question stringlengths 200 50k | answer stringclasses 1
value | source stringclasses 2
values |
|---|---|---|
# We are bringing you all the important calculators and converters at single place so you don't have to download different application for your all need. We have
The squares of the Fibonacci numbers are, you guessed it, the Fibonacci numbers squared. Given a Fibonacci number , observe that − + = + (−). For
Substituti... | HuggingFaceTB/finemath | |
# 8380.2 Gal To L
Gal To L Calculator
Let's convert 8380.2 gallon to liter.
Gallon to liter conversion rate is 3.78541 .
So if we multiply 8380.2 with 3.78541 rate, we will find 8380.2 gallon is how much liter. ## How to convert 8380.2 gallons to liters ?
To convert gallons to liters, multiply the number of gallons... | HuggingFaceTB/finemath | |
Solutions by everydaycalculation.com
## Divide 45/4 with 90/25
1st number: 11 1/4, 2nd number: 3 15/25
45/4 ÷ 90/25 is 25/8.
#### Steps for dividing fractions
1. Find the reciprocal of the divisor
Reciprocal of 90/25: 25/90
2. Now, multiply it with the dividend
So, 45/4 ÷ 90/25 = 45/4 × 25/90
3. = 45 × 25/4 × 90 =... | HuggingFaceTB/finemath | |
# Phorgy Phynance
## Network Theory and Discrete Calculus – Quantized Conductance
This post is part of a series
### The Graph Operator
In my last post, I mentioned the graph operator
\begin{aligned} \mathbf{G} = \sum_{i,j} \sum_{\epsilon\in[i,j]} \mathbf{e}_\epsilon^{i,j}\end{aligned}
and the fact the exterior de... | HuggingFaceTB/finemath | |
Actions
HP Customer Support - Knowledge Base
Actions
Actions
Actions
# HP 12c Financial Calculator - Logarithm and Exponential Functions
## Basic logarithm and exponential relationships
Exponential and logarithm are related functions as expressed by b = ax, where 'x' is unknown power, 'a' is the base (known), and... | HuggingFaceTB/finemath | |
# What is 201/77 as a decimal?
## Solution and how to convert 201 / 77 into a decimal
201 / 77 = 2.61
Fraction conversions explained:
• 201 divided by 77
• Numerator: 201
• Denominator: 77
• Decimal: 2.61
• Percentage: 2.61%
201/77 converted into 2.61 begins with understanding long division and which variation bri... | HuggingFaceTB/finemath | |
# How can Newton first law of motion can obtain from the second law of motion?
2
by sargu
2016-03-05T16:09:53+05:30
Let us consider an isolated system( no ext force is acting)
acc. to Newton's law
F = ma
for an isolated system, it will
ma= 0
m can't be zero and as no force is acting the acce (a) = 0 which means the b... | HuggingFaceTB/finemath | |
In an arithmetic sequence, the first term is -2, the fourth term is 16, and the nth term is 11998, how do you find n and the common difference?
May 12, 2016
common difference, $d = 6$
$n = 2001$
Explanation:
${a}_{n} = a + \left(n - 1\right) d$
Here, $a$ is the first term, $d$ is the common difference and ${a}_{n... | HuggingFaceTB/finemath | |
# Quantum Wells
Exploring Quantum Physics – Week 3, Lecture 5
## Types of problems for the Schrödinger equation
Single-particle quantum mechanics, $i\hbar \dot{\Psi} = \left[ \frac{\hat{p}^2}{2m} + V(r) \right] \Psi$
Different potential functions present different types of problems
## Quantization in a guitar stri... | open-web-math/open-web-math | |
## Feature #3845
### "in" infix operator
[ruby-core:32454]
Status: Rejected Normal Yukihiro Matsumoto
Description
=begin
Hi,
I'd propose "in" infix operator.
( in ) yields true when is included in .
Otherwise it yields false.
p "found" if 1 in 1, 2, 3 #=> found
"in" operator is clearer to the reader than Array#... | open-web-math/open-web-math | |
# Yukawa Potential
nickjer
Got a bit confused now, this is what I have noted down in addition to the previous post (I think this is more correct):
$$\left<\psi V_{\gamma}(r)\psi\right> = \int^{\infty}_{0}\left[-\left(\frac{1}{\pi r a^{3}}\right)e^{-r\left(\frac{2}{a}-\gamma\right)}\right]dr$$
so then get this:
$$=\... | HuggingFaceTB/finemath | |
# Evaluate the value of $\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$ where $x_n=x_{n-1}^2-2, x_1=5$ [duplicate]
Evaluate the value of $$\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$$ where $$x_n=x_{n-1}^2-2, (x_1=5).$$
I've found that $$x_n$$ is an increasing sequence so that the limit becomes an in... | HuggingFaceTB/finemath | |
# Check my proof of the polynomial uniqueness
Problem 169 from the book I.M. Gelfand, "Algebra".
"Assume that $x_1, \ldots , x_{10}$ are different numbers, and $y_1 , \ldots , y_{10}$ are arbitrary numbers. Prove that there is one and only one polynomial $P(x)$ of degree not exceeding $9$ such that $P(x_1) = y_1,$ $P... | HuggingFaceTB/finemath | |
# How much water can be heated from 15 ° C to boiling, if you give it 178.5 kJ of heat?
t1 = 15 ° C.
t2 = 100 ° C.
C = 4200 J / kg * ° С.
Q = 178.5 kJ = 178500 J.
m -?
The amount of heat Q required for heating water is expressed by the formula: Q = C * m * (t2 – t1).
m = Q / C * (t2 – t1).
m = 178500 J / 4200 J ... | HuggingFaceTB/finemath | |
# ratio percent Write fractions as percents and percents as fractions.
## Presentation on theme: "ratio percent Write fractions as percents and percents as fractions."— Presentation transcript:
ratio percent Write fractions as percents and percents as fractions.
A comparison of two quantities by division. When a rat... | HuggingFaceTB/finemath | |
# Chi Square Test with Minitab
### Chi Square (Contingency Tables)
We have looked at hypothesis tests to analyze the proportion of one population vs. a specified value, and the proportions of two populations, but what do we do if we want to analyze more than two populations? A chi-square test is a hypothesis test in ... | HuggingFaceTB/finemath | |
1. ## Proof by Induction
n^2 - n is even for any n >= 1
So far i have the base case:
n=1 1^2-1 = 0 and 2^2-2=2 which are both even.
then prove for n = k so k^2 - 2 for k>=1
then n= (k+1)^2 - (k+1).... having problems with further steps.
2. $\displaystyle (k+1)^2 = k^2+2k+1$.
3. Why do you have to use induction?
I... | HuggingFaceTB/finemath | |
# - The 4th COE Conference for Young Researchers -
### アブストラクト：プログラム
タイトル：Construction of a solution to the Gierer-Meinhardt system with saturation（サチュレーション効果のあるGierer-Meinhardt 系の解の構成）
アブストラクト：
We are concerned with stationary solutions to the Gierer-Meinhardt system with saturation. In this lecture, we study about ... | open-web-math/open-web-math | |
# What is the magnitude of the average stopping force?
• vshah
In summary, the conversation was about two physics problems - one involving a man dropping onto a concrete patio and the other involving a landing craft approaching the surface of a moon. The expert provided equations and hints to solve both problems, emph... | HuggingFaceTB/finemath | |
# Singular Value Decomposition (SVD) – A Tutorial with an Application to Wireless Systems By
Singular Value Decomposition (SVD) is a powerful concept in linear algebra whose relevance has significantly increased in recent times. Some of the notable examples are its applications in machine learning, data science and w... | HuggingFaceTB/finemath | |
What is so important to remember when preparing for the calculus exam? The most common answer is the answers are not that important. The problem is that this is incorrect. While it may seem a little silly to say that knowledge of formulas and equations is not important, it really is that important. Without this knowled... | HuggingFaceTB/finemath | |
MCAT Content / Solubility / Solubility Units Of Concentration
### Solubility Units of Concentration
Topic: Solubility
In chemistry, the concentration of a solution is often measured in molarity (M), which is the number of moles of solute per liter of solution.
Molar concentration (ci) is calculated by dividing the ... | HuggingFaceTB/finemath | |
## Series
A series is a sum of terms specified by some rule. If each term increases by a constant amount, it is said to be an Arithmetic Series. If each term equals the previous multiplied by a constant, it is said to be a Geometric Series. A series usually has an Infinite number of terms, but the phrase Infinite Seri... | HuggingFaceTB/finemath | |
# What is definite integral? integral sign low limit 0, upper limit pie/2 ln(1+sinx)/ln(1+sinxcosx+sinx+cosx)dx?
Posted on
Let I=`int_0^(pi/2)ln(1+sinx)/ln(1+sinxcosx+sinx+cosx)dx`
= `int_0^(pi/2)ln(1+sinx)/ln{(1+sinx)(1+cosx)}dx`
= `int_0^(pi/2)ln(1+sinx)/{ln(1+sinx)+ln(1+cosx)}dx` (I)
Now by rule `int_0^a... | HuggingFaceTB/finemath | |
# Galvanic cell involving a hydrogen electrode and copper electrode in sodium hydroxide
A galvanic cell consists of a standard hydrogen electrode and a copper electrode. Suppose that the copper electrode is immersed in a solution that is $0.100\ \mathrm{M}$ in $\ce{NaOH}$ and that is saturated with $\ce{Cu(OH)2}$. Fin... | HuggingFaceTB/finemath | |
Brand X Pictures/Brand X Pictures/Getty Images
When determining the value of a piece of jewelry, one of the most important factors is figuring out how much the item weighs. Unfortunately, most of us don't keep jewelry scales around our houses and household scales won't do the trick. Luckily, with a little ingenuity an... | HuggingFaceTB/finemath | |
### Home > APCALC > Chapter 1 > Lesson 1.3.1 > Problem1-105
1-105.
Given $f(x) = 2x^2 − 3$:
1. Evaluate $f(2)$.
Substitute $2$ in for every $x$ in the equation.
$2(2^²) − 3$
$f(2) = 5$
2. Without writing the equation of the inverse, determine $f ^{-1}(5)$. Explain your process.
Recall that that the inputs and... | HuggingFaceTB/finemath | |
# The science behind how much rain hits your windshield
While i sit at a stoplight during a light rain, a given amount of drops seems to hit my windshield. When the light changes and I pull away, it seems as if more drops are hitting the windshield, and I need to turn the wipers on and off more frequently or leave the... | HuggingFaceTB/finemath | |
It is currently Mon Sep 16, 2019 5:29 am
All times are UTC - 5 hours [ DST ]
Page 1 of 1 [ 8 posts ]
Print view Previous topic | Next topic
Author Message
Post subject: GMAT Algebra (Data Sufficiency)Posted: Mon Jun 07, 2010 2:41 pm
Joined: Sun May 30, 2010 3:15 am
Posts: 424
For the integers m, n, r, and s, if ... | HuggingFaceTB/finemath | |
# Question about Strict Preference Relation
Strict Preference usually states that
x is strictly preferred to y if : < x is weakly preferred to y and not y is weakly preferred to x >.
Let me split the < > part into two segments:
1. x is weakly preferred to y
and
1. not y is weakly preferred to x
Why do you need t... | open-web-math/open-web-math | |
##### Question
In: Statistics and Probability
# A die was rolled 300 times. The following frequencies were recorded. Outcome 1 2 3 4...
A die was rolled 300 times. The following frequencies were recorded.
Outcome 1 2 3 4 5 6
Frequency 62 45 63 32 47 51
Do these data indicate that the die is unfair ? Use a 1% level o... | HuggingFaceTB/finemath | |
Search a number
BaseRepresentation
bin100110100010…
…000101101110
3201000012002220
4212202011232
510041213402
61000300210
7151600164
oct46420556
921005086
1010101102
11577a120
123471666
1321288ab
15d47dbc
hex9a216e
10101102 has 32 divisors (see below), whose sum is σ = 22754304. Its totient is φ = 2961600.
The previo... | HuggingFaceTB/finemath | |
# B-sharp major 7th suspended 2nd chord
The Solution below shows the B-sharp major 7th suspended 2nd chord in root position, 1st, 2nd, and 3rd inversions, on the piano, treble clef and bass clef.
The Lesson steps then explain how to construct this 7th chord using the 3rd, 5th and 7th note intervals, then finally how ... | HuggingFaceTB/finemath | |
# Application of Maximum Power Transfer
What is maximum power transfer?
In DC circuits this theorem state that the source can transfer maximum power when the total resistance viewed from the load is equal to the value of the resistance of that load.
Applications of Maximum Power Transfer
1. In communication system, m... | HuggingFaceTB/finemath | |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Extensive and Intensive Properties
## Types of attributes used to describe matter
Estimated3 minsto complete
%
Progress
Practice Extensive and Intensive Properties
MEMORY METER
This ... | HuggingFaceTB/finemath | |
# Standard Error of the Mean vs. Standard Deviation
0
141
The standard deviation (SD) measures the amount of variability, or dispersion, for a subject set of data from the mean, while the standard error of the mean (SEM) measures how far the sample mean of the data is likely to be from the true population mean. The S... | HuggingFaceTB/finemath | |
# All Questions
652 views
### How to show that this weak scheme is a cubature scheme?
Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
685 views
It is known (see for e... | open-web-math/open-web-math | |
# What is the difference between a Hilbert space and Euclidean space?
According to Wikipedia,
Hilbert space [...] extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions
However, the article on ... | HuggingFaceTB/finemath | |
## Creator
Dan Anderson (@dandersod)
## On to the Challenge!
Can you create the following graph using desmos.com or some other graphing tool? If you’re victorious, leave us a note in the comments when you’re done.
Note: This set of 4 graphs was not made with trigonometric functions. Can you replicate it? ## 10 thou... | HuggingFaceTB/finemath | |
# Elementary function
For the complexity class, see ELEMENTARY. For the logical system, see Elementary function arithmetic.
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations (+ – × ÷), exponentials, logarithms, constants, and solu... | HuggingFaceTB/finemath | |
## 3 Ways to Solve a Cubic Equation
First, factor the sum of cubes with a = x and b = 6. The first factor gives the answer x = -6. Using the quadratic formula for the rest, we have So the only real solution is x = -6. b. First
Explain mathematic problem
Math is the study of numbers, shapes, and patterns.
Figure out... | HuggingFaceTB/finemath | |
# Sector|Definition & Meaning
## Definition
A sector of a circle is a closed region bounded by an arc and any two radii connecting the ends of that arc to the center of the circle. It looks like a slice of cake or pizza. The area of a sector is always less than the circle’s area. The sector’s arc forms an angle at th... | HuggingFaceTB/finemath | |
# Symmetry
## Basic
### Axes of symmetry
Axes of symmetry have to do with a crystal's balance of shape when rotated around these imaginary axes.
Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these syst... | HuggingFaceTB/finemath | |
# Solve for: 5 1/3*6 3/5*1 4/11
## Expression: $5\frac{1}{3}\cdot 6\frac{3}{5}\cdot 1\frac{4}{11}$
Convert mixed numbers to improper fractions $:{\quad}5\frac{1}{3}=\frac{16}{3}$
$=\frac{16}{3}\cdot 6\frac{3}{5}\cdot 1\frac{4}{11}$
Convert mixed numbers to improper fractions $:{\quad}6\frac{3}{5}=\frac{33}{5}$
$=\... | HuggingFaceTB/finemath | |
# Trigonometry
posted by .
Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two
decimal places.
• Trigonometry -
* Solve tan^2x + tanx-1=0 for the principal value(s) to two decimal places.
• Trigonometry -
Let y=tan(x)
y²+y-1=0
y=(-1±√(5))/2
or
tan(x)=(-1±√(5))/2
## Similar Questions
1. ### math
roun... | HuggingFaceTB/finemath | |
## Intersection of Two Linked Lists
Write a program to find the node at which the intersection of two singly linked lists begins.
For example, the following two linked lists:
A: a1 → a2
↘
c1 → c2 → c3
↗
B: b1 → b2 → b3
begin to intersect at node c1.
Notes:
• If the two linked lists have no intersection... | HuggingFaceTB/finemath | |
# Planar graph
Example graphs
PlanarNonplanar
In graph theory, a planar graph is a graph that can be drawn so that no edges intersect (or that can be embedded) in the plane. A nonplanar graph cannot be drawn in the plane without edge intersections.
A planar graph already drawn in the plane without edge intersections... | HuggingFaceTB/finemath | |
14. Floating Point Arithmetic: Issues and Limitations¶
Floating-point numbers are represented in computer hardware as base 2 (binary) fractions. For example, the decimal fraction
```0.125
```
has value 1/10 + 2/100 + 5/1000, and in the same way the binary fraction
```0.001
```
has value 0/2 + 0/4 + 1/8. These two ... | HuggingFaceTB/finemath | |
Open In App
Related Articles
# Check if it is possible to sort an array with conditional swapping of adjacent allowed
We are given an unsorted array of integers in the range from 0 to n-1. We are allowed to swap adjacent elements in array many number of times but only if the absolute difference between these element ... | HuggingFaceTB/finemath | |
University of Virginia
Physics Department
## Compound Machines
A Physical Science Activity
### Student Activity
Materials
• Inclined plane, 50-60 cm long, at least 20° incline angle
• Spring scale (10 N max)
• Small car with wheels, 400-800 g (Suggestion: Wheeled Cart from Frey Scientific Catalog 1-888-222-1332, i... | HuggingFaceTB/finemath | |
# Thread: Determinant of a block matrix of a specific form
1. ## Determinant of a block matrix of a specific form
Let $\displaystyle m_{1},m_{2}$ be two $\displaystyle n\times n$ matrices, and consider the $\displaystyle 2n\times 2n$ block-matrix $\displaystyle M=\begin{pmatrix}m_{1} & -m_{2} \\ m_{2} & m_{1}\end{pma... | HuggingFaceTB/finemath | |
# What is the surface area produced by rotating f(x)=x^3-8, x in [0,2] around the x-axis?
Jun 21, 2018
first find dS, note the radius of the rotation is x.
$\mathrm{dS} = \sqrt{1 + 9 {x}^{4}} \mathrm{dx}$
${\int}_{0}^{2} 2 \pi x \mathrm{dS}$
to solve make a substitution of $w = 3 {x}^{2}$
#### Explanation:
If you m... | HuggingFaceTB/finemath | |
# Number converter: 342,456 in Roman numerals, how to write?
## Latest conversions of numbers to Roman numerals
103,170 = (C)MMMCLXX Mar 24 01:19 UTC (GMT) 200,215 = (C)(C)CCXV Mar 24 01:19 UTC (GMT) 103,172 = (C)MMMCLXXII Mar 24 01:19 UTC (GMT) 342,456 = (C)(C)(C)(X)(L)MMCDLVI Mar 24 01:19 UTC (GMT) 222,384 = (C)(C... | HuggingFaceTB/finemath | |
# Electric Force
1. Dec 1, 2007
### pinkyjoshi65
Two identical small spheres of mass 2 g are fastened to the ends of an insulating thread of length 0.6m. The spheres are suspended by a hook in the ceiling from the centre of the thread. The spheres are given identical electric charges and hang in static equilibrium w... | HuggingFaceTB/finemath | |
# Distinct elements in range query with single element updation
Get FREE domain for 1st year and build your brand new site In this article, we have explored how to find the number of unique elements in a given range of an array with single updation using Mo's algorithm. We will see the brute force approach, learn some... | HuggingFaceTB/finemath | |
The Kaya Identity: The Case of Turkey
The Kaya Identity expresses carbon dioxide emission levels as a product of population, Gross Domestic Product per capita (personal wealth), energy intensity (energy per GDP) and carbon intensity (CO2 emissions per energy consumed). Developed by Yoichi Kaya, its mathematical notati... | open-web-math/open-web-math | |
# Lesson Notes By Weeks and Term - Primary 2
3-D shapes
TERM: 3rd Term
WEEK: 11
CLASS: Primary 2
AGE: 7 years
DURATION: 5 periods of 40 minutes each
DATE:
SUBJECT: Mathematics
TOPIC: 3-D shapes
SPECIFIC OBJECTIVES: At the end of the lesson, the pupils should be able to
1. Recognise, describe, sort and compar... | HuggingFaceTB/finemath | |
Spearman Correlation Coefficient is a close sibling to Pearson's Bivariate Correlation Coefficient, Point-Biserial Correlation, and the Canonical Correlation. Each random variable (Xi) in the table is correlated with each of the other values in the table (Xj). Using Spearman’s Correlation Statistic in Research. To asse... | HuggingFaceTB/finemath | |
# Which lists all the factors of a composite number?
A prime number is made up of only two factors: one and itself. A composite number is made up of more than two elements. There is no prime or composite number greater than one. Because each of these numbers has just two components, itself and 1, the prime numbers bet... | HuggingFaceTB/finemath | |
Early detection of ovarian cancer has the potential to impact mortality. A multimodal screening strategy where rising CA125 values over time, analyzed with the risk of ovarian cancer algorithm (ROCA), triggers transvaginal sonography and possible surgery has high sensitivity and specificity, but still fails to detect t... | open-web-math/open-web-math | |
# An example of adding points on an elliptic curve in Elliptic Curves, Number Theory and Cryptography by Lawrence Washington.
This question addresses an example that appears in Lawrence Washington's book, Elliptic Curves, Number Theory and Cryptography on page 16. Example 2.1. The author asserts that the following sta... | HuggingFaceTB/finemath | |
## very very elementary lemma on pullbacks which I just cannot prove [closed]
I am new in category theory. I am trying to prove the well known fact that if you have a commutative diagram of the form □□, where each square is a pullback, then the whole diagram is a pullback too, and hence deduce that the pullback of a p... | open-web-math/open-web-math | |
It is currently 19 Sep 2017, 08:30
### 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
for You
we will pick new questions that match your level based o... | HuggingFaceTB/finemath | |
Closed Loop Voltage Gain Of An Instrumentation Operational Amplifier
TECTechnics Classroom TECTechnics Overview
Closed Loop Voltage Gain Of An Instrumentation Operational Amplifier Figure 13.1 illustrates the instrumentation operational amplifier (IA).
Find the closed loop voltage gain of the instrumentation amplifi... | HuggingFaceTB/finemath | |
# Two Sheriffs and Eavesdroppers - 2
“The Two Sheriffs” puzzle was already discussed here Two Sheriffs and Eavesdroppers. This puzzle has only one difference: we have seven suspects instead of eight.
Two sheriffs in neighboring towns are on the track of a killer, in a case involving seven suspects. By virtue of indep... | HuggingFaceTB/finemath | |
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Sum of the numbers | AMC-10A, 2001 | Problem 16
Try this beautiful problem from Algebra based on Sum of the numbers....
Sum of the numbers - AMC-10A, 2001- Problem 16
The mean of three numbers is $10$ more than the least of the numbers and $15$ less... | HuggingFaceTB/finemath | |
+0
Working out the triangle length and prism length of a equilateral triangular prism?
+5
497
1
A chocolate company needs to manufacture cardboard containers with the shape of equilateral-triangular prisms and that have a volume of exactly 5178 mL. What are the optimum dimensions (in cm) such that a minimum amount o... | HuggingFaceTB/finemath | |
#### Important 1 Mark Creative Questions (New Syllabus) 2020
12th Standard
Reg.No. :
•
•
•
•
•
•
Time : 00:25:00 Hrs
Total Marks : 28
Part A
28 x 1 = 28
1. If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =
(a)
3
(b)
± 3
(c)
± ... | HuggingFaceTB/finemath | |
# 1959 IMO Problems/Problem 1
## Problem
Prove that the fraction $\frac{21n+4}{14n+3}$ is irreducible for every natural number $n$.
## Video Solution
~ pi_is_3.14
### Solution
Denoting the greatest common divisor of $a, b$ as $(a,b)$, we use the Euclidean algorithm: $$(21n+4, 14n+3) = (7n+1, 14n+3) = (7n+1, 1) = ... | HuggingFaceTB/finemath | |
# [Leetcode][python]Combination Sum/组合总和
【Leetcode题解】 同时被 2 个专栏收录
146 篇文章 0 订阅
145 篇文章 10 订阅
## 题目大意
candidates 中的数字可以无限制重复被选取。
## 代码
class Solution(object):
def combinationSum(self, candidates, target):
"""
:type candidates: List[int]
:type target: int
:rtype: List[List[int]]
"""
if not candidates:
return []
cand... | HuggingFaceTB/finemath | |
# Variables on both sides?... No Problem
4 teachers like this lesson
Print Lesson
## Objective
SWBAT solve equations with variables on both sides.
#### Big Idea
Equations may look difficult, but once students see and know what to do, they become confident, and actually enjoy solving these.
## Launch
10 minutes
... | HuggingFaceTB/finemath | |
In our notes for Class 8, we had learned about linear equations and simultaneous linear equations. We suggest that you quickly revise the basic concepts of linear equations and how to solve two such equations simultaneously.
Linear Equation in Two Variables
An equation of the form $ax + by + c = 0$, where $a, \ b, \ ... | HuggingFaceTB/finemath | |
# Using Strip Diagrams as a Problem-Solving Strategy
There’s a lot to be learned from the data that comes from state testing if we use it correctly. Oftentimes, we’ll take a problem that students, as a whole, perform poorly on and we create a bunch of problems just like that one and “teach” them how to work that type ... | HuggingFaceTB/finemath | |
## Searching for a maximum-sum subsequence ### Problem 149
Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is 16 (= 8 + 7 + 1).
−2 5 3 2 9 −6 5 1 3 2 7 3 −1 8 −4 8
Now, let us repeat the search, bu... | HuggingFaceTB/finemath | |
# Playing with interior and closure
Let’s play with the closure and the interior of sets.
To start the play, we consider a topological space $$E$$ and denote for any subspace $$A \subset E$$: $$\overline{A}$$ the closure of $$A$$ and $$\overset{\circ}{A}$$ the interior of $$A$$.
### Warm up with the closure operator... | open-web-math/open-web-math | |
# What is 5sqrt(-64) + 4sqrt4?
Jun 25, 2018
$\textcolor{b l u e}{8 \left(5 i + 1\right)}$
#### Explanation:
Note that $\sqrt{- 64}$ can only be evaluated as a complex number: $i \sqrt{64}$
$5 \sqrt{- 64} + 4 \sqrt{4}$
$\textcolor{w h i t e}{\text{XXX}} = 5 i \sqrt{64} + 4 \sqrt{4}$
$\textcolor{w h i t e}{\text{X... | HuggingFaceTB/finemath | |
# Divisors of 11346
## Divisors of 11346
The list of all positive divisors (that is, the list of all integers that divide 22) is as follows :
Accordingly:
11346 is multiplo of 1
11346 is multiplo of 2
11346 is multiplo of 3
11346 is multiplo of 6
11346 is multiplo of 31
11346 is multiplo of 61
11346 is multip... | HuggingFaceTB/finemath | |
# Help with Homework Problem on Acceleration
1. Sep 5, 2004
### shawonna23
The land speed record of 13.9 m/s (31 mi/h) for birds is held by the Australian emu. An emu running due south in a straight line at this speed slows down to a speed of 10.5 m/s in 2.7 s.
What is the direction of the bird's acceleration?
Ass... | HuggingFaceTB/finemath | |
Courses
# Stability - MCQ Test
## 15 Questions MCQ Test RRB JE for Electronics & Communication Engineering | Stability - MCQ Test
Description
This mock test of Stability - MCQ Test for Railways helps you for every Railways entrance exam. This contains 15 Multiple Choice Questions for Railways Stability - MCQ Test (m... | HuggingFaceTB/finemath | |
What Does Range Mean in Math Terms?
In math terms, the "range" is the difference between the maximum and minimum values of a given data set. It is a calculation that measures the spread of a data set. However, range can also mean all the output values of a function.
The equation used to find the range of a data set i... | HuggingFaceTB/finemath | |
#### stevecanuck
• 205
##### An inconvenient hemiplane.
« on: December 01, 2020, 06:46:35 PM »
Assuming the distance from the North Pole (NP) to the Equator (E) is 10,000 km whether speaking of FE or RE, and that the Equator to the southern edge (or South Pole) is an additional 10,000 km, we can easily calculate the ... | HuggingFaceTB/finemath | |
# dimension of a connected Manifold
Currently, I am studying smooth manifolds and I want to solve some exercises. There is a question that says:
Show that the dimension of a connected topological manifold is defined without ambiguity! Meaning that if $$\dim M=n$$, with the change of charts, the dimension still is $$n... | HuggingFaceTB/finemath | |
Chapter 4 Practice Test
# Chapter 4 Practice Test
## Chapter 4 Practice Test
- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript
1. Chapter 4 Practice Test Consumer Math Mastery test a
2. Chapter 4 Practice Test 1. Eric’s i... | HuggingFaceTB/finemath | |
# Statistical test for two categorical ordinal variables with four levels
There are two categorical variables with four levels, so ordinal variables. Specifically, they are responders and non-responders with heart function that is graded from mild, mild-moderate, moderate, severe. So each patient will either be a resp... | HuggingFaceTB/finemath | |
# Speed of Wavepacket
For the given wavepacket
$ψ(x,t)=A*e^{-(a^2 x^2+b^2 t^2+2abxt)}$
show that it satisfies the 1D wave equation and find its speed and direction of propagation.
Wave equation is
$(∂^2 ψ)/(∂x^2 )=1/v^2 (∂^2 ψ)/(∂t^2)$
The results are:
$(∂^2 ψ)/(∂x^2 )=A(-2a^2 x-2abt)^2*e^{-(…) }-A*2a^2*e^{-(…) ... | HuggingFaceTB/finemath | |
# Solve a vector equation?
$$\vec{a} + \vec{b} \times \vec{x} = \lambda\vec{x}$$
$\vec{a}, \vec{b}$ are known vectors and $\lambda$ is a known scalar. How can i solve that equation ($\times$ between $\vec{b}$ and $\vec{x}$ is a vector product)?
• If you mean by vector product; cross product so you can set it in the f... | HuggingFaceTB/finemath | |
# Finding a basis and an orthogonal vector
Just stuck on a small problem:
The set
$V = {{(x_1, x_2, x_3, x_4) \in R^4 \ | \ x_1 -2x_2 + 3x_3 +x_4=0}}$
is a subspace of $R^4$.
Find a basis ${(v_1, v_2, v_3, v_4)}$ for $R^4$ such that ${(v_1, v_2, v_3)}$ is a basis for V and $v_4$ is a vector orthogonal to V (i.e $v... | HuggingFaceTB/finemath | |
# THE SEVEN BENCHMARK NUMBERS WHY IS IT A POWERFUL TOOL FOR PRIMARY GRADES?
Jun 1, 2023 | Red Deer
Before we talk about the seven benchmark numbers, ask your child (grade 5 or above) a simple fraction operation question like what is ½ + ½ (many kids would answer 2/4) or what is ½ of ½ (many kids would answer ‘zero’).... | HuggingFaceTB/finemath | |
# Quant Questions
### If a - b = 4 and a^2 + b^2 = 40 where a and b are positive integers
If a - b = 4 and a2 + b2 = 40 where a and b are positive integers, where a and b are positive integers, then a3 + b6 is equal to
1. 264
2. 280
3. 300
4. 324
### If the roots of the equation Ax^2 + Bx + C = 0 are -1 and 1
If t... | HuggingFaceTB/finemath | |
## Conversion formula
The conversion factor from feet per second to kilometers per hour is 1.0972799999991, which means that 1 foot per second is equal to 1.0972799999991 kilometers per hour:
1 ft/s = 1.0972799999991 km/h
To convert 62 feet per second into kilometers per hour we have to multiply 62 by the conversion... | HuggingFaceTB/finemath | |
Use Google's Chrome browser for proper viewing.
IB Physics SL (2019-2020)
8/15
• Informational Packet / Syllabus
• Introduction to class
• Homework - brainstorm a notation for keeping track of how far an object moves AND in which direction it travels, e.g. a man walks 20 meters eastward, then 20 meters northward, th... | HuggingFaceTB/finemath | |
```Question 168501
painting of 50 feet by 30ft they want to put a border to be 25% of the painting what is the exact width of the border?
--------------------
If I read you correctly the area of the border is to be 25% of the area
of the painting.
--------------
The area of the painting is 50x30 = 1500 sq ft
25% of 150... | HuggingFaceTB/finemath | |
Purchase Solution
# Roller Coaster Physics
Not what you're looking for?
ROLLER COASTER DESIGN
Designing a roler coaster is very tricky. Patrons of theme and amusement parks want to be thrilled , but generally do not want to be injured.
Downard accelerations of greater than 10 g cause bodily harm.
Negative (i.e upwa... | HuggingFaceTB/finemath | |
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here i... | HuggingFaceTB/finemath | |
# Average rate of change word problem:Â table
Common Core Math:
## Video transcript
Let T of T, so capital T of lowercase T denote the temperature capital T in Windhoek, Namibia measured in degrees Celsius when it's T lowercase T hours after midnight on a given day. The table below lists a few selected values of the... | HuggingFaceTB/finemath | |
# Is Ppm Mass Or Moles?
## How do you convert moles to PPM?
If you take molarity (with units mol/L), and multiply it by the molar mass (with units g/mol), you get g/L.
Just multiply g/L by 1000 to convert g to mg, and you have ppm (in mg/L of water)..
## How many ppm is 1%?
Percent to ppm conversion tablePercent (... | HuggingFaceTB/finemath | |
# Request for gentle explanation of defining a topology with its universal property
I am reading a book which says that whenever we can define a topology by saying "its the largest topology which satisfy $p$" then it is possible to define the same topology by saying it is the "smallest topology which satisfy $q$". Why... | open-web-math/open-web-math | |
## anonymous 4 years ago a particle starts SHM from the mean position. its amplitude is A and time is T.at what time when its speed is half of the maximum speed, its displacement is y is?
1. JamesJ
You mean its period is T?
2. anonymous
here i did v^2=A^2-X^2 and here we know max velocity is Aw=vmax w=2pie/T but nw... | open-web-math/open-web-math | |
# Help me "Hugo pays $188 for 8 new video games. How much will he pay for 16 video games? 2 by Chapis mulpity 188× 16 and u ahould get ur anawer i think 188 times 2 You divide 188 by 8 which is 23.50 then multiply 23.50 by 16 umm first of all i pressed 2 but my phone put 16 so bye oh my bad whoever made the q I multipl... | HuggingFaceTB/finemath | |
# A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
I am not sure whether this is right. Can anyone verify, whether this proof is valid? Thanks!
Define a sequence $\{a_n\}_{n\ge0}$ as follows: $$a_0=1,\qquad,a_1=3,\qquad,a_2=9,\qquad,a_n=a_{n-1}+a_{n-2}+a_{n-3}\text{ for }n\ge3.$$ Prove... | HuggingFaceTB/finemath |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.