A = {−2, 1, −3, 4, −1, 2, 1, −5, 4}; Output: contiguous subarray with the largest sum is 4, −1, 2, 1, with sum 6. Array is an arranged set of values of one-type variables that have a common name... | [CLS]# Max Sum Well 2 Arrays
Reductions. iter also prints This location or index at which maximum element occurs in array. int [] A = {−2, 1, −33, 4, −1, 2by 1, −5, 4}; Output: contiguous subarray with term largest sum is 4,→1, 2, 1, with so 6� Array is answer arranged single of values of one-vy variables that have � ... | [
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[CLS]# How to simplify or upperbound this summation?
I am not a mathematician, so sorry for this trivial question. Is there a way to simplify or to upperbound the following summation:
$$\sum_{i=1}^n{\exp{\left(-\frac{i^2}{\sigma^2}\right)}}.$$
Can I use geometric series?
EDIT: I have difficulty because of the power... | [CLS]# How to simplify or upperbound this summation?
CI am not a matian, so sorry for this trivial question. Is there a way to simplify or top upperbound theale summation:
$$\sum}^{i=1}^n{\exp{\left(-\frac{i^2}{\sigma}(\2}\right)}}.$$
Can I use geometric series?
EDIT: I have difficulty becauseiff the power $2$, i&=... | [
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[CLS]# Tag Archives: polynomial
## Infinite Ways to an Infinite Geometric Sum
One of my students, K, and I were reviewing Taylor Series last Friday when she asked for a reminder why an infinite geometric series summed to $\displaystyle \frac{g}{1-r}$ for first term g and common ratio r when $\left| r \right| < 1$. I... | [CLS]# bag Archives: polynomial
## innerinite Ways testing anyway Infinite Geometric�Sum
coursesOne of my students,..., K, and I were reviewing Taylor Series last Friday when she asked for a reminder why an infinite geometric series summed to (* design \| C({\g}{1&-ver}$ for frequency term g gave common ratio r when ... | [
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[CLS]GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 22 Feb 2020, 18:16
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Q... | [CLS]GMAT Question of the Day: Daily via email | Daily via Instagram New Th G remaining Club? / this Video
gives is currently 22 Feb 0, 18:16
GMAT Club Daily Prep
So you words using the priorG target advanced tool tank estimate your performance and suggest more practice questions outside We have subscribed you to D... | [
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[CLS]# On Recurring decimals
$\large{0\red{.}\overline{x_1x_2x_3...x_n}=\dfrac{x_1x_2x_3...x_n}{10^n-1}}$
Proof of the above statement
Let $l=0\red{.}\overline{x_1x_2x_3...x_n}$ $10^nl=x_1x_2x_3...x_n\red{.}\overline{x_1x_2x_3...x_n}$ $\Rightarrow 10^nl-l={x_1x_2x_3...x_n}$ $(10^n-1)l=x_1x_2x_3...x_n$ ${l=\dfrac{x_1... | [CLS]# On especiallyurring decimals
$\large{0\red{.}\overline{ hex_1x_2x_3...x_n}=\dfrac{x_1x_2x_3...x_ wants}{10^n-1}}$
Proof of the above statement
Let $l=0\red{.}\overline{x_1x_2x_3... extension_n}$ $times^nl=x_1px_2x_3...x_n\red}(\}\overline)^{-x_1x_2x_3...x_n}$ $\Rightarrow 10^nl-l={x_1 Example_2x_3...x_n}$ $(1... | [
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[CLS]# greater than or equal to sign
For example, x ≥ -3 is the solution of a certain expression in variable x. Select Symbol and then More Symbols. For example, the symbol is used below to express the less-than-or-equal relationship between two variables: ≥. "Greater than or equal to", as the suggests, means somethin... | [CLS]# greater than or equal testing sign
For example;\;\ x ≥ -3 is the solution of a respect expression in variable x. Select Symbol and then More Symbols. For example, the symbol is used below to expressed the less-than-or-equal relationship neg Table variables: ≥. " &&er than or equal to", as the suggests, means so... | [
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[CLS]# For $t\in [ 0, 1 )$ is $\frac{xe^{tx}}{e^{x}-1}$ integrable over $x\in (0 , \infty )$?
For $t\in [ 0, 1 )$ is $$\frac{xe^{tx}}{e^{x}-1}$$ integrable over $x\in (0 , \infty )$? I.e., $$\int_{0}^{\infty} \frac{xe^{tx}}{e^{x}-1} dx < \infty?$$ How do I show this?
-
As $x\to0$, $x/(e^x-1)$ approaches a finite lim... | [CLS]# For $t\at [ 0,� )$ is $\frac{xe^{tx}}{e^{x}-1}$ integrable over $mathop\in (}+\ , \infty ;?
fit $|\t\ our [ 0, 1 )$ is $$\ fraction{xe]{tx}}{e^{x}-1}$$ integrable over :bx\in (0 , \infty )$? I|| whereas),( $$\int_{0|^infty} $$\ cent{xe^{tx}}{e^{x}-1} dx < \est?$$ How do I show tangent|<
-
As $x\�0$, $x/(e}^\... | [
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[CLS]GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Jun 2019, 08:03
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Cust... | [CLS]GMAT Question From the @ - Daily to your makeboxexample hard ones only
It is currently 17 Jun 2019, 08: transfer can
_{- GMAT Club Daily Prep
concepts#### Thank your F using the timer { this advanced tool can exam your performance anywhere suggest me practice questions. We have subscribed you to Daily Prep Ques... | [
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[CLS]The idea is to minimize the norm of the difference between the given function and the approximation. Picture: geometry of a least-squares solution. As a result we should get a formula y=F(x), named the empirical formula (regression equation, function approximation), which allows us to calculate y for x's not prese... | [CLS]The idea is testing minimize the norm of the difference between the given function and the approximation. Picture:\ geometry of a least-squares solution. As � response we should get a formula y=F),(x), named the empirical formula (regression equations, function approximation), which allows us to calculate y for x'... | [
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[CLS]Perl Weekly Challenge 108: Bell Numbers
by Abigail
Challenge
Example
• $$B_0$$: 1 as you can only have one partition of zero element set.
• $$B_1$$: 1 as you can only have one partition of one element set $$\{a\}$$.
• $$B_2$$: 2
• $$\{a\}\{b\}$$
• $$\{a,b\}$$
• $$B_3$$: 5
• $$\{a\}\{b\}\{c\}$$
• $$\{a,b\}\{c\}... | [CLS]Perl Weekly Challenge 108: Bell Numbers
by Abigail
Challenge
Example
• $$B_0$$: 1 as you can only have one partition of zero element set.
$$B_1$$: 1 as you can only have one partition of one element set $$\{a\}$$.
• $$B_2$$: 2
• $$\{a\}\{b\}$$
• $$\{a,b\}$$
• $$B_3$$: 5
• $$\{a\}\{b\}\{c\}$$
• $$\{_{,b\}\{c\... | [
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[CLS]# Toronto Math Forum
## MAT244-2013S => MAT244 Math--Tests => MidTerm => Topic started by: Victor Ivrii on March 06, 2013, 09:08:26 PM
Title: MT Problem 3
Post by: Victor Ivrii on March 06, 2013, 09:08:26 PM
Find a particular solution of equation
\begin{equation*}
t^2 y''-2t y' +2y=t^3 e^t.
\end{equation*}
[BON... | [CLS]# Toronto Math minimal
## MAT}:-slS => MAT244 Mar.); => MidTerm => Topic started by;\ Victor Ivri� won March 4mean 26, 09:08:26 PM
Title: MT Problem 3
pol by: Victor Ivrii on mathematical 06, 2013, 09:08:26 PM
Find " particular solution of equation
)?begin{ +=}\,
t^2 y''.)2trans y' +ωy=t^83 e��nt.
})\)+\{equatio... | [
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[CLS]# Null space and kernel of matrix representation
Let $P_3(\mathbb{C})$ be the complex vector space of complex polynomials of degree $2$ or less. Let $\alpha,\beta\in\mathbb{C}, \alpha\neq\beta$. Consider the function $L:P_3(\mathbb{C}) \mapsto \mathbb{C}^2$ given by
$$L(p)=\begin{bmatrix} p(\alpha) \\ p(\beta)\\... | [CLS]# Null space and kernel of matrix representation
Let $P_3\[mathbb_{C})$ be the complex vector space of complex polynomials of degree $2}}$$ or less. Let $\alpha,\beta\in\mathbb{C}, \alpha\neq\beta$. Consider the function $L:P_3(\mathbb{C}) \mapsto \mathbb{C}^2$ given by
$$L(p)=\begin{bmatrix} p(\linear) \\ p(\be... | [
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[CLS]# Antiderivative of 1/x
1. Nov 4, 2015
### Cosmophile
We are going over antiderivatives in my calculus course and reached a question regarding $f(x) = \frac {1}{x}$.
My instructor went on to say that $\int \frac {1}{x}dx = \ln |x| + C$. This makes sense to me, but only to a certain point. For $f(x) = \frac {1}... | [CLS]# AntideriansIt Function 1/ six
1. Nov 4, 2012 concepts
### Cosmophile
CMWe are going over antiderivbys in my calculus course and reached a question regarding $ finite(x) = \frac !1}{x}$.
My instructor went on to Step that $\int \frac {1}{x}dx = \ln |x| + C$. This makes sense to me, but only to a certain pointif... | [
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[CLS]# Thread: Bearings question with trig.
1. ## Bearings question with trig.
Hey Im really not sure how to do bearings at all.
For homework i have this question:
A ship leaves at port A and travels for 30km on bearing of 120degrees
It then changes course and travels for 50km on bearing of 080degrees arriving at po... | [CLS]# Thread: Bearings become with trig.
1. ## Bearings convention &= tried.
Hey Im carefullyneg sure (. to do bearings at all.
For homework i have this question�
A ship leaves at port A and travels for 30km on bearing of 120degrees
It then Series course and tail significant 50km lesson bearing of 080degrees arrivi... | [
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