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# Geometry and Topology Seminar
## Warwick Mathematics Institute, Term I, 2013-2014
Please contact Agelos Georgakopoulos, Damiano Testa, Saul Schleimer, or Caroline Series if you would like to speak or suggest a speaker.
Thursday October 3, 15:00, room MS.04 Max Karoubi (Universitée Paris Diderot) Algebraic and He... | open-web-math/open-web-math | |
# If $x^2+ax+b+1=0$ ($a,b\in\mathbb{Z}$) has integral roots, prove that $a^2+b^2$ is composite.
If $$x^2+ax+b+1=0$$ ($$a,b\in\mathbb{Z}$$) has integral roots, prove that $$a^2+b^2$$ is composite.
Would someone please help me to solve the above question? I'm not able to understand how I should proceed. Take $$b\ne-1$$... | HuggingFaceTB/finemath | |
## Categorical data
Contingency Table Confidence Interval for a Proportion Confidence Interval for the Difference Between Two Proportions Expected Frequencies Observed Frequencies Chi-Squared Goodness of Fit Test Chi-Squared Test of Association Chi-Squared Test of Homogeneity
Contingency Table
A contingency table i... | HuggingFaceTB/finemath | |
# What are Parse Trees (Derivation Trees)?
Derivations mean replacing a given string’s non-terminal by the right-hand side of the production rule. The sequence of applications of rules that makes the completed string of terminals from the starting symbol is known as derivation. The parse tree is the pictorial represen... | HuggingFaceTB/finemath | |
# Optimal Strategy for a Game
Optimal Strategy for a Game: Here, we are going to learn to find maximum outcomes in a two player game played in an optimal way. Submitted by Radib Kar, on February 03, 2020
## Description
This is a very popular interview problem to find maximum outcomes in a two player game played in a... | HuggingFaceTB/finemath | |
# Geometry
posted by .
The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.
A. 9
B. 13.5
C. 27
• Geometry -
I would say C but I'm not that far in Geometry
• Geometry -
area ratio = length ratio^2
if area ratio is 9
length... | HuggingFaceTB/finemath | |
My Math Forum inflection points analysis
Calculus Calculus Math Forum
January 12th, 2013, 01:28 PM #1 Newbie Joined: Jan 2013 Posts: 2 Thanks: 0 inflection points analysis Hello everybody, I have a hesitation about one problem. I have to analyse the following polynomial with respect to inflection points: x^4 + 2x... | HuggingFaceTB/finemath | |
##### Two coins are tossed once, where(i) E : tail appears on one coin, F : one coin shows head(ii) E : no tail appears, F : no head appearsDetermine P(E|F)
The sample space of the given experiment will be:
S = {HH, HT, TH, TT}
(i) Here, E: tail appears on one coin
And F: one coin shows head
E = {HT, TH} and F = {... | HuggingFaceTB/finemath | |
### Home > GB8I > Chapter 7 Unit 3 > Lesson CC3: 7.3.2 > Problem7-106
7-106.
Simplify and solve the following equations.
1. $\frac { 1 } { 4 } x + \frac { 1 } { 10 } = - \frac { 3 } { 20 } x - \frac { 7 } { 10 }$
Find a common denominator to get rid of the fractions.
Use $20$.
$5x+2=−3x−14$
Combine like terms and ... | HuggingFaceTB/finemath | |
# Triangle inequality - math word problems
In any triangle, the sum of the lengths of any two sides is greater than the length of the remaining third one. The triangle inequality is three inequalities that are true simultaneously. The inequalities result directly from the triangle's construction. If one side were long... | HuggingFaceTB/finemath | |
# Matematika Smp Klas 9 Materi Kesebangunan
Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house sea... | HuggingFaceTB/finemath | |
Related Articles
Find geometric sum of the series using recursion
• Difficulty Level : Expert
• Last Updated : 23 Apr, 2020
Given an integer N we need to find the geometric sum of the following series using recursion.
1 + 1/3 + 1/9 + 1/27 + … + 1/(3^n)
Examples:
```Input N = 5
Output: 1.49794
Input: N = 7
Output: ... | HuggingFaceTB/finemath | |
# MMXVI
The idea is to only use the year’s digits — preferably in order — and mathematical symbols $(+, -, \cdot , \sqrt{}, \lfloor\rfloor, \lceil\rceil, \dots)$ to create an equation that evaluates to a specific day of the month.
The 0th of December, 2016 would, for example, be $2 \cdot 0 \cdot 1 \cdot 6$, $2^0 - 1^6... | HuggingFaceTB/finemath | |
Web Development
# Master Dynamic Programming: The Simplified Beginner's Guide
Last Updated: 6th July, 2023
Vibha Gupta
Technical Content Writer at almaBetter
Dynamic Programming is a powerful technique used to solve complex optimization problems. It is widely used in computer science, mathematics, etc. Read more!
... | HuggingFaceTB/finemath | |
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# MEKANIKA TEKNIK
OLEH:
PRAMONO
FT UNNES
## Apa itu Mekanika?
Cabang ilmu fisika yang berbicara tentang
yang mengalami kerja atau aksi gaya
Mechanics
Rigid Bodies
Deformable Bodies
(Things that do not change shape) (Things that do change shape)
Statics
Dynamics
Fluids
Incompressible
... | HuggingFaceTB/finemath | |
1. ## limit of sequence
I need to show that the limit of the sequence,
$\frac{{n + 1}}{{{n^2}}} + \frac{{{{(n + 1)}^2}}}{{{n^3}}} + \cdots + \frac{{{{(n + 1)}^n}}}{{{n^{n + 1}}}}$
is e-1. What's sad is I have the solution in front of me and I can't understand the simple algebra.
$\frac{{n + 1}}{{{n^2}}}\left[ {\fra... | HuggingFaceTB/finemath | |
# types of angles working model – maths exhibition – diy – simple and easy steps | DIY pandit
Creating a working model to demonstrate different types of angles for a math exhibition using cardboard and paper can be a fun and educational project.
Here’s a simple and easy DIY (Do It Yourself) project that showcases var... | HuggingFaceTB/finemath | |
# Find the expectation of an exponential distribution estimator
So we've got a sample data coming from exponential distribution with parameter $$\lambda$$, and we take an estimator $$\lambda_n = \frac{n}{X_1+X_2+\cdots+X_n}$$.
I need to show that this is a biased and consistent estimator. Normally what you'd do is sa... | HuggingFaceTB/finemath | |
IB exams A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
1
2015-05-02T14:48:37+05:30
This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Br... | HuggingFaceTB/finemath | |
# Search by Topic
#### Resources tagged with Manipulating algebraic expressions/formulae similar to Almost Total Inequality:
Filter by: Content type:
Stage:
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##### Stage: 4 Challenge Le... | HuggingFaceTB/finemath | |
Simplifying Expressions like $-a(3b - 2c - d)$
Now we're ready to look at several extensions of the distributive law. Recall that the ‘basic model’ of the distributive law is: For all real numbers $\,a\,,$ $\,b\,,$ and $\,c\,,$ $\,a(b+c) = ab + ac\,.$
There may be more than two terms in the parentheses:
$a(b + c + d... | HuggingFaceTB/finemath | |
# Operando tribochemical formation of onion-like-carbon leads to macroscale superlubricity
## Abstract
Stress-induced reactions at the sliding interface during relative movement are known to cause structural or chemical modifications in contacting materials. The nature of these modifications at the atomic level and f... | open-web-math/open-web-math | |
# mW to dBm Conversion Milliwatt to dBm power converter
Decibel conversion of electric power units. mW to dBm (dB-milliwatt) and/or dBW (dB-Watt). Here is the answer to the question: Convert 66 mW to dBm or 66 mW to Decibel-Watts. Use the calculator below to convert any mW values to dBm or dBW.
### mW to dBm / W to d... | HuggingFaceTB/finemath | |
# Monty Hall Proof – The Formula
Get the free App – Monty Hall Game with Monty Hall Proof.
Monty Hall Proof – The Formula is here. My two previous posts described the Monty Hall Problem – Can You Solve This Maths Puzzle? and Monty Hall Solution – Advanced! Well, this is the next installment of the trilogy, a simple m... | HuggingFaceTB/finemath | |
# Prove or Disprove: ∃x ∈ N such that ∀y ∈ N, 2x ≤y + 1
The first thing that I tried to do is: let y be an arbitrary natural number. I then tried to choose a value for x, but I cannot think of a value in which 2x ≤ y + 1..
So I then tried to prove the negation: ∀x ∈ N, ∃y ∈ N, 2x > y + 1
So I then let x be an arbitr... | HuggingFaceTB/finemath | |
### Free Online Practice Test for Bank/Government Examination
Online Practice Test
In this online Practice Test Series we are going to share some most important Questions from various Subjects including reasoning, Maths, Current affairs and other. Recently we share Free GK Quiz based on Current Affairs those who miss ... | HuggingFaceTB/finemath | |
(13 votes, average: 4.08 out of 5)
# Example of Cascaded Integrator Comb filter in Matlab
by on July 1, 2007
## Equivalence of Moving Average and CIC filter
Let me briefly share my understanding on the cascaded integrator comb (CIC) filter, thanks to the nice article. For understanding the cascaded integrator comb ... | HuggingFaceTB/finemath | |
# Diophantine equation: x^2 - p*y^2 = -4
Warut Roonguthai warut822 at gmail.com
Mon Aug 6 01:34:56 CEST 2007
```Recently, there was a discussion in the number theory mailing list
about the existence of a solution to the Diophantine equation: x^2 -
p*y^2 = -4 when p is a prime of the form 8k + 5 and x, y are odd.
(No... | HuggingFaceTB/finemath | |
## Intermediate Algebra (12th Edition)
$y=3x$
$\bf{\text{Solution Outline:}}$ Use the Slope-Intercept Form to find the equation of the line with the following characteristics: \begin{array}{l}\require{cancel} m=3 \\\text{Through: } (0,0) .\end{array} Express the answer in Slope-Intercept Form. $\bf{\text{Solution Deta... | HuggingFaceTB/finemath | |
Question
# A particle starts from rest at time t=0 and moves on a straight line with acceleration as plotted in figure. The speed of the a particle will be maximum at time
A
1 s
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B
2 s
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS cours... | HuggingFaceTB/finemath | |
# Large Numbers and One Million
Large numbers are seldom used by ordinary people like us. Most of our lives, we only use numbers less than 100. We usually have 3-5 siblings, 5-10 friends, 30-40 classmates per academic year, 80 books.
Money is probably the first quantity that we count in thousands. A baseball or baske... | HuggingFaceTB/finemath | |
# Complex quadratic polynomial
A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.
## Properties
Quadratic polynomials have the following properties, regardless of the form:
• It is a unicritical polynomial, i.e. it has one finite critical point in the compl... | HuggingFaceTB/finemath | |
# A person borrows \$10000 and agrees to repay a loan in equal instalments over 20 years. Interest is 12% pa on any money owing compounded quarterly. Solve this using the present value formula ( he needs the money now )
`P= (x(1- (1+i)^-n))/ i` substitute all the known values
`10 000= (x(1-(1+ 0.12/4)^-(20times 4))... | HuggingFaceTB/finemath | |
## College Physics (4th Edition)
The required fractional change in pressure is $0.021$
We can find an expression for the original pressure: $P_1V = nRT_1$ $P_1 = \frac{nRT_1}{V}$ We can find an expression for the new pressure: $P_2V = nRT_2$ $P_2 = \frac{nRT_2}{V}$ We can divide $P_2$ by $P_1$: $\frac{P_2}{P_1} = \fra... | HuggingFaceTB/finemath | |
# Mechanical Engineering - Thermodynamics - Discussion
### Discussion :: Thermodynamics - Section 1 (Q.No.25)
25.
If the value of n = 0 in the equation pvn = C, then the process is called
[A]. constant volume process [B]. adiabatic process [C]. constant pressure process [D]. isothermal process
Explanation:
No an... | HuggingFaceTB/finemath | |
# Rule of 72 The Rule of 72 is a simple calculation that can be used to estimate the amount of time it will take for an investment to double, no calculator necessary! Well I concede, maybe a basic one…unless you can divide numbers like 3.4 into 72 in your head, in which case, props to you…but most probably can’t, so gr... | HuggingFaceTB/finemath | |
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 21 Oct 2019, 05:34
### 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.
Customize... | HuggingFaceTB/finemath | |
# Exploring 3rd Grade Math With Jori
Sale ends in
Teacher: Jori
Customers Who Have Viewed This Course: 1328
\$149.00
\$67.00
#### 0 Introduction 07:50
This course dives into the mathematics of the 3rd grade. The teacher of the course finds reasons to study each different area, making it easier for the students to mo... | HuggingFaceTB/finemath | |
html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11p... | HuggingFaceTB/finemath | |
# Sarin learns Perimeter, Area and Volume in school part 110 (Math Question)
Standard
The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singap... | HuggingFaceTB/finemath | |
# WHY do harmonics happen?
The answers to the question 'How do harmonics work?' were most interesting.
OK, that's the HOW it happens. But WHY does it happen ? What is the physics here ? Why doesn't a guitar string vibrate at one frequency only?
-
Vibrational Modes: en.wikipedia.org/wiki/Normal_mode – Caleb Hines May... | HuggingFaceTB/finemath | |
does 8b−10+b+3b+2=7+2b+10b−18−3 have a solution
Question
does 8b−10+b+3b+2=7+2b+10b−18−3 have a solution
in progress 0
4 days 2021-07-20T11:04:44+00:00 1 Answers 3 views 0
No.
Step-by-step explanation:
If we combine all like terms first on the left, then the right-
We will have a solution of
-8+12b=12b-14
This... | HuggingFaceTB/finemath | |
Convert kilometers to feet (km to ft conversion)
1 kilometer (km) = 3280.84 feet (ft)
How to convert kilometers to feet?
To convert kilometers to feet, multiply the kilometer value by 3280.84. Hence, 1 kilometer equals 3280.84 feet.
• 1 kilometer = 3280.84 feet
• 2 kilometers = 6561.68 feet
• 3 kilometers = 9842.52... | HuggingFaceTB/finemath | |
# To 200 g of a 30% KBr solution was added 50 g of the same acid. What% concentration of the solution will you get?
First, we find the mass of KBr in the initial solution. We use the following formula.
W = m r.v / mr-ra × 100%.
m r.v = m solution × W / 100% = 200 × 0.3 = 60 g KBr.
Next, we find the entire mass of the ... | HuggingFaceTB/finemath | |
1. ## 5 Trig Problems
moved!
2. Originally Posted by Macabro
$3^{2 - 3x} = 4^{2x + 1}$
Taking the ln of both sides:
$ln \left ( 3^{2 - 3x} \right ) = ln \left ( 4^{2x + 1} \right )$
$(2 - 3x)~ln(3) = (2x + 1)~ln(4)$
which is now simply a linear equation in x.
-Dan | HuggingFaceTB/finemath | |
## Thursday, May 2, 2013
### Calculation of interest on amortized loans
Interest is being charged on each payment period if there is no exception. The loan amount influences the interest. For moderate amount, the interest is moderate and for big amount of loan such car or home loan, the interest is charged much. In m... | HuggingFaceTB/finemath | |
# Onto Proof
• Feb 24th 2009, 06:34 PM
yvonnehr
Onto Proof
Can someone give me some feedback, please?
********
f: Ζ⇒Ζ
f(x) = { x/2 if x is even, 0 if x is odd
Prove whether f is onto and one-to-one.
Here's my proof.
******
Proof. To show that f is onto, let b∈Ζ. Consider the 2 following cases:
1. If b=0, f(x)=0 imp... | HuggingFaceTB/finemath | |
# Bounds for integral
How can one prove that assuming $n>1$ there exists an $c>0$ such that:
$$S_n = \int\limits_{x=0}^{\infty} e^{-\dfrac{(\sqrt{x}-1)^2}{2n}} dx <cn$$
I can plug the integral into WA (assuming $n$ is real) and get the result that way but is there a nice way to derive the inequality by hand? In fact... | HuggingFaceTB/finemath | |
# The LCM (1,000,000,000,000 and 1,000,000,000,000) = ? Calculate the Least Common Multiple, LCM, of the Numbers
## The least (the lowest) common multiple, LCM: the latest 10 calculated values
What is the least (the lowest) common multiple, LCM, of the numbers 1,000,000,000,000 and 1,000,000,000,000 and how to calcu... | HuggingFaceTB/finemath | |
# Divisors of 3610
## Divisors of 3610
The list of all positive divisors (that is, the list of all integers that divide 22) is as follows :
Accordingly:
3610 is multiplo of 1
3610 is multiplo of 2
3610 is multiplo of 5
3610 is multiplo of 10
3610 is multiplo of 19
3610 is multiplo of 38
3610 is multiplo of 95... | HuggingFaceTB/finemath | |
# 56998 (number)
56,998 (fifty-six thousand nine hundred ninety-eight) is an even five-digits composite number following 56997 and preceding 56999. In scientific notation, it is written as 5.6998 × 104. The sum of its digits is 37. It has a total of 2 prime factors and 4 positive divisors. There are 28,498 positive in... | HuggingFaceTB/finemath | |
Alternative Form of Goldbach's Conjecture
The Goldbach Conjecture states that every number from 4 onwards can be written as a sum of primes in at least one way. It is equivalent to the statement that every number can be written as a sum of three primes.
For, suppose the Goldbach conjecture holds. Then for
$n \ge 4, \;... | HuggingFaceTB/finemath | |
# 1024448 (number)
1,024,448 (one million twenty-four thousand four hundred forty-eight) is an even seven-digits composite number following 1024447 and preceding 1024449. In scientific notation, it is written as 1.024448 × 106. The sum of its digits is 23. It has a total of 7 prime factors and 14 positive divisors. Th... | HuggingFaceTB/finemath | |
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# A simple question on rotation
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
4 replies to this topic
### #1yasmin_bd Members - Reputation: 121
Lik... | HuggingFaceTB/finemath | |
# Difference between position time, velocity time and acceleration time graph
1. Sep 14, 2011
### h2chawwaa
What is the difference between position time graph, velocity time graph and acceleration time graph and how would each of them look like when drawn?
2. Sep 14, 2011
### easwaran.sr
exponential, ramp,straigh... | HuggingFaceTB/finemath | |
# Digital Principles and System Design
Share this
Systems design implies a systematic approach to the design of a system. It may take a bottom-up or top-down approach, but either way the process is systematic wherein it takes into account all related variables of the system that needs to be created—from the architect... | HuggingFaceTB/finemath | |
# Question: What Is The Greatest Common Factor Of 15 And 22?
The GCF of 15 and 22 is 1.
## What is the greatest common factor of 22?
GCF of 22 and 44 by Listing Common Factors
• Factors of 22: 1, 2, 11, 22.
• Factors of 44: 1, 2, 4, 11, 22, 44.
## What is the greatest common factor of 15?
The greatest common fact... | HuggingFaceTB/finemath | |
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### Grade 8 - Mathematics6.10 The Power of a Quotient Property - III
Example: (a2b3/c)3 = _____. a2*3b3*3/c1*3 = a6b9/c3 Directions: Solve the following problems. Also... | HuggingFaceTB/finemath | |
Predicting a coin toss
Published on
I flip a coin and it comes up heads. What is the probability it will come up heads the next time I flip it?
“Fifty percent,” you say. “The coin tosses are independent events; the coin doesn’t have a memory.”
Now I flip a coin ten times, and ten times in a row it comes up heads. S... | HuggingFaceTB/finemath | |
# How do you evaluate 4\frac { 4} { 7} \div \frac { 4} { 9} ?
Mar 4, 2017
$10 \frac{2}{7}$
#### Explanation:
Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a number looks without changing its inherent value.
4 -> color(green)(4color(red)(xx1)" " =" " 4color(... | HuggingFaceTB/finemath | |
## Number Series Practice Set 11 : Quantitative Aptitude
### Share Post:
Dear Students, Here, we are going to provide some questions of number series. given questions in set 11 are generally asked in SBI,IBPS PO, IBPS clerk exams. Prepare Exams gives a chance to test yourself that will help you testing your prepartio... | HuggingFaceTB/finemath | |
# gaussian elimination
• Jul 9th 2006, 02:07 AM
cheesepie
need help urgent !!
Gaussin Elimation
1)x+2y+6z=12
2z=2
-3x-6y-9z=-27
2)x-y+z=22
2y-z=-23
2x+3y=-11.2
3)x+2y+4z=7
3x+y+4z=-2
2x+9y-2x=10
4)x+2y+4z=7
3x+y+4z=-2
2x+9y-2z=10
• Jul 9th 2006, 06:37 AM
Soroban
Hello, cheesepie!
#1 is a set of dependent equation... | HuggingFaceTB/finemath | |
# How Does a Uniform Electric Field Affect Charge Density Distribution?
• smantics
In summary: But if the electric field is not a constant, then the charge density can be anything, right? In summary, the conversation discusses the concept of divergence and how it relates to the charge density distribution in a space w... | HuggingFaceTB/finemath | |
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# Does Money Really Double Every 7 Years? How Can The Rule Of 72 Help You?
Rule 72 provides a simple method for calculating the time frame in which you can double your money. You may have found additional useful formulas for calculatin... | HuggingFaceTB/finemath | |
# Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
Result
S = 92.006 cm2
#### Solution:
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
B... | HuggingFaceTB/finemath | |
### Home > CC1 > Chapter 6 > Lesson 6.1.3 > Problem6-36
6-36.
Multiply the following fractions. 1. $\frac { 7 } { 8 } \cdot \frac { 5 } { 6 }$
Multiply the numerators together and the denominators together.
$\left ( \frac{7}{8} \right )\left ( \frac{5}{6} \right )=\frac{(7)(5)}{(8)(6)}$
Now, simplify the fractio... | HuggingFaceTB/finemath | |
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# Number of Provinces LeetCode Solution
## Problem – Number of Provinces
There are `n` cities. Some of them are connected, while some are not. If city `a` is connected directly with city `b`, and city `b` is connected directly with city `c`, then city `a` is connect... | HuggingFaceTB/finemath | |
# 1739 (number)
1,739 (one thousand seven hundred thirty-nine) is an odd four-digits composite number following 1738 and preceding 1740. In scientific notation, it is written as 1.739 × 103. The sum of its digits is 20. It has a total of 2 prime factors and 4 positive divisors. There are 1,656 positive integers (up to... | HuggingFaceTB/finemath | |
# Calculating Interest Rate in TVM Problems
Interest rate is a percentage measure of interest, the cost of money, which accumulates to the lender.
The interest is either paid through periodic payments, for example in case of bonds, or accumulated over the period of loan/investment such that it is paid at the maturity... | HuggingFaceTB/finemath | |
X
X
# Calculate the Greatest Common Factor or GCF of 1166
The instructions to find the GCF of 1166 are the next:
## 1. Decompose all numbers into prime factors
1166 2 583 11 53 53 1
## 2. Write all numbers as the product of its prime factors
Prime factors of 1166 = 2 . 11 . 53
## 3. Choose the common prime fac... | HuggingFaceTB/finemath | |
# Integrate $\int_{1}^{2}\frac{\ln x}{\ln x + \ln(3-x)}dx$ Option 1) 1 Option 2) 1/2 Option 3) 3/2 Option 4) 2
As we learnt
Properties of Definite Integration -
$\int_{a}^{b}f\left ( x \right )dx= \int_{a}^{b}f\left ( a+b-x \right )dx$
$\int_{a}^{b}\frac{f\left ( x \right )}{f\left ( x \right )+f\left ( a+b-x \rig... | HuggingFaceTB/finemath | |
College Physics for AP® Courses
# Test Prep for AP® Courses
College Physics for AP® CoursesTest Prep for AP® Courses
### 10.3Dynamics of Rotational Motion: Rotational Inertia
1.
A piece of wood can be carved by spinning it on a motorized lathe and holding a sharp chisel to the edge of the wood as it spins. How do... | HuggingFaceTB/finemath | |
Solutions by everydaycalculation.com
1st number: 4/18, 2nd number: 1 2/10
4/18 + 12/10 is 64/45.
1. Find the least common denominator or LCM of the two denominators:
LCM of 18 and 10 is 90
2. For the 1st fraction, since 18 × 5 = 90,
4/18 = 4 × 5/18 × 5 = 20/90
3. Likewise, for the 2nd fraction, since 10 × 9 = 90,
12... | HuggingFaceTB/finemath | |
# What is the standard form of y= (3x-5)(2x+3)(x+5)?
May 16, 2018
$6 {x}^{3} + 29 {x}^{2} - 20 x - 75 - y = 0$
#### Explanation:
expand the brackets.
Expanding the first two brackets give you:
$y = \left(6 {x}^{2} - x - 15\right) \left(x + 5\right)$
Expand the rest of it gives you:
$y = 6 {x}^{3} + 29 {x}^{2} - ... | HuggingFaceTB/finemath | |
# Non-unique Elements
Elementary+
We have prepared a set of Editor's Choice Solutions. You will see them first after you solve the mission. In order to see all other solutions you should change the filter.
If you have 50 different plug types, appliances wouldn't be available and would be very expensive. But once an e... | HuggingFaceTB/finemath | |
# Tutorial:Ideal Orbits for Communication Satellites
With the additions in Communications networks in 1.2, getting continious communication in any given system is an important factor. While the exact method of execution depends on personal taste there are fairly easy ways to set up a Comm network, even in early career... | HuggingFaceTB/finemath | |
Is Tonelli's Theorem a Useful Tool for Determining the Existence of Integrals?
• HeinzBor
In summary, Measure theory analysis is a branch of mathematics that deals with the study of measures, which are used to quantify the size or extent of a set. It is important as it provides a foundation for other fields and helps ... | HuggingFaceTB/finemath | |
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Difference between revisions of "2017 AIME II Problems/Problem 6"
Problem
Find the sum of all positive integers $n$ such that $\sqrt{n^2+85n+2017}$ is an integer.
Solution 1
Manipulating the given expression, $\sqrt{n^2+85n+2017}=\frac{1... | HuggingFaceTB/finemath | |
(G) Geometry Categories All categories Not categorized (G) Geometry (MD) Measurement and Data (NBT) Number and Operations in Base Ten (OA) Operations and Algebraic Thinking Prioritized Standards
# Geometry
## Narrative for the (G) Geometry
In Grade 1, students reason about shapes. They describe and classify shapes, ... | HuggingFaceTB/finemath | |
How to Prepare a Break-Even Analysis with More Than One Product A Collection of Images from Converting to Xero from MYOB In A Day For Dummies Activity-Based Costing for Overhead Allocation
# Prediction Error Evaluation in Cost Accounting
A prediction error occurs in cost accounting when actual costs differ from your ... | HuggingFaceTB/finemath | |
# Why the Singapore Approach to Maths Works
## The Dawn of Singapore Maths
Mathematics has always been a subject that instils a sense of awe and intimidation in many students. But what if there was an approach that could demystify this complex subject and empower learners with a deep understanding of mathematical con... | HuggingFaceTB/finemath | |
No wonder mathematicians find numbers to be the passion of a lifetime. Deceptively simple things can lead to such amazing complexity, to intriguing links between seemingly unconnected concepts.
Take the simple concept of the factorial. The factorial of a positive integer $n$ is defined as the product of all the integ... | HuggingFaceTB/finemath | |
Search a number
BaseRepresentation
bin1001111101100
320222220
41033230
5130400
635340
720604
oct11754
96886
105100
113917
122b50
132424
141c04
1517a0
hex13ec
5100 has 36 divisors (see below), whose sum is σ = 15624. Its totient is φ = 1280.
The previous prime is 5099. The next prime is 5101. The reversal of 5100 is 1... | HuggingFaceTB/finemath | |
# Search by Topic
#### Resources tagged with Inequalities similar to Shades of Fermat's Last Theorem:
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### There are 43 results
Broad Topics > Algebraic expressions, equations and formulae > Inequalities
### Shades of Fermat's Last Theorem
##### Age 16 to 18 Cha... | HuggingFaceTB/finemath | |
# 7.4 Conic Exponential Optimization¶
Conic optimization is a generalization of linear optimization, allowing constraints of the type
$x^t \in \K_t,$
where $$x^t$$ is a subset of the problem variables and $$\K_t$$ is a convex cone. Since the set $$\real^n$$ of real numbers is also a convex cone, we can simply write ... | HuggingFaceTB/finemath | |
The Dynamics of Poisson Distribution and Sports
Thanks to the ingenious works of French Mathematician Simeon Denis Poisson in the 19th century, sportsbetting enthusiasts can calculate the probability of sports betting wagers using the Poisson distribution betting strategy. The most common definition of Poisson distri... | HuggingFaceTB/finemath | |
Solve x^3-3x^2+4x+1=0 | Uniteasy.com
# Solve the cubic equation:
## $$x^3-3x^2+4x+1=0$$
Quick Answer
Since the discriminant $$\Delta >0$$, the cubic equation has one real root and two conjugate complex roots.
$$\Delta=2.287037037037$$
$$\begin{cases} x_1=\sqrt[3]{-\dfrac{3}{2}+\dfrac{1}{6}\sqrt{\dfrac{247}{3}}}... | HuggingFaceTB/finemath | |
# 48÷2(9+3)=?
#### silversnake4133
##### New member
It may have changed over the unfortunate years that this species has seen of a rapidly declining intellect, but when I was in grade school, the formula for figuring out order of operations (or O^3) was PEMDAS (Parentheses, Exponents, Multiplication, Division, Additi... | HuggingFaceTB/finemath | |
# Abutting Equilateral Triangles on a Line I
10 August 2013, Created with GeoGebra
### Problem
Points $A,C,B\space$ are collinear; triangles $ACB_1,$ $ACB_2,$ $CBA_1,$ $CBA_2$ are equilateral.
The circumcenters $O_{B1},O_{B2},O_{A1},O_{A2},O_{C1},O_{C2}$ of triangles $ACB_1,$ $ACB_2,$ $CBA_1,$ $CBA_2,$ $A_1B_1C,$ $... | HuggingFaceTB/finemath | |
Cody
# Problem 44360. Pentagonal Numbers
Solution 1327459
Submitted on 4 Nov 2017 by suyako
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x1 = 1; x2 = 25; [p,d] = pentagonal_numbers(x1,x2) assert... | HuggingFaceTB/finemath | |
Don't lose your points!
### Free Educational Resources
• > Mathematics
• > Geometry
• > Proving Lines Proportional/Proportional Segments of Parallel Lines
+
# Proving Lines Proportional/Proportional Segments of Parallel Lines
##### Rating:
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Author: Michele Harris
##### Description:
... | HuggingFaceTB/finemath | |
intparts - Integration by Parts The message of the fundamental theorem of calculus is that integration and differentiation are inverse processes
# intparts - Integration by Parts The message of the...
• Notes
• 4
This preview shows page 1 - 2 out of 4 pages.
Integration by Parts The message of the fundamental theor... | HuggingFaceTB/finemath | |
## The Obstacles You Think You Know…Don’t Matter
Polynomials suck, but they aren’t the obstacle that matters most…
I used to hear one question a lot when I was a kid.
Whether an adult was asking me, or another kid my age, it was always the same:
What are you going to be when you grow up?
In second grade, I knew I ... | HuggingFaceTB/finemath | |
# FIND AMPLITUDE PERIOD PHASE SHIFT AND VERTICAL SHIFT
The graph of y = A sin (Bx - C) + D is obtained by horizontally shifting the graph of y = A sin Bx so that the starting point of the cycle is shifted from x = 0 to x = C/B.
• If C/B > 0, the shift to the right
• If C/B < 0, the shift to the left.
• If C/B is 0, ... | HuggingFaceTB/finemath | |
## Back from Maine with Squares and Triangles
6 October 2009
Ah, how I’ve missed my little blog. Sorry about the hiatus, but now I’m back from the number theory conference with a head full of new ideas. Unfortunately, most of the topics of the conference have far too many prerequisites to fit in this blog. Let’s j... | HuggingFaceTB/finemath | |
# Joules to Therms - J to thm
## How to convert from Joules to Therms
The conversion factor between Joules and Therms is 9.4804342797335E-9. To convert an amount in Joules in Therms, multiply the the desired amount in Joules by 9.4804342797335E-9:
Amount(Joules) × 9.4804342797335E-9(Conversion Factor) = Result(Therm... | HuggingFaceTB/finemath | |
## Introductory Algebra for College Students (7th Edition)
$\frac{8x}{9}$
$\frac{x}{3}\div\frac{3}{8}$ Invert the divisor and multiply. $\frac{x}{3}\times\frac{8}{3}$ Multiply numerator by numerator and denominator by denominator. $\frac{8x}{9}$ | HuggingFaceTB/finemath | |
# Continuation of Coordinates Across Black Hole Horizons
• A
• Antarres
In summary, the conversation discusses the regularization of coordinate singularities in the context of general relativity. The first case involves a coordinate transformation in Schwarzschild geometry, which allows for an extension of the solutio... | HuggingFaceTB/finemath | |
# A 60 kg worker pulls buckets of sand from height of 10 m using a pulley fixed to a wooden beam.While he is pulling a 20 kg bucket filled with sand he slips and falls down holding the rope.Assuming that the worker did not collide with bucket,find the velocity of the worker at the moment of striking the ground and the ... | HuggingFaceTB/finemath | |
After substituting above values in equation 1 we get Qd 502458 11741 10914
# After substituting above values in equation 1 we get
This preview shows page 5 - 8 out of 8 pages.
After substituting above values in equation (1), we get, Qd = 5024.58 + 117.41 * 109.14 136.62 * P 0.2823 * 7620.601 + 7.87 * 1247.31 Qd = 25... | HuggingFaceTB/finemath |
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