text stringlengths 172 11.8k | corrupted_text stringlengths 179 11.8k | input_ids listlengths 2.05k 2.05k | attention_mask listlengths 2.05k 2.05k | labels listlengths 2.05k 2.05k |
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[CLS]Commutative Property Of Addition 2. If A is an n×m matrix and O is a m×k zero-matrix, then we have: AO = O Note that AO is the n×k zero-matrix. Matrix Matrix Multiplication 11:09. We have 1. To understand the properties of transpose matrix, we will take two matrices A and B which have equal order. The identity mat... | [CLS]Commutative Property Of Addition 2.” If A is ω n× mm > and O is gave malgebrak More-mat, then weak have: AO &=& O changes that AO is the n×k zero-matrix. Matrix Matrix Multiplication 11:09. We hour 1. two understand the properties of transpose matrix,. needed will take twice matrices A and B which have equal order... | [
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[CLS]# Comparing the magnitudes of expressions of surds
I recently tackled some questions on maths-challenge / maths-aptitude papers where the task was to order various expressions made up of surds (without a calculator, obviously).
I found myself wondering whether I was relying too much on knowing the numerical valu... | [CLS]# Comparing the magnitudes of expressions of surds
I recently tackled some space on math!-challenge / maths- Ititude papers where the task was to order various expressions made up find startds (without a calculator,uous).
I found myself wondering Herm I was relying too much on knowing There numerical value of Sl... | [
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[CLS]# In Calculus, how can a function have several different, yet equal, derivatives?
I've been pondering this question all night as I work through some problems, and after a very thorough search, I haven't found anything completely related to my question. I guess i'm also curious how some derivatives are simplified ... | [CLS]# In Calculus, how can a function have several defined, yet equal, derivatives)*(
I've been ponderIntegr this question triangle night as I work Thus some problems, and after away very thorough search, Is haven't found anything outcomes related to my question. identity guess i'm also curious (. some derivatives ar... | [
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[CLS]# Math Help - working backwards - cubics
1. ## working backwards - cubics
Write an equation that has the following roots: 2, -1, 5
Answer key: x^3 - 6x^2 + 3x + 10 = 0
For quadratic equations, I use the sum and product of roots, this is a cubic equation, how do I solve this?
Thanks.
2. Originally Posted by s... | [CLS]!\ Math Help - working backwards (* cubics
1. ## working backwards - cubics
Write an equation to has typ following roots: 2, -1, 5
Answer key:nx^3 - 6 Excel^2 + 3 quant + 10 = 0
For quadratic equations, I use the sum and product of got, this is a C expressions, how do Its seven this\,\
Thanks.cccoc2bys True ... | [
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[CLS]# Work and time, when work is split into parts
I'm stuck on a particular type of work and time problems.
For example,
1) A,B,C can complete a work separately in 24,36 and 48 days. They started working together but C left after 4 days of start and A left 3 days before completion of the work. In how many days wil... | [CLS]# Work Rad time, when work is split into parts
I'm stuck on a particular type of work and time problems.centercccFor ex,
1) A,B,C can complete a work separately in 24These36 and 48 days. They states working together but C polyg after 4 days of start and A left 3 days before completion of test work. In how many |... | [
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[CLS]# Algebraic Manipulation
## Definition
Algebraic manipulation involves rearranging variables to make an algebraic expression better suit your needs. During this rearrangement, the value of the expression does not change.
## Technique
Algebraic expressions aren't always given in their most convenient forms. Thi... | [CLS]# Algebraic Manipulation
## Definition
Algebraic manipulation involves rearranging variation to make an algebraic expression Att suit your needs` During this rearrangement, the value of the expression does not change.
{\ Technique
Algebra Contin expressions aren't always given in their most convenient forms. T... | [
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[CLS]Inequality involving sums with binomial coefficient
I am trying to show upper- and lower-bounds on
$$\frac{1}{2^n}\sum_{i=0}^n\binom{n}{i}\min(i, n-i)$$
(where $$n\geq 1$$) in order to show that it basically grows as $$\Theta(n)$$.
The upper-bound is easy to get since $$\min(i, n-i)\leq i$$ for $$i\in\{0, \dot... | [CLS]I NOTquality involving sums with binomial coefficient
I am trying too show upper- any lower-bounds on
scientific$$\frac{1}{)))^n)}{sum_{i=000000}^n\binom{n}{i})\min)(vy, n-i)$$
( whole $$n.\geq /$$)}\ by order to step that it basically grows as ....Theta(n)$$.
Our upper-bound is easy to get since ~min(i., n- ... | [
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[CLS]The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one. The dimensions of $B$ are $3\times 2$ and the dimensions of $A$ are $2\times 3$. The dot product involves multiplying the corresponding elements in the row of the first matri... | [CLS]The main condition of matrix multiplication is that the number of columns of tell *)st May must equal to This number of rows of the 2nd one. The dimensions of $B$ are $3\times 2$ and the dimensions of $A$ are $2)\\times 3$. The dot product integer multiplying the corresponding information in the row of the first m... | [
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[CLS]# Definite Integral: $\int_0^1\frac{\ln^4(x)}{x^2+1}\,dx$
I'm trying to derive a closed-form expression for
$$I=\int_0^1\frac{\ln^4(x)}{x^2+1}\,dx$$
Letting $u=-\ln(x), x=e^{-u}, dx=-e^{-u}\,du$ yields
$$I=\int_0^{\infty}\frac{u^4e^{-u}}{e^{-2u}+1}\,du$$
Setting $u\to-u$ and manipulating the integrands yield
... | [CLS] ## Definite Integral: $\int[{0^1\frac{\ln^4(x)}{x^2+1}\,dx$
I'm trying to derive ''re-form expression for
$$I=\int_0^1\frac{\ln^4(x)}{bx\|_{�1}\,dx$$
Letting $u=-\ln(x), x=ert^{-u}, dx=-e^{-u}\,du$ yields
$$I=>ik_0^{\infty)}\frac{u^+4e^{-u}}{e^{-2urs}+ behind}\,du$$
Setting $u\to-u$ and manipulating the inte... | [
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[CLS]# Divisibility Rule for 9
I'm working through an elementary number theory course right now and I think I've come up with a proof here but wanted some feedback on my logic.
Question: If the sum of the digits in base 10 is divisible by 9, then the number itself is divisible by 9.
Proof: Suppose that $9|d_1+d_2+..... | [CLS]# Divisibility Rule for 9 Circ
I'm working through an elementary number theory course right now and I then I've come up with a program Euler but wanted some feedback on my logic.
Question: id the sum of Tr digits in base 10 (. divisible by 9, ten the number itself ' divisible blue 9.
Proof: Suppose that $9|d_1+d... | [
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[CLS]# What is the remainder when a_{2013} is divided by 7?
#### anemone
##### MHB POTW Director
Staff member
Consider a sequence given by $$\displaystyle a_n=a_{n-1}+3a_{n-2}+a_{n-3}$$, where $$\displaystyle a_0=a_1=a_2=1$$.
What is the remainder of $$\displaystyle a_{2013}$$ divided by $$\displaystyle 7$$?
#### c... | [CLS]# What is the remainder when a_{ wanted} is divided by 7?
#### anemone
##### MHB POTW Director circumference Heat member
giving a sequence given by $$\displaystyle a_enn=a_{n-1}+3a_{n ||2}+a_{n-3}$$, where $$\displaystyle a_0=-\a_1=))._2=};$$.
What Im the remainder of $$\displaystyle a \{2013'$ divided Both $$... | [
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[CLS]The radius of convergence is half the length of the interval of convergence. We noticed that, at least in the case of the geometric series, there was an interval in which it converged, but it didn’t converge at the endpoints. Show that the following alternating harmonic series converges: Series of Both Positive an... | [CLS]The radius of convergence is levels the length of the interval of convergence. We noticed that, at least in the case of the geometric series, there was an interval in which it converged, but it didn’t converge at the endpoints. Show that the following alternating harmonic series converges: Series of Both Positive ... | [
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[CLS]# Math Help - Trigonometry three dimensional question
1. ## Trigonometry three dimensional question
I need help to solve:
A cylinder with radius 4 cm and perpendicular height 15 cm is tilted so that it will just fit inside a 12 cm high box. At what angle must it be tilted?
Answer given at the back of the text b... | [CLS]&=\ Markov Help - Trigonometry three dimensional question
1. ## termigonotimes three dimensional confused course
I need help to solve:
A cylinder with radius 4 cm and perpendicularATH 15 cm gives tilted Series Trans it L just fit inside a 12mm high box. · what angle must α be tilted?
Answer given at the back of ... | [
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[CLS]# Golden Ratio and Fibonacci Numbers
Golden Ratio is considered to be one of the greatest beauties in mathematics. Two numbers $$a$$ and $$b$$ are said to be in Golden Ratio if $a>b>0,\quad and\quad \frac { a }{ b } =\frac { a+b }{ a }$ If we consider this ratio to be equal to some $$\varphi$$ then we have $\varp... | [CLS]# Golden Ratio magnitude Fibonacci Numbers
Golden Ratio is considered to neg one of Te greatest beauties in mathematics. to numbers $$!!$$ radical $$b$$ are said to be in Golden Rot if $a>b ->0,\ although and\quad \frac { a {\ b } |\frac { a+b }{ a }$ If we consider this ratio to Bin equal to some .$$varphi$$ the... | [
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[CLS]# Evaluating Triple integral
1. May 7, 2005
### MattL
I'm having trouble with evaluating
[Triple Integral] |xyz| dx dy dz
over the region (x/a)^2 + (y/b)^2 + (z/c)^2 <= 1
Do I need to use some sort of parametrisation for the region, and is there some way of dealing with the absolute value function without in... | [CLS]# Evaluating Triple integral
1. mar 7: 2005
### MattL Cent
I'm having trouble with evaluating
Cos[Triple Integrital] |xyz| dx dy dzcirc
)=\ the region (Ax/a)^2 + (y/b)^2 + (pez/c^*2 <= 1
Do I need to use some sort of parametrisation for the region, and is there some way of dealing with the abstract value funct... | [
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[CLS]# Proving or disproving basic facts about sequences in Real Analysis
I am self-learning real analysis from Stephen Abott's Understanding Analysis. In Exercise 2.3.7, the author asks to prove or disprove basic results on convergence. I'd like to verify my solution, to ensure, I've understood the concepts, and if p... | [CLS]# Proving or disproving basic facts But sequences in Real Analysis
I am self-learning real analysis from Stephen Abott's Understanding Analysis. In Exercise 2.3.7, the author asks to prove or disprove basic results on convergence expressions I'd like to verify my solution, to ensure, imaginary've understood the c... | [
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[CLS]Is it true that the only matrix that is similar to a scalar matrix is itself Hot Network Questions Was the title "Prince of Wales" originally claimed for the English crown prince via a trick? matrice scalaire, f Fizikos terminų žodynas : lietuvių, anglų, prancūzų, vokiečių ir rusų kalbomis. An example of a diagona... | [CLS]Is it true that the only matrix that is similar to a scalar matrix is itself Hot Network dimension Was the title "Prince of Wales" originally claimed for the English crown prince via · trick? ((rice scalaire, f Fizikos terminų žody net : lietuvių, anglų, prancūzų, valuesokiečių ir rusų kalbomis. An example of a di... | [
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[CLS]posted by Dina
Simplify the expression.
3 [ (15 - 3)^2 / 4]
a. 36
b. 108
c. 18
d. 9
1. TutorCat
http://www.jiskha.com/display.cgi?id=1285004701
2. Dina
???108
3. PsyDAG
3 (12^2/4) = 3 (144/4) = 3 * 36 = 108
Yes!
## Similar Questions
1. ### Math(radicals or square roots)
i need a explanation for this eq... | [CLS]posted by Dina
Simplify the expression.
3 [ (15 - 3)^2 / *]
a. 36
b. 108
c. 18
d. 9
1. TutorCat
http://www.jiskha.com/&-.cgi?id=1285004701
2. radicalina
ccc???108
3. Psy dxAG
3 (12^2/4) = 3 .$$144/4) = 3 * 36 = 108
Yes!
},\ Similar Questions
1. ### Math(radUD or square roots)
i need a explanation for t... | [
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[CLS]# Is “ln” (natural log) and “log” the same thing if used in this answer?
Find $$x$$ for $$4^{x-4} = 7$$.
Answer I got, using log, was $${\log(7)\over 2\log(2)} + 4$$
but the actual answer was $${\ln(7)\over2\ln(2)} + 4$$
I plugged both in my calculator and turns out both are the equivalent value.
Anyways, is ... | [CLS]# Is “ln” ( natural log) and “log” the same ten if used in this answer?
Find $$x,$$ for $$4^{x-4} = 7$$.code
Answer gives got., using log, was $${\log(})$.)\over 2\log(--)} + 4$$
but the actual answer was $${\ln(7)\over2\ln(2}}} + 4$$ccc
I plugged both in my calculator and turns out both are the equivalent value... | [
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[CLS]# $\{a_n\}$ be a sequence such that $a_{n+1}^2-2a_na_{n+1}-a_n=0$, then $\sum_1^{\infty}\frac{a_n}{3^n}$ lies in…
Let $$\{a_n\}$$ be a sequence of positive real numbers such that
$$a_1 =1,\ \ a_{n+1}^2-2a_na_{n+1}-a_n=0, \ \ \forall n\geq 1$$.
Then the sum of the series $$\sum_1^{\infty}\frac{a_n}{3^n}$$ lies i... | [CLS]# &=a_n\}$ be a sequence such that $a_{n+1}^2-2a_na_{n+1}-a*(n=0$, then $\ Simple_1^{\infty}\frac{a_n}{3^n}$ lies in $( Acc
Let $$\{a_agon\}$$ be a sequence of positive real numbers such that
$$a_1 =1,\ \ a_{n+1}^2-2a_na_{n+)}(}-a_n=0, \ \ \forall n\geq 1$$.
Then the sum of the series $$\sum_1^{\infty}\frac{a_n}... | [
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[CLS]For which primes p is $p^2 + 2$ also prime?
Origin — Elementary Number Theory — Jones — p35 — Exercise 2.17 —
Only for $p = 3$. If $p \neq 3$ then $p = 3q ± 1$ for some integer $q$, so $p^2 + 2 = 9q^2 ± 6q + 3$ is divisible by $3$, and is therefore composite.
(1) The key here looks like writing $p = 3q ± 1$. Wh... | [CLS]For which primes p iteration� Properties^}}$ + 2$ save prime?
Origin —ition Number True — Jones — part35 — Exercise 2.17 —
${\ for --p = 3$. If $p \neq03$ then $pp = 3q ± 1$ for some integer $q$, so $$(p^2 + 2 9q^2 â 6q + 3$ is divisible by $3$, and is here composite.
(1) The key here looks like); $ Comp = q ±... | [
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[CLS]1. ## Integrate [x^3/sqrt(1-x^2/k^2)]dx
Can someone please check my process, also please can you advise on an easier way to write mathematical notation on this forum?
Integrate ( x^3/(1-x^2/k^2))dx
where k is a constant.
Let u = x^2, dv = x/sqrt(1-x^2/k^2)
Integration by parts.
Integral fx = uv - integral vdu
... | [CLS]1. ## Integrate [x^3/sqrt(1-x^2/k^2)]dx
Can someone please check my process, also please can you advise on an easier way to write mathematical notation on this forum?
Integrate ( x^3/(1-x^2/k^2))dxackwhere k is a constant.
Let u = x^2, dv = x/sqrt(1-x^2/k^2)
Integration by parts.
Integral fx = uv - integral vd... | [
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[CLS]It is currently 20 Apr 2018, 13:06
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[CLS]# A Most Curious Algebraic Identity
I recently found a very interesting Algebraic Identity: $xyz+(x+y)(y+z)(z+x)=(x+y+z)(xy+yz+zx)$
What's so special about it? Note that going from one side of the equality to the other, all products are switched with sums, and all sums are switched with products!
This may be se... | [CLS]# A Most Curious Algebraic Identity
I recently found a very interesting Algebraic Identity: $xyz+( X+y)(y={z)(z+x)=( composition+y+z)(xy+yz+zx)$
What's so special about it? Note that going from one side fix the equality to the other, all products are switched with sums, and all sums are switched with products!oc... | [
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[CLS]1 Definition; 2 Examples; 3 Symmetric part of a tensor; 4 Symmetric product; 5 Decomposition; 6 See also; 7 Notes; 8 References; 9 External links; Definition. Decomposition of tensor power of symmetric square. (1.5) Usually the conditions for µ (in Eq. Decomposition of Tensors T ij = TS ij + TA ij symmetric and an... | [CLS]1 Definition; 2 Examples; 3 Symmetric part of a tensor; 4 Symmetric product; 5 Decomposition; 6 See also; 7 Notes; 8 References; 9 External links; Definition. Decomposition of tensor power of symmetric square. (1.5) Usually the conditions for µ (in Eq. Decomposition of Tensors T ij = TS ij -( TA ij symmetric and a... | [
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[CLS]# Yet another proof for $\zeta (2) = \frac { { \pi }^{ 2 } }{ 6 }$
Let us consider the integral
$\displaystyle i\int _{ 0 }^{ \pi }{ ln(1-{ e }^{ i\theta } } )d\theta$
Now using
$\displaystyle i\int _{ 0 }^{ \pi }{ ln(1-{ e }^{ i\theta } } )d\theta \\ \\ 1-{ e }^{ i\theta } = 1-cos\theta -isin\theta = 2sin(\fr... | [CLS]# Yet another proof for $\zeta -->2) = \frac { { \pi }^{ 2 :) }{ 6 }$ C
Let So consider the integral
$\displaystyle idea\int _{ 0 }^{ \pi }{ ln(1-{ e }^{ i'\ Contin }}$ )d#####theta$
Now using
$\displaystyle i}-\ implicit _{ 0 ${\ \pi }{ ln|=1-{ e }^{ i\theta)}} } )d\theta \\ \\ 1-{ e }^{ Im\theta } = *)|cos\th... | [
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[CLS]# Thread: Solving Exponential Equations (logs involved)
1. ## Solving Exponential Equations (logs involved)
Okay, so second question from my homework.... IT's a simple "Solve for x" question, but I can't figure out what to do in this case!
6^(3x)=4^(2x-3)
6^(3x)=2^(4x-6)
We can use the log laws .... And it's ... | [CLS]# these: Solving Exponential Equations <logs involved)
1. ## solves tail Exponential Equations (logs involved)
Okay, so second question from my homework.... IT's a simple "Solve for x" question, but I can't figure out what T do in this Che!
osc62^(3x)=4^(2x-3)
6^(3x)=2)^{-4x-6)(
We can use the log laws .... An... | [
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[CLS]# difference between scalar matrix and diagonal matrix
{ For example, $$A =\begin{bmatrix} 0\\ â3\\-1 \\1/2 \end{bmatrix}$$ is a column matrix of order 4 Ã 1. In a scalar matrix, all off-diagonal elements are equal to zero and all on-diagonal elements happen to be equal. When the order is clear from the contex... | [CLS]}_{ difference between scalar matrix and diagonal matrix
{ For example,).$$!) =\begin{bmatrix} 0\\ â3\\-1 \\1/2 \ finally{bmatrix}$$ is a column matrix of plotting 4 Ã 1 identical In a scalar matrix, all off-diagonal elements are equal to zero and all on-diagonal eliminate happen to be equal.wh the order � cle... | [
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[CLS]# Bipolar coordinate system
I want to extend some work presented in a paper "Analysis of TM and TE Modes in Eccentric Coaxial Lines Based on Bipolar Coordinate System" using SageMath. Is there any possibility to work with bipolar coordinate system in SageMath?
Thanks
edit retag close merge delete
Sort by » old... | [CLS]}\, Bipolar coordinate system
I want totally extend some work presented in a paper "Analysis of Tr and TE Modes in Eccentric Coaxial Lines Based on Bipolar Coordinate System" using Sage +way Is there any possibility to --> with bipolarance system in SageMath?
Thanks
edit sentenceag selection merge delete
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[CLS]In how many ways can we pair ourselves?
Say we have an even number of elements and we sort them into pairs in a way that every element belongs to a pair and no element belongs in two pairs.
Given $2n$ elements how many different arrangements of this sort can be made?
For example given elements named $1$, $2$, $... | [CLS]In how match ways candw pair ourselves?
Say we have an even number of elements and we shift them Inter pairs in a way that eq create belongs to a pair and no element belongs in This pairs.
Given $2n $ elements how many different arrangements of this sort can be Mac|\
For example given elements named $1$, $2$, "... | [
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[CLS]Does the "field" over which a vector space is defined have to be a Field?
I was reviewing the definition of a vector space recently, and it occurred to me that one could allow for only scalar multiplication by the integers and still satisfy all of the requirements of a vector space.
Take for example the set of a... | [CLS]Does Time "field" over which · vector space images defined have to be a ${?
I was reviewing the definition of a vector space repeated, did it occurred to me that one could allow for only scalar multiplication by the integers and still satisfy all of the requirements of a factor space.
Take for example the set of... | [
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[CLS]# If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
Let $f:A\rightarrow B$ and $g:B\rightarrow C$ be functions, prove that if $g\circ f$ is injective and $f$ is surjective then $g$ is injective.
I need advise or correction if something is incorrect with my proof. Thank you beforehand.
We mu... | [CLS]# If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
Let $f:A\rightarrow B$ and $g:B\rightarrow C$ be functions, prove that if $g\circ f$ is injective and $f$ is surjective then $g$ is injective.
I need advise or correction if something is incorrect with my proof. Thank you beforehand.
We mu... | [
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[CLS]It is currently 22 Nov 2017, 04:20
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[CLS]# Necklace combinations with three group of beads
I have a hard question about a way how many different necklaces can be made.
Suppose that we have the following restrictions:
1. We have 3 groups of beads:
All the beads in one group are completely identical. This means that if you put two triangle beads next t... | [CLS]# Necklace combinations with cart group of beads
I have a hard question about a way how many different neck roleav can bond made.
Suppose that we have the following restrictions:
0001. few have 3 groups of beads:
All the beads in one group are computation identical. T means that iter you put two triangle bead... | [
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[CLS]# Is $V$ isomorphic to direct sum of subspace $U$ and $V/U$?
Given a vector space $$V$$ and a subspace $$U$$ of $$V$$. $$V \cong U \oplus(V/U)$$ Does the above equation always hold? Where $$\oplus$$ is external direct sum. For finite dimensional vector space $$V$$, here is my attemp of prove:
Let dimension of $$... | [CLS]_{-\ Is $V$ isomorphic to direct sum of subspace $U$ and $V/U$?
Given a vector space $$V$$ and a subspace $$U$$ of $$V $$|$. $$V \conggg \oplus(V/U)$$ Does the above equation always hold? Where $$\oplus$$ is external direct sum. For finite dimensional vector space $$V$$, here is my attemp of prove:
whatever dim... | [
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[CLS]# Query on a Solution to the Problem: $\gcd(5a+2,7a+3)=1$ for all integer $a$.
I wish to show that the numbers $$5a+2$$ and $$7a+3$$ are relatively prime for all positive integer $$a$$.
Here are my solutions.
Solution 1. I proceed with Euclidean Algorithm. Note that, for all $$a$$, $$|5a+2|<|7a+3|$$. By Euclide... | [CLS]# Query never � sol to the Problem: $\g adjacent=\{5a+2,7a+3)=1$ for all integer $a$.oc
iply why to show Tr the numbers $$5a+two$$ and $$7a+3$$ are relatively prime for all positive integer�a$,$$
Here are my solutions.
Solution 1ING IS proceed with ed Algorithm. Note that, for all $${{$$,))$5a+2|<|7a+3|$$. By mi... | [
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[CLS]# For any arrangment of numbers 1 to 10 in a circle, there will always exist a pair of 3 adjacent numbers in the circle that sum up to 17 or more
I set out to solve the following question using the pigeonhole principle
Regardless of how one arranges numbers $1$ to $10$ in a circle, there will always exist a pair... | [CLS]# For any arrangment of numbers 1 to 10 in a circle, there will always exist a pair of 3 adjacent numbers in the circle that sum up to 17r more
I set out to solve the following question using the pigeonhole principle
â of how one arranges numbers $1$ to $10$ in a circle, there will always exist a pair of three a... | [
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[CLS]# To find number of real roots
Consider the equation $$x^5-5x=c$$ where c is a real number.
Determine all c such that this equation has exactly 3 real roots.
I know that between consecutive real roots of $$f$$ there is a real root of $$f'$$. Now $$f'$$ in this case is $$5x^4-5$$ which always has two real roots.... | [CLS]# this find number of real roots
Consider the equation $$x^5-5x=c$$ where cost is a real number.frac
Determine all c such tests this equation has exactly 3 real rootsplace
I know test dont consecutive real roots of $$f$$ there is � real root of $$f'$),$$ Now $$f'$$ inf this case is $$5xy^(4-5$$ which always has ... | [
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[CLS]# Difference between continuity and uniform continuity
Tags:
1. May 7, 2015
### Yunjia
I noticed that uniform continuity is defined regardless of the choice of the value of independent variable, reflecting a function's property on an interval. However, if on a continuous interval, the function is continuous on ... | [CLS]# Difference between continuity and uniform continuity
Tags:
1. May 7, 2015
### Y({\jia
I noticed tr uniform continuity is defined regardless of the choice of the value of independent variable, reflecting a convolution's property on an interval. your, if on a continuous interval, the function is continuous on e... | [
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[CLS]## Linear Algebra And Learning From Data Github
Each point correspondence generates one constraint on F. Complete Linear Algebra for Data Science & Machine Learning 4. My research interests lie in network science, statistical inference, causal inference, information theory, machine learning, data mining, and sign... | [CLS]## Linear alternate An Learning From tra suggestedithub
Each point correspondence generates one constraint on F. Complete Linear Algebra for Data Science & Machine Learning 4. My research interests lie in network courses, setting inference, causal inference, information theory, machine learning, test min, and sig... | [
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[CLS]It is also a matrix and also an array; all scalars are also vectors, and all scalars are also matrix, and all scalars are also array You can put this solution on YOUR website! See the picture below. Equal Matrices: Two matrices are said to be equal if they are of the same order and if their corresponding elements ... | [CLS]It is also · matrix and also an array with all scalars are × vectors, and all scalark are also matrix, and all scalars areas also array You can put this solution on YOUR website! See the partial below. Equal Matrices: thing matrices are Stack to be equal if they are of the same order and if their corresponding ele... | [
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[CLS]# Binomial theorem
Series binomial theorem series contents page contents binomial theorem notation n as a nonnegative integer proof of the binomial theorem proof when n and k are. The binomial theorem date_____ period____ find each coefficient described 1) coefficient of x2 in expansion of (2 + x)5 80 2) coeffici... | [CLS]# Binomial theorem
Series binomial theorem series contents page contents Sol theorem notation n as a nonnegative integer proof of the binomial theorem proof when n and k are. The binomial theorem date_____ period____ find each coefficient described 1) coefficient of x2 in expansion of (2 + x)5 80 2) coefficient o... | [
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[CLS]# Smallest set such that all arithmetic progression will always contain at least a number in a set
Let $$S= \left\{ 1,2,3,...,100 \right\}$$ be a set of positive integers from $$1$$ to $$100$$. Let $$P$$ be a subset of $$S$$ such that any arithmetic progression of length 10 consisting of numbers in $$S$$ will con... | [CLS]# Smallest set such that all arithmetic progression will always contained at Total a number in a set
Let "$S= \left\{ 1,2,3,...,100 \right\}$$ be a set of positive integers random $$1$$ to $$100$$. Let $$aps$$ be a subset of $$S$$ such that y arithmetic progression of length 10 consisting of numbers in $$S$$ will... | [
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[CLS]# Mutlivariable Calculus: Surface Area
This was a question a students had asked me earlier today regarding surface area.
Find the surface area of the hemisphere $x^2+y^2+z^2 = 4$ bounded below by $z=1$.
I decided to approach this problem using spherical coordinates and got the following
\begin{eqnarray} \int_{... | [CLS]# Mutlivariable Calculus: Surface Area
This was a question a students had asked me earlier today regarding surface area.
Find the surface area of the hemisphere $x^2+y^2+z^2 = 4$ bounded below by $z=1$.
I decided to approach this problem using spherical coordinates and got the following
\)),{eqnarray} \int_{0}... | [
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[CLS]Tag Archives: factoring
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 was g... | [CLS]Tag Archives: factoringosc
Infinite Ways to an infinityinite Geometric Sum
ex of my students, K, around I were Review t Series last Friday when she asked for � reminder why an definingges series someone to $\displaystyle `frac{g}{1-r}$ for first term g and common ratio r when $\left]{ r \We| < 1]$, I was glad sh... | [
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[CLS]# Distinguishable objects into distinguishable boxes
How many ways are there to distribute $15$ distinguishable objects into $5$ distinguishable boxes so that the boxes have one, two, three, four, and five objects in them respectively?
$\begin{gather} &\_\_\_ &\_\_\_ &\_\_\_ &\_\_\_ &\_\_\_ \\ &1 &2 &3 &4 &5 \en... | [CLS]# Distinguishable objects In distinguishable boxes
How many ways are there to distribute $15$ distinguishable objects into $}+$ distinguishable boxes so that the boxes haveoff, two, three, four”, and five objects in them respectively?
$\Step{gather} &\_\_\_ &\_\_\_ &\_\_\_ &\_\_\_ &\_\_\_ \\ ''1 &2 &3 &4 &5 \end... | [
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[CLS]GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 17 Aug 2018, 08:09
### 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]GMats Question of the Day - Daily to your Matbox; hard7 only
II digits currently 17 Aug 2018mean 08];09
###degmm Jacob Daily Polar
}+\ thing y for using the timer - this advanced tool '' estimate your performance and suggest Method practiceations| We have subscribates \\ to Daily Prep Questions via email.
Cus... | [
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[CLS]Evaluate: $\frac{1}{(1+1)!} + \frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}$ using combinatorics.
Evaluate $\frac{1}{(1+1)!} + \frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}$. This is from a combinatorics textbook so I'd like a combinatorial proof. I find doing this kind of problem difficult especially when you have to sum - I do... | [CLS]Evaluate: $\frac)}{1}{(1+1)!} + \frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}$ using combinatorics.
Evaluate $\ cent{1}{(1+1)!} + \frac{2}{(2+1)!}(...+\frac{n}{- lesson+1)!}}( This is from a combinatorics textbook so I'd like ? combinatorial proof. I findingoid this kind of problem difficult specify then you have to sum ... | [
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[CLS]Since a right kite can be divided into two right triangles, the following metric formulas easily follow from well known properties of right triangles. Okay, so that sounds kind of complicated. The triangle ABD is isosceles. It looks like the kites you see flying up in the sky. A second identifying property of the ... | [CLS]Since a right kite can be divided into two right triangles, the following metric formulas easily follow from well known properties of right triangles. Okay, so that sounds kind of complicated. The triangle ABD is isosceles. It looks like the kites you see flying up in the sky. A second identifying property of the ... | [
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[CLS]Fibonacci equality, proving it someway
$F_{2n} = F_n(F_n+2F_{n-1})$
$F_n$ is a nth Fibonacci number. I tried by induction but i didn't get anywhere
-
An answer just by induction on $n$ of the equality $F_{2n}=F_n(F_{n-1}+F_{n+1})$ is as follows:
For $n=2$ we have $3=F_4=(1+3)\cdot 1=(F_1+F_3)F_2$.
To go from... | [CLS]Fibonacci equality, proving it someway
$F_2n)}{\ = F_n(F_n>\2inf_{n-1})$
BC$F_n$ is a n Both Fib]\acci number. I tried Y induction but i'dxt get anywhere
ca!
.\ answer just by induction on $n $| of the equality {(F_{2 net}=F_n(F_{n-1}+F}+\n+1})$ is ask follows visual
For $n=))$ we have $3=F|\4=(1+3)\cdot 1=(F_... | [
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[CLS]# Solutions to Congruence Modulo 50
1. Jan 12, 2013
### knowLittle
1. The problem statement, all variables and given/known data
Find all solutions to the equation $35x\equiv 10mod50$
3. The attempt at a solution
gcd( 35,50)= 5
So, there is a solution to this, since 5| 10. Also, there is a theorem that guarant... | [CLS]# school to Cong temperatureence Modulo 50
}_ once Jan , 2013
### knowLittle
1 identity T problem statement, all gave and givenitsOne data
Find all solutions to these equation $35 extra\equiv 10mod 500$
calcul3. The attempt at a solution c
gcd( 30):}$,))= 5
ised, their is a solution to this formed since 5| 10.... | [
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[CLS]# Math Help - Complex numbers-finding real number pairs
1. ## Complex numbers-finding real number pairs
Hello,
I am having trouble with this question:
"Find all possible real number pairs p, q such that 3+5i/1+pi =q+4i"
Im sure it's easy but I think I am overlooking something. I multiplied both sides by the co... | [CLS]# Math Help - Complex numbers-finding real number pairs
1. ## Complex numbers-finding real number pairs
Hello,
I am having trouble with this question:
",Find all possible real number pairs p, q such that 3+5i/1+pi =q]}4i"
Im sure it's easy but I think I am overlooking something. I multiplied both sides by the ... | [
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[CLS]# What is the probability that Jan and Jon are chosen?
Jan , Jon and $10$ other children are in a classroom. The principal of the school walks in and choose $3$ children at random. What is the probability that Jan and Jon are chosen?
My approach:
Including Jon and Jan, number of ways of selection is $1\cdot1\cd... | [CLS]# What is the probability that → radicals Jon are chosen?
Jan , Jacob and $10$ other children are in a classroom. The principal of the school walks in and choose $3.$ children stack random. What is the probability that Jan and conjugate are chosen?
My quadrant,.
Including Jon and Jan likely number of ways of se... | [
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[CLS]# Number of ways to place $k$ non-attacking rooks on a $100\times 100$ chess board
I need to show that the number of ways to place $k$ non-attacking rooks (no two share the same column or row) on a $100\times 100$ chessboard is $k!{100 \choose k}^2$.
When I try to formulate this equation I end up getting ${100 \... | [CLS]# Number of ways topics place $k$ non-attacking ro) on a .$$100\times 100$ chess board specific
I need to show that Thanks number of ways to Pro $k$ non)- denoteacking recall) ( known two share the same columnstr row) on a $100\times 100$ chessboard is $ks! }_{100 \choose k}^two$.
When I try to formulate testing ... | [
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[CLS]# Permutation representation argument validity
#### kalish
##### Member
Hello,
I would like to check if the work I have done for this problem is valid and accurate. Any input would be appreciated. Thank you.
**Problem statement:** Let $G$ be a group of order 150. Let $H$ be a subgroup of $G$ of order 25. Consid... | [CLS]# Permutation representation argument validity
#### kalish
inc##### Member
Hello,
I would like to check if t work imply give done for this problem is valid and accurate. Any inputs would be appreciated. Thank you.
**Problem statement:** Res $G$ be aG of order 150. Let $H$ be a subgroup of $G$ of order 25. Consid... | [
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[CLS]# Spring Gun
1. Mar 7, 2014
### Steven60
I have a question about a spring gun. Suppose the barrel of a spring gun is placed horizontally at the edge of a horizontal table. You put say a marble in the barrel and compress the spring x cm and after releasing the marble it travels a horizontal distance of y cm befo... | [CLS]# Spring Gun
1. MAT 7, 2014
### Steven60
I have a question about a spring gun. Suppose the barrel of a spring gun is placed horizontally at the edge of a horizontal table. You put say a marble in the barrel and compress the spring x cm and after releasing the marble it travels a horizontal distance of y cm befo... | [
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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^ lesson<n!$)
I Sum rather new to mathematical induction. Specially inequalities, as seen here How T use mathematical induction He inequalities?. Thanks to that question”, I've been able to solve small of the form $1 + --frac}{-1}{2} + \frac{1}{3} + \TH + \frac{1}{n} \le... | [
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[CLS]### Bfs Time Complexity
Optimality : It is optimal if BFS is used for search and paths have uniform cost. For example, if the heuristic evaluation function is an exact estimator, then A* search algorithm runs in linear time, expanding only those nodes on an optimal solution path. In this tutorial, We are going to... | [CLS]###### Bfs Time Complexity
Optimality : It is optimal if BFS is used for search and paths have uniform cost. For example, if the heuristic evaluation function is an exact estimator, then A* search algorithm runs in linear time, expanding only those nodes on an optimal solution path. In this tutorial, We se going ... | [
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[CLS]The Chain Rule is used when we want to differentiate a function that may be regarded as a composition of one or more simpler functions. J'ai constaté que la version homologue française « règle de dérivation en chaîne » ou « règle de la chaîne » est quasiment inconnue des étudiants. While its mechanics appears relat... | [CLS]The Chain Rule is used when we want test differentiate a function that may be regarded as a composition of oner more terms functions. J'acci constaté que la version hourue française « règle de dérivation en cha correctnp » ou « radègle de la chaî 13 » est quasiment inconnue des étudiantsHow While its mechanics appe... | [
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[CLS]# Kernel of successive powers of a matrix
For any $n \times n$ matrix $A$, is it true that $\ker(A^{n+1}) = \ker(A^{n+2}) = \ker(A^{n+3}) = \dots$ ? If yes, what is the proof and is there a name to this theorem? If not, for what matrices will it be true? How can I find a counterexample in the latter case?
I know... | [CLS]# Kernel of successive powers of a matrix
For any $n \times n$ matrix $A$, is it true that $\ker(A^{n+1}) = \ker(A^{n+2}}{ = +\ker(A^{n+3}) = \ displacement$ ? If yes, what II the proof and is there a name to this there? If not, for what matrices will it be true? How can I didn a counterexample in the latter case... | [
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[CLS]Relative to the air, the paper is moving downwards, and so there will be an upward resistive force on the paper. https://study.com/academy/lesson/air-resistance-and-free-fall.html The question assumes there is a formula for projectile trajectory with air resistance. Q.1: A plane moving with a velocity of $$50 ms^{... | [CLS]Relative to the air, the paper is moving downwards)); and so there will be an upward resisten force on the paper. https://study.com/ Clickademy/lesson/air-resistance-andSomefree-fall.html The region assumes there ideas a formula for projectile trajectory with air resistance. quant.1text A plane moving with a veloc... | [
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[CLS]# How does the middle term of a quadratic $ax^2 + bx + c$ influence the graph of $y = x^2$?
Every parabola represented by the equation $$y = ax^2 + bx + c$$ can be obtained by stretching and translating the graph of $$y = x^2$$.
Therefore:
The sign of the leading coefficient, $$-a$$ or $$a$$, determines if the ... | [CLS]# How does the middle term of & quadratic $ax^2 + bsquare + c$ influence the graph of $y = x^2$?
vecEvery par Febola represented by the equation $$y = ax^2 + b cross + c$$ can be obtained by St and translating the [- of.$$y = x},\2$$.
)::
The sign of the definitely coefficient, $$-a$$ or $$a$$, determines if the... | [
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[CLS]# Cone shaped related rates of change question
A container is in the shape of a cone of semi-vertical angle $30^\circ$, with it's vertex downwards.
Liquid flows into the container at ${{\sqrt {3\pi } } \over 4}{\rm{ }}c{m^{^3}}/s$
At the instant when the radius of the circular surface of the liquid is 5 cm, fin... | [CLS]# Cone sp related rates of change question
A container is in the shape of a cone of semi-vertical angle $(30^\circ$, with im's vertex downdim.
laiquid flows into the container at ${{\sqrt {3\pi } } \^{- 4}{\rm{ }}c{m^{^3}}/s).$$oc
At the instant when the radius definition the circular surface of the liquid Δ 5 c... | [
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[CLS]1. watchmath
The term of the absolute series is $$|\arctan(1/n)|/n^2<\frac{\pi/2}{n^2}$$. But the series $$\sum 1/n^2$$ is convergent (since it is a p-series with p=2), so the absolute series converges. Then the series is absolutely convergent.
2. anonymous
how did you come up with pi/2/x^2
3. watchmath
the r... | [CLS]1. watchmath
The term of the absolute series is $$|\arctan(1/n)|/n^2<\frac{\pi/2}{n^2}$$. But the series $$\sum 1/n^2$$ is convergent (since it is a p-series with p=2), so the absolute series converges. Then the scal is absolutely convergent.
2. anonymousC
how did you come up with pi/2/ exterior^2
3.” watchmath... | [
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[CLS]# Power set of a set with an empty set
When a set has an empty set as an element, e.g.$\{\emptyset, a, b \}$. What is the powerset?
Is it: $$\{ \emptyset, \{ \emptyset \}, \{a\}, \{b\}, \{\emptyset, a\} \{\emptyset, b\}, \{a, b\}, \{\emptyset, a, b\}\}$$
Or
$$\{ \emptyset, \{a\}, \{b\}, \{\emptyset, a\} \{\emp... | [CLS]# Power set of a set with an empty set
When a set has an empty set asN element, e.g.$\{\emptyset, a, b \}$. What is the powerset?
Is it: $$\{ \emptyset, \{ \emptyset \}, \{a\}, \{b\}, \{\emptyset, a\} \{\emptyset, b\}, \{a, b\}, \{\emptyset, a),( b\}\}$$
Or
$$\{ \time, \{a\}, \{b\}, \{\emptyset, a\} \{\emptyse... | [
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[CLS]GMAT Changed on April 16th - Read about the latest changes here
It is currently 26 May 2018, 12:52
### 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.
Custo... | [CLS]GMAT Changed on April 01th - Read about the content changes here
It is currently 26 May 2018, 12:}}}
### G Im Club Daily Prep
#### Thank fully for using the timer - this ad tool can estimate your performance annual suggest more practice questions. We leave subscribed you to Daily Prep Questions via email.
Cus... | [
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[CLS]# Integration of secant
\begin{align} \int \sec x \, dx &= \int \cos x \left( \frac{1}{\cos^2x} \right) \, dx \\ &= \int \cos x \left( \frac{1}{1-\sin^2x} \right) \, dx \\ & = \int\cos x\cdot\frac{1}{1-\frac{1-\cos2x}{2}} \, dx \\ &= \int \cos x \cdot\frac{2}{1+\cos2x} \, dx \end{align}
I am stuck in here. Any h... | [CLS]# Integration of secant
\begin{align} \int \sec x \, dx &= \int \cos Express \left( \frac{1}{\cos^2x} \right) \, dx \\ * \int \cos x \left( \frac{1}{1-\sin^2x} \right) \, dx \\ & = \int\cos x\cdot\frac{1}{1-\frac{1-\cos2x}{2}} \, dx \\ &= \int \cos x \cdot\frac{2}{1+\cos2x} \, dx \end{align}
I am stuck in here. ... | [
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[CLS]But you might be surprised because nature seems to favor a particular numbers like 1, 2, 3, 5, 8, 13, 21 and 34. Lucas Sequences The above work on the Fibonacci sequence can be generalized to discuss any difference equation of the form where and can be any real numbers. The Fibonacci sequence is a series where the... | [CLS]But you might be surprised because nature seems to F a particular numbers like 1, 2, -->, 5 implemented 8, 13, 21 and Circ. Lucas Sequ expectation The above work on twice FibonAC sequence can be nice to discuss any difference equation of the form where and can be any real numbers. total Fibonacci sequence is a Sin... | [
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[CLS]# What is the dimension of two subspaces?
Let $V$ be the vector space with a basis $x_1, \ldots, x_9$ and $$V_1 = \{(a,a,a,b,b,b,c,c,c): a,b,c \in \mathbb{C}\}, \\ V_2=\{(a,b,c,a,b,c,a,b,c): a,b,c \in \mathbb{C}\}.$$ Then $V_1,V_2$ are subspaces of $V$. What is the dimension of $V_1 \cap V_2$?
I first try to fin... | [CLS]# What is the dimension of two subspaces?
Let ->V$ be the vector space with a basis $x_1, \ldots, x_9$ and $$V_}_ = \{(a,a,a,b,bi,b,c,c,c] a,b,c \in \mathbb{ Course}\}, \\ive_2=\{(a,.b,c,a,b,c..a,b,c): a,b,c \in \mathbb{C}\}.$$ Then " Ver_1,V'_2$ are subspaces of $V$. somewhat is the descent of ...V_1 \cap V_2$?
... | [
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[CLS]# Evaluating a double integral in polar coordinates
#### skatenerd
##### Active member
I've done this problem and I have a feeling it's incorrect. I've never done a problem like this so I am kind of confused on how else to go about doing it. The goal is to change the cartesian integral
$$\int_{-a}^{a}\int_{-\sqr... | [CLS]# Evaluating a obvious integral in polar coordinates
)}{\ skatenerd
##### Active model
IVar done this problem and :) have a Fig it's incorrect. I've never Determ a problem like this so I am kind of confused on having else to go about doing itWhat The goal is to change the cartesian integral
$$\int_{-a}^{~~}\int_... | [
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[CLS]# What kind of combinatorial problem is this?
Is there a theory from which the following problem comes? Does this type of problem have a name?
Find the largest possible number of $k$-element sets consisting of points from some finite set and have pairwise singleton or empty intersections.
I hope that was clear.... | [CLS]# What kind of deck problem is this?
Is there a theory from which the following problem comes? Does this type of problem have � name?
Find the largest pi number of $k),$$element saying consisting of power from some finite set and have pairwise singleton greater empty intersectionswhat
I hope that 120ression. If... | [
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[CLS]# Math Help - 1+2+3+...+n
1. ## 1+2+3+...+n
Hi, can anyone tell me why
1+2+3+...+n=n(n+1)/2
I can see that it works when I choose a number for n, but I don't really see how I could have come up with it myself.
2. ## Re: 1+2+3+...+n
I think I can explain it like that:
1, 2, 3, 4, 5, 6, ... n
This is an arit... | [CLS]# Math Help - 1+2^+3+...)_{n
1Definition ## 1+2+ indices+...+n
Hiius can anyone tell me why
1+2+3+ implemented+n'(n(n+1)/Two
I can see that it works when I choose a number for nTo but I don't really see how If could give come up with it myself.
2. ## Re: 1+two+3+...+n
MacI think I can explain it like that� s... | [
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[CLS]Question
# Assertion :If $$bc+qr=ca+rp=ab+pq=-1$$, then $$\begin{vmatrix} ap & a & p \\ bq & b & q \\ cr & c & r \end{vmatrix}=0\quad (abc,pqr\neq 0)$$ Reason: If system of equations $${ a }_{ 1 }x+{ b }_{ 1 }y+{ c }_{ 1 }=0,\quad { a }_{ 2 }x+{ b }_{ 2 }y+{ c }_{ 2 }=0,{ \quad a }_{ 3 }x+{ b }_{ 3 }y+{ c }_{ 3 }... | [CLS]Question
# Assertion :If $$bc+qr=ca+rp=ab+pq=-1$)$, then $$\begin{vmatrix} ap &G & p \\ bq & b & q \\ cr & c &π \/\{vmatrix}=0\osc (abcimalspqr_\neq 0)$$ Reason: If systeminf equations $${ a }_{ 1 }ient+{ b }_{ 1 }y+{ c }_{ 1 }=}\,,\quad { a }_{ 2 \}x+{ b }_{ 2 }y}{\_{ c }_{ 2 }$^{(0)_{ \quad a }_{ 3 }x+}^{\ $( }... | [
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[CLS]Binary search works on sorted arrays. Finding the Predecessor and Successor Node of a Binary Search Tree All implementation of finding sucessor or predecessor takes O(1) constant space and run O(N) time (when BST is just a degraded linked list) - however, on average, the complexity is O(LogN) where the binary … Re... | [CLS]Binary search works on Since arrays. defines the Predecessor and Seor Node of a Binary Search Tree All implementation of finding sucess))= or predecessor takes OK(1) constant space and run O(N) Te (when BST is just a degraded linked list) Gauss however,enn average, the complexity is O( edgesN) where the binary … R... | [
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[CLS]Question
# PQ and RS are two parallel chords of a circle whose centre is O and radius is $$10$$ cm. If PQ $$= 16$$ cm and RS $$= 12$$ cm. Then the distance between PQ and RS, if they lie.(i) on the same side of the centre O and(ii) on the opposite of the centre O are respectively
A
8 cm & 14 cm
B
4 cm & 14 cm
... | [CLS]Question
# PQ and RS air two parallel successiveords of a circle whose centre is O and radius is $$10$$ bottom. If PQ $$= 16 2000 cm and RS $$= 12$$ cm..., Then +|the distance between Pqu and RS, if they variety.(i*( on throw same says of the centre O and(ii) on the opposite found theory centre O are iterative
... | [
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[CLS]# If matrix product $AB$ is a square, then is $BA$ a square matrix?
## Problem 263
Let $A$ and $B$ are matrices such that the matrix product $AB$ is defined and $AB$ is a square matrix.
Is it true that the matrix product $BA$ is also defined and $BA$ is a square matrix? If it is true, then prove it. If not, find... | [CLS]# If matrix product $AB$ is a square, then is $BA).$$ a square matrix|<
C## Problem 263
Let $A.$$ and $B$ are matrices Sc that than matrix product $AB$ is defined and $AB$ is a scale matrix.
"? it There that the matrix product $BA$ ω also defined and $BA$ is at square matrix? μ it is true, then prove it. If not, ... | [
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[CLS]# Math Help - somebody please teach me to complete the square
1. ## somebody please teach me to complete the square
hello
could you please be that nice to teach me how to complete the square, step by step, i think i understand most of it, except when it comes to factorize, i'm being taught about ellipses and hy... | [CLS]# Math Help - somebody please teach me to complete the square
1. ## somebody please teach me to complete the square
hello
could you please be that nice to teach me how to complete the square, step by step, i think i understand most of it, except when it comes to factorize, i'm being taught about ellipses and hy... | [
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[CLS]# Proof by mathematical induction in Z
Is it possible to proof the following by mathematical induction? If yes, how?
$a\in \mathbb{Z} \Rightarrow 3$ | $(a^3-a)$
I should say no, because in my schoolcarrier they always said that mathematical induction is only possible in $\mathbb{N}$. But I never asked some ques... | [CLS]# Proof by mathematical induction in Z
Is it possible to proof the following by mathematical induction? If yes, how?
$a\in \mathbb{Z} \Rightarrow 3$ | $(a^3-a)$
I should say no, because in my schoolcarrier they origin said that mathematical induction is only possible in $\mathbb{N}$. But I never asked some ques... | [
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[CLS]# Conics Section : Properties
This Note is for Those who love to use Properties and some innovative Techniques while Solving Question of Conics Section ! These Properties are Highly reduce our Calculation and are very useful sometimes , Specially when we have Time Constrained !
So Please Share Properties and Tec... | [CLS]# Conics Section : Properties
This respectively is for Those who love to use Properties and some innovative Techniques while Solving Question of Conics Section ! These Properties are Highly reduce our Calculation and are very useful sometimes , Specially when we have Time Constrained !
So Please Share Properties... | [
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[CLS]# Having sign problem with algebraic fractions
• Jan 26th 2013, 05:48 PM
KevinShaughnessy
Having sign problem with algebraic fractions
Hi,
I'm having a problem with an algebraic fractions equation. It goes:
5/3(v-1) + (3v-1)/(1-v)(1+v) + 1/2(v+1)
The first thing I do is factor out the negative in the first fra... | [CLS]# Having sign problem with algebraic fractionsck
balls Jan 26th 2013, 05:48 PM
KevinShaughnessycent Suppose sign problem with algebraic fractions
Hi,
ocSo'm having a possibly with an algebraic fractions equation. It (-\|_
5/3)*(v-1) + ->3v-1)/(}&-v)(1+v) _ 1plement2(v+}}$)
The worst thing I do is few out Test n... | [
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[CLS]# 'If…then…' and '…if…' and '…only if…' and 'If… only then…' statements?
Suppose you have two statements A and B and "If A then B". I am trying to think of what this implies and alternative ways of writing this.
I think
"If A then B"
= A$\rightarrow$B
= "A is sufficient but not necessary for B. B is neither n... | [CLS]# 'If…then…' and '…if…' and '…only if…' and 'If… only then _' statements?
Suppose you have two statements A and B and "If A then Bination I am trying to talk of what this implies and alternative ways of writing this.
I think
"If A then $("
= A$\rightarrow$ ab
= "A is sufficient but not necessary for B. B � ne... | [
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[CLS]Confirm definite integral equals zero $\frac{\sin(x)}{(1-a\cos(x))^{2}}$
Is this statement about the definite integral of a particular function $F$ true? $$\int_0^{2\pi}F(x)\, \mathrm{d}x = \int_0^{2\pi}\frac{\sin(x)}{(1-a\cos(x))^2}\, \mathrm{d}x = 0 \ \text{ for }\ 0<a<1$$
I have evaluated this expression (in ... | [CLS]Confirm definite integral equals zero $\frac{\sin( x)}{[\1-a\cos(x))^{2}}$ c
Is this statement about the definite integral of a particular function $ft$ true? $$\int_0^{2\pi}F(x)\, \mathrm{d}x = \int_0^{2\pi}\frac{\sin(x)}{(1-a\cos(x))^2}\, \mathrm{d}x = 0 \ \text{ for }\ 0<a<1$$
I have evaluated this expression ... | [
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[CLS]# knapsack problem optimization
i {\displaystyle v_{i}} 2 The bounded knapsack problem (BKP) removes the restriction that there is only one of each item, but restricts the number In this variation, the weight of knapsack item items numbered from 1 up to , [ ∪ The knapsack problem or rucksack problem is a problem ... | [CLS]##### knaps� problem optimization
i {\displaystyle v_{i}} 2 The bounded knapsack problem (B topics) removes the r that there is only one of Che item, but restricts the number In this variation]/ the weight find onperp Oct item items numbered from 1 up to , [ ∪ The knpacy problem or rucksack problem is a problem i... | [
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[CLS]# Is my proof, by strong induction, of for all $n\in\mathbb{N}$, $G_n=3^n-2^n$ correct?
Let the sequence $G_0, G _1, G_2, ...$ be defined recursively as follows:
$G_0=0, G_1=1,$ and $G_n=5G_{n-1}-6G_{n-2}$ for every $n\in\mathbb{N}, n\ge2$.
Prove that for all $n\in\mathbb{N}$, $G_n=3^n-2^n$.
Proof. By strong i... | [CLS]# Is my proof, by strong induction, of for all $ hint\in\mathbb{N}$, $G_n=3^n-2^n$ correct?
Let the sequence $G_0, G _1, G_2, #$ be defined recursively as follows:
$G_0=0, G_1=1,$ and $G_n=5G_{n-1}-6G_{n-2}$ for every $n\in\)^{{N}, n\ge2$.
Prove that for all $n\in\mathbb{N}$, $G_n=3^n-2^n$.
Proof.� strong indu... | [
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[CLS]# applications using rational equations distance rate time answers
Translate the sentence to get the equation. Solve work-rate applications. Work problems often ask us to calculate how long it will take different people working at different speeds to finish a task. While traveling on a river at top speed, he went... | [CLS]# applications using rational equations distance rate time answers
subtractlate the se to get the equation. Solve �-rate applications. network problems often ask us to calculate how long it will take different people working at different speeds to finish a task. While traveling on a river at top sl, he went 10 m... | [
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[CLS]# Rate of water level for cone shaped water tank
A water tank in the form of an inverted cone is being emptied at the rate of $6$ ft$^3$/min. The altitude of the cone is $24$ ft, and the base radius is $12$ ft. Find how fast the water level is lowering when the water is $10$ ft deep.
I am not how to do this prob... | [CLS]# Rate of water level for cone set water tank
A water tank in the form finish an inverted cone is beingpsied a the rate of $}},$ ft$^3$/min. The altitude of the cone λ "24 $$\ ft, and Tri base David is $12$ ft. Find how fast the water level is lowering when the water is $ 101$ ft deep.
namely am not how to do t... | [
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[CLS]GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 25 Sep 2018, 02:33
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.
Customized
fo... | [CLS]GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 25 Sep 2018, 02:33
GMAT Club distributed Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed @ to deal Prep Questions via email.
oddized
fo... | [
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[CLS]# rank of product of matrices
is a linear combination of the rows of dimension of the linear space spanned by its columns (or rows). Proposition All Rights Reserved. be a the dimension of the space generated by its rows. If , The number of non zero rows is 2 ∴ Rank of A is 2. ρ (A) = 2. such C. Canadian0469. Find... | [CLS]# rank of product of matrices
is a linear combination of the rows of dimension of the linear space spanned by its columns (or rows). Proposition All Rights Reserved. be a the dimension of the space generated by its rowsoring If , The number of non zero rows is 2 ∴ Rank of A is 2 iterative ρ (A) = 2. such C. Canad... | [
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[CLS]Doing the math to determine the determinant of the matrix, we get, (8) (3)- … If the generated inverse matrix is correct, the output of the below line will be True. You don’t need to use Jupyter to follow along. Yes! Subtract 1.0 * row 1 of A_M from row 3 of A_M, and Subtract 1.0 * row 1 of I_M from row 3 of I... | [CLS]Doing the math to determine the determinant of the Mac, we get, (8) (3)- … Its the generated inverse matrix is correct, the output of the absolutely line will be True. You don•t need to use Jupyter test follow along. Yes! Subtract 1.0 * row 1 of arrays_M from row 3 of A_M, and SubWhat 1mean0 * row 1 of I_M fro... | [
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[CLS]# How do you calculate Arcsin?
Samuel Appleberry asked, updated on August 13th, 2021; Topic: arcsin
👁 390 👍 16 ★★★★☆4.7
Using arcsine to find an angle First, calculate the sine of α by dividng the opposite side by the hypotenuse. This results in sin(α) = a / c = 52 / 60 = 0.8666. Use the inverse function with ... | [CLS]# How do you locally Arcsin? sc
Sam Rel Appleberry—, updated on August 13th, 2021; Topopic: arcsin
👁 8 👍 16 ★★★★�4.7
Using arcsine to find an angle First,... calculate the sine of α by dividng the opposite side by t hypotenuse. Table results intersection sin(α) = a / c = 52 / 60 = 0.8666. Use Tang inverse func... | [
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[CLS]# x^2 = 4 versus x = 4 ^ (1/2)
#### avr5iron
##### New member
Can someone explain why the solution for x in x^2 = 4 is x = 2, -2
while the solution for x in x = 4 ^ (1/2) is 2
#### MarkFL
Staff member
1.) $\displaystyle x^2=4$
Now, using the square root property, we find:
$\displaystyle x=\pm\sqrt{4}=\pm2$
... | [CLS]# x^). = 4 versus axes == _{ ^ (1sigma2)
#### avr5iron
##### New member
Can someone explain why the solution for $[ in x^2 = (. its x = (., -2
..., the solution front x in x = 4 ^ (1)*2) is 2
#### MarkFL
Staff member
1.) $\displaystyle x^{2=8),$$
Now</ using the square root property, we find:
$\displaystyle ... | [
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# 𝘶-substitution warmup
AP.CALC:
FUN‑6 (EU)
,
FUN‑6.D (LO)
,
FUN‑6.D.1 (EK)
Before diving in... | [CLS]If you're seeing this message, it means we're having trouble loading external resources on or website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.ops are unblocked.
# 𝘶-substitution warmup
AP.CALC:
FUN‑6 (EU)col,
FUN‑6.D (LO)
,
FUN‑6.D.1 (EK)
Before diving i... | [
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[CLS]# Every function $f$ can be factored into $f = i \circ s$, with $i$ injective and $s$ surjective
As in the title, if $$X$$ and $$Y$$ are two arbitrary sets and $$f:X \to Y$$, my proof was by taking $$x_1 \sim x_2 \iff f(x_1) = f(x_2),$$ $$s: X \to X/\sim$$ to be the canonical surjection of $$X$$ into the quotient... | [CLS]# Every function $ Fl$ can be conored into $ half = i \circ s$, => $i$ injective and $s$ surjective
CAs in the title., if $$X$$ and $$Y$$ are two arbitrary sets and $$f:X \to $$, my proof was by taking $$x_)}} \ display x_2 \iff f(x_}_{) = factorization(x_2),$$ $$s: X \to X/\sim$$ to be the canonical surjection of... | [
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[CLS]# Prove $\gcd(nn!, n!+1)=1$
For any $n \in \mathbb{N}$, find $\gcd(n!+1,(n+1)!+1)$. First come up with a conjecture, then prove it.
By testing some values, it seems like $\gcd(n!+1,(n+1)!+1) = 1$
I can simplify what's given to me to $\gcd(nn!, n!+1)=1$ but I can't find out how to get it into the form I want it.... | [CLS]# printve $\gcd()nn!, n!+1)=1$cl
For any $n \in \mathbb{ NC}$, find $\gcd=>n!+1`n+1)!+1$) First come up with a conjecture, then prove it.
`` testing some values, it seems like $\gcd(n!+1,(n+1}(\+1) = 1$
I can simplify what's given to me type $\gcd])nn!, gain!+1)=1$$\ but I can Abstract find out how to get it int... | [
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[CLS]Is it possible to accomplish calculations of complex numbers specially in polar form with scientific calculators? This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. A calculator to calculate the equivalent impedance of a resistor, a capacitor and and i... | [CLS]Is it possible to accomplish calculations of Fib numbers specially in polar form with scientific calculators? This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. A calculator to calculate the equivalent impedance of a resistor, a capacitor and and induc... | [
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[CLS]# Probability chord of bigger circle intersects smaller circle
You are given two concentric circles $$C_1$$ and $$C_2$$ of radius $$r$$ and $$r/2$$ respectively. What is the probability that a randomly chosen chord of $$C_1$$ will intersect $$C_2$$?
Answer: $$1/2, 1/3$$ or $$1/4$$
The first method I used (gives... | [CLS]# Probability chord of bigger circle intersects smaller circle
You are given two concentric circles $$C_1$$ and $$C_2$$ of radius $$r$$ and $$r/2$$ respectively. What is the probability that a randomly chosen chord of $$C_1$$ will intersect $$C_2$$?
Answer: $$1/2, 1/3$$ or $$1/4$$
The first method I used (gives... | [
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[CLS]# What is the expected number of coin tosses needed to obtain a head?
Due to my recent misunderstandings regarding the 'expected value' concept I decided to post this question. Although I have easily found the answer on the internet I haven't managed to fully understand it.
I understood that the formula for the ... | [CLS]# What is the expected chain of coin Thesees needed to obtain a head?
Due to my requires misunderstandings regarding the�expected value' concept I decided to post this question. Although I have easily found the answer on the internet I haven't managed to fully understand it.
I understood that the formula for the... | [
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[CLS]# Prove that A Real Root Exists in [-1, 1]
#### anemone
##### MHB POTW Director
Staff member
Given $$\displaystyle f(x)=5tx^4+sx^3+3rx^2+qx+p$$ for $f(x)\in R$. If $r+t=-p$, prove that there is a real root for $f(x)=0$ in $[-1,1]$.
#### Ackbach
##### Indicium Physicus
Staff member
Some ideas:
We rewrite the p... | [CLS]# Prove that A Real Root Exists in [-1)), 1]
#### anemone
##### MHB POTW Director
Staff member
Given $$\displaystyle f(x)=5tx^4+sx^3=\3rx^2+qquadx+p$$ for $f(x)\in R$. If $r)+(t=-p$, prove that there is a real root for $f( x)=0$ in $[121,1]$.
_{\ Ackbach
##### Indicium Physicus
Staff member
Some ideas:
ccccWe ... | [
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[CLS]# find arc BN=?
#### Albert
##### Well-known member
Points A,B are on circle C ,segment MN is a diameter of circle C, and point P is on
segment MN , if :
$\angle CAP=\angle CBP =10^o ,\,\, \overset{\frown} {MA}=40^o,\,\, find :\,\, \overset{\frown} {BN}=?$
Last edited:
#### HallsofIvy
##### Well-known membe... | [CLS]# find arc BN=?
#### Albert
##### Well-known member
Points A,B are on circle C ,segment MN is a diameter of circle C, and point par is on
segment MN , if :
$\angle CAP=\angleccccBP =10^o ,\,\, \overset{\frown} {MA}=40^o,\,\, find :\,\, \overset{\frown} {BN}=?$
Last edited:
#### HallsofIvy
{| Well-known memb... | [
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[CLS]# Factoring a quadratic polynomial (absolute beginner level), are both answers correct?
I'm following video tutorials on factoring quadratic polynomials. So I'm given the polynomial:
$$x^2 + 3x - 10$$
And I'm given the task of finding the values of $a$ and $b$ in:
$$(x + a) (x + b)$$
Obviously the answer is: ... | [CLS]# Factoring a quadratic polynomial (absolute beginner level), are both answers correct?
I'm following video tutorials on factoring quadratic polynomials. So I'm given the polynomial:
$$x^2 + 3x - 10$$
And I'm given the task of finding the values of $a$ d $b$ induction:
$$(x + a) (x + b)$$
Obviously the answer... | [
50281,
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