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http://www.mathwarehouse.com/algebra/complex-number/absolute-value-complex-number.php | # Absolute Value of a Complex Number
How to calculate a complex number's absolute value
The absolute value of a real number like $$|4|$$ is its distance from 0 on the number line.
The absolute value of is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a compl... | 2018-07-23 10:04:45 | {
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"url": "http://ww... | What is the absolute value of the complex number \( -7 + 24i \)? | 48 | math-ai/AutoMathText |
https://socratic.org/questions/how-do-you-write-the-point-slope-form-of-the-equation-given-1-3-and-2-5 | # How do you write the point slope form of the equation given (-1,3) and (-2,5)?
##### 1 Answer
Jan 26, 2017
$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{- 2} \left(x + \textcolor{red}{1}\right)$
Or
$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- 2} \left(x + \textcolor{red}{2}\right)$
#... | 2021-12-03 10:35:13 | {
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"url": "https://socrat... | What is the point-slope form of the equation of the line passing through the points (-1, 3) and (-2, 5)? | 19 | math-ai/AutoMathText |
http://mathhelpforum.com/calculus/83329-how-do-i-integrate-basic-equation-print.html | # How do I integrate this basic equation?
• Apr 12th 2009, 04:13 AM
Phatmat
How do I integrate this basic equation?
I was wondering how I integrate this basic equation:
y' = 1 / (3 + 5x + x^2)
Any help would be great, thanks.
• Apr 12th 2009, 04:42 AM
stapel
Complete the square in the denominator to convert to one o... | 2016-10-28 23:34:19 | {
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"url": "http://... | What is the exact integral of the function \( y' = \frac{1}{3 + 5x + x^2} \) with respect to \( x \)? | 4 | math-ai/AutoMathText |
http://mathoverflow.net/feeds/question/107620 | Non-isomorphic finite simple groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T14:11:06Z http://mathoverflow.net/feeds/question/107620 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107620/non-isomorphic-finite-simple-groups Non-isomorphic finite simpl... | 2013-05-19 14:11:07 | {
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"url": "http://matho... | What is the smallest integer \( n \) such that there exist two non-isomorphic finite simple groups of order \( n \), and can you provide an example of such groups? | 2 | math-ai/AutoMathText |
http://mathhelpforum.com/advanced-statistics/119474-conjugate-prior-laplace-distribution.html | Math Help - Conjugate prior of a Laplace distribution
1. Conjugate prior of a Laplace distribution
Does anyone know what the Bayesian conjugate prior of a Laplace distribution likelihood is?
Most of the exponential family of distributions have known conjugate priors but the Laplace is not in the exponential family i... | 2016-07-31 02:15:58 | {
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"url": "http://ma... | What is the conjugate prior distribution for a Laplace distribution likelihood, and can you provide its parameters in terms of the likelihood's parameters? | 60 | math-ai/AutoMathText |
https://addjustabitofpi.com/2019/10/19/what-are-imaginary-numbers/ | # What are imaginary numbers?
We’ve always been told we can’t take the square root of a negative number, since the square of a negative number is a positive number. But remember, in maths nothing is impossible, not even dividing by 0!
Imagine you want to take the square root of -1;
$\sqrt{-1}$
or the square root of... | 2021-12-03 10:09:29 | {
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"url": "https://addj... | What is the value of \( i^3 \) and how does it relate to the properties of imaginary numbers? | 125 | math-ai/AutoMathText |
http://math.stackexchange.com/questions/314936/how-to-show-that-a-finite-comutative-ring-without-zero-divisors-is-a-field | How to show that a finite comutative ring without zero divisors is a field?
$R$ is finite commutative ring without zero divisors which has at least two elements. How to show that $R$ is field?
I'm just starting with abstract algebra and I'd really appreciate if someone could explain it to me.
-
By "zero factors" you... | 2014-03-07 15:21:48 | {
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"url": "http://math... | Prove that if \( R \) is a finite commutative ring without zero divisors and has at least two elements, then \( R \) is a field. | 54 | math-ai/AutoMathText |
https://number.subwiki.org/w/index.php?title=Poulet_number&oldid=617 | # Poulet number
## Definition
A Poulet number or Sarrus number is an odd composite number such that:
.
In other words, divides . Equivalently, is a Fermat pseudoprime modulo .
## Occurrence
### Initial examples
The first few Poulet numbers are .
These include, for instance:
### Infinitude
Further informati... | 2022-08-11 21:38:00 | {
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"url": "https://number.... | What is the smallest Poulet number, and can you prove that it is a Fermat pseudoprime modulo 2? | 45 | math-ai/AutoMathText |
http://lara.epfl.ch/w/sav08:satisfiability_of_sets_of_formulas | • English only
# Satisfiability of Sets of Formulas
We next introduce sets of formulas as a way of talking about potentially infinite conjunctions of formulas. We will need this when reducing reasoning in first-order logic to reasoning in propositional logic.
We say that interpretation is a model for a set of formul... | 2018-08-14 19:45:57 | {
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"url": "http://lara.epfl.c... | Given a countably infinite set of propositional variables, can you construct an infinite set of formulas such that the set is satisfiable, and provide a specific interpretation that serves as a model for this set? | 74 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/2164968/proving-that-a-4-regular-graph-has-two-edge-disjoint-cycles | # Proving that a 4-regular graph has two edge-disjoint cycles
Note: This is not an assignment/homework question, just review for an exam
We call two cycles edge-disjoint if they do not share any common edges, but they may share vertices.
Prove that any 4-regular graph contains at least two edge-disjoint cycles.
I w... | 2019-06-19 15:42:24 | {
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"url": "https://math.... | Prove that any 4-regular graph contains at least two edge-disjoint cycles. | 165 | math-ai/AutoMathText |
http://mathhelpforum.com/algebra/98629-sum-differences-9th-grade.html | # Math Help - sum and differences? 9th grade?
1. ## sum and differences? 9th grade?
Use these patterns to factor polynomials that are sums and differences of cubes.
a^3 + b^3 = (a+b)(a^2-ab+b^2)
a^3-b^3=(a-b)(a^2+ab+b^2)
a)x+8
b)8x^3+27
c)64-y^3
d)2u^3 + 16V^3
e)d^5 + f^3
f) w^6 -1
2. if the sum of two numbers is 6... | 2016-07-24 19:11:19 | {
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"url": "http://ma... | If the sum of two numbers is 6 and the sum of their cubes is 18, what is the sum of their squares? | 101 | math-ai/AutoMathText |
https://www.encyclopediaofmath.org/index.php/Solid_angle | # Solid angle
A part of space bounded by all the half-lines going from one point (the vertex) through the points of a closed curve (see Fig. a, Fig. b).
Figure: s086060a
Figure: s086060b
A particular case of a solid angle is that of a polyhedral angle. One takes as measure of a solid angle the ratio of the surface ... | 2019-09-18 07:07:04 | {
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"url": "http... | What is the measure in steradians of the solid angle corresponding to a solid angle that occupies one third of the space around a point? | 114 | math-ai/AutoMathText |
https://socratic.org/questions/55bfe01a581e2a0e009bc307 | # Question #bc307
Aug 3, 2015
${x}^{2} + 36$ has no zeros in the set of Real numbers.
#### Explanation:
The is no Real number whose square is $- 36$.
In many textbooks, this kind of equation is said to have "no solution until the author gets around to introducing $\sqrt{- 1}$.
(The square of a positive is positive... | 2019-02-22 01:43:36 | {
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"url": "https://socrat... | Consider the equation \( x^2 + 36 = 0 \). What is the minimum possible value of \( x^2 \) for \( x \) in the set of real numbers? | 88 | math-ai/AutoMathText |
https://socratic.org/questions/58c7f1897c01494ffedf5e2e | # Question #f5e2e
Jul 14, 2017
I got $13.6 \frac{m}{s} ^ 2$ in opposite direction to the car motion (a deceleration).
#### Explanation:
We can use the Kinematic relationship:
${v}_{f} = {v}_{i} + a t$
with:
${v}_{f} = 0$ final velocity;
${v}_{i} = 45 \frac{m}{s}$ initial velocity;
$t = 3.3 s$ time;
$a =$accelera... | 2020-10-30 14:50:33 | {
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"url": "https://socra... | A car is moving with an initial velocity of 45 m/s and comes to a stop in 3.3 seconds. What is the magnitude of the car's acceleration, and in what direction does this acceleration act? | 17 | math-ai/AutoMathText |
http://mathhelpforum.com/calculus/122613-easly-limit-problem-dont-know-how-start.html | # Thread: Easly limit problem dont know how to start
1. ## Easly limit problem dont know how to start
Could any body please give me a hint about the first step
Find $\lim_{x \to 2} \left[ \frac{x-1}{x-2} - \frac{1}{ln(x-1)} \right]$
2. The difficulty with a question like this, where you show no work at all, is that... | 2013-12-19 21:20:42 | {
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"url": "http:/... | Evaluate the limit:
\[
\lim_{x \to 2} \left[ \frac{x-1}{x-2} - \frac{1}{\ln(x-1)} \right].
\] | 41 | math-ai/AutoMathText |
https://socratic.org/questions/5885631fb72cff1ab68610f0 | # What is the atomic mass of a gas that has rho=2.50*g*L^-1 at a pressure of 0.974*atm, and a temperature of 371*K?
Jan 24, 2017
Given $P V = n R T$..........$\text{molar mass}$ $\cong$ $80 \cdot g \cdot m o {l}^{-} 1$
#### Explanation:
$\frac{P}{R T} = \frac{n}{V} = \frac{\text{mass"/"molar mass}}{V}$
And thus $\... | 2020-07-15 18:43:36 | {
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"url": "https://socratic... | What is the molar mass of a gas that has a density of 2.50 g/L at a pressure of 0.974 atm and a temperature of 371 K? Please provide your answer in g/mol. | 36 | math-ai/AutoMathText |
https://socratic.org/questions/what-is-the-degree-of-the-polynomial-x-4-3x-3y-2-8x-12#112128 | # What is the degree of the polynomial x^4-3x^3y^2+8x-12?
Since the highest combined power is $3 + 2 = 5$, the degree is $5$. | 2022-07-01 07:06:35 | {
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"url": "https://socrati... | What is the degree of the polynomial \( p(x, y) = x^4 - 3x^3y^2 + 8x - 12 \) and how is it determined? | 46 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/1488555/improper-integrals-with-u-substitution-int-limits-1-infty-frac-log-xx-d | # Improper integrals with u-substitution $\int\limits_1^\infty \frac{\log x}{x}\,dx$
I am going over improper integrals and I have a question about approaching a certain problem.
The question is the the integral $$\int_1^\infty \frac{\log x}{x}\,dx$$
The most obvious (to me) solution would be to take the limit as $t... | 2020-09-26 17:51:56 | {
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"url": "https://m... | What is the value of the improper integral $$\int_1^\infty \frac{\log x}{x}\,dx$$? | 84 | math-ai/AutoMathText |
http://math.stackexchange.com/questions/227681/how-to-find-chromatic-number-of-the-hypercube-q-n/227689 | # How to find chromatic number of the hypercube $Q_n$?
How to find chromatic number the hypercube $Q_n$?
I know $\chi(Q_2)$=2 , $\chi(Q_3)$=2 , $\chi(Q_4)$=4
-
What is $Q_n{}$? – Chris Eagle Nov 2 '12 at 17:38
The $n$-cube graph. – user02138 Nov 2 '12 at 17:39
## 2 Answers
Every hypercube is bipartite (and so the ... | 2016-05-24 14:11:00 | {
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"url": "http://math.... | What is the chromatic number of the hypercube \( Q_n \) for \( n \geq 1 \)? Specifically, determine \( \chi(Q_5) \) and explain your reasoning. | 97 | math-ai/AutoMathText |
https://wikimili.com/en/3_21_polytope | # 3 21 polytope
Last updated
Orthogonal projections in E7 Coxeter plane 321 231 132 Rectified 321 birectified 321 Rectified 231 Rectified 132
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset, published in his 190... | 2023-02-06 10:30:31 | {
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"url": "https://wikimil... | What is the total number of edges in the 321 polytope, and how does this relate to its vertex and facet counts? | 83 | math-ai/AutoMathText |
https://anecdotalmath.wordpress.com/2015/01/03/my-favorite-number/ | # My Favorite Number
A few weeks ago, one of my friends asked me the following question:
As a mathematician, what is your favorite number?
My first response was tongue-in-cheek. I said that I would probably pick 2 or 3. After all, I rarely work with large numbers in any of my mathematics classes. Furthermore, as ... | 2017-10-21 04:46:06 | {
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"url": "https://anecdo... | What is the value of \( M_{67} = 2^{67} - 1 \), and can you show it as a product of its prime factors? | 71 | math-ai/AutoMathText |
https://encyclopediaofmath.org:443/wiki/Principal_curvature | Principal curvature
Jump to: navigation, search
The normal curvature of a surface in a principal direction, i.e. in a direction in which it assumes an extremal value. The principal curvatures $k _ {1}$ and $k _ {2}$ are the roots of the quadratic equation
$$\tag{* } \left | \begin{array}{ll} L - kE &M - kF \\ M - kF... | 2022-11-29 20:25:59 | {
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"url": "... | Given a surface with principal curvatures \( k_1 = 3 \) and \( k_2 = 4 \) at a certain point, calculate the mean curvature \( H \) and the Gaussian curvature \( K \) at that point. | 43 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/4256562/find-the-general-expression-for-the-n-th-derivative/4256581 | # Find the general expression for the n-th derivative
I want to find the $$n$$-th derivatives of the function $$f(x)=\frac{1}{(1-x^2)^b}$$ with respect to x. Here $$b$$ is a positive constant. By using the chain rule, I can get the first derivative is $$f'(x)=(-b)(1-x^2)^{-b-1}(-2x).$$ By using the chain rule and prod... | 2022-01-21 00:40:03 | {
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"url": "https://math... | What is the general expression for the \( n \)-th derivative of the function \( f(x) = \frac{1}{(1-x^2)^b} \), where \( b \) is a positive constant? Can you express this in a closed form? | 61 | math-ai/AutoMathText |
https://cs.stackexchange.com/questions/47355/for-tiling-simply-connected-regions-with-shapes-beyond-just-rectangles-is-there | # For tiling simply connected regions with shapes beyond just rectangles, is there a lower # of tile shapes needed for NP-completeness?
In "TILING SIMPLY CONNECTED REGIONS WITH RECTANGLES" by Igor Pak and Jed Yang, they show there is a set of "no more than $10^6$ rectangles" such that the problem of tiling an arbitrar... | 2021-03-01 10:58:07 | {
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"url": "https://cs... | What is the minimum number of simply connected tile shapes (which can be non-rectangular) required to demonstrate NP-completeness for tiling arbitrary simply connected regions? | 130 | math-ai/AutoMathText |
https://plainmath.net/3888/evaluate-the-following-integrals-intfrac-e-sin-x-sec-x-dx | # Evaluate the following integrals. intfrac{e^{sin x}}{sec x}dx
Evaluate the following integrals.
$\int \frac{{e}^{\mathrm{sin}x}}{\mathrm{sec}x}dx$
You can still ask an expert for help
• Questions are typically answered in as fast as 30 minutes
Solve your problem for the price of one coffee
• Math expert for every... | 2022-08-17 21:47:03 | {
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"url": "https://plainma... | Evaluate the integral \( I = \int \frac{e^{\sin x}}{\sec x} \, dx \) and express the result in terms of elementary functions. What is the final answer? | 94 | math-ai/AutoMathText |
https://quantumcomputing.stackexchange.com/questions/18077/exercise-4-41-in-nc-book-qcqi-how-can-i-implement-r-z-theta-using-the-circ | # Exercise 4.41 in N&C book QCQI: how can i implement $R_z(\theta)$ using the circuit shown and $Z$?
I'm studying Nielsen and Chuang's book.
I cannot solve one of the questions in the exercise 4.41.
The question is the last one that is
Explain how repeated use of this circuit and Z gates may be used to apply a $$R_... | 2022-05-17 06:51:36 | {
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"url": "https://qu... | What is the probability of successfully applying the \( R_z(\theta) \) gate using the described circuit with repeated applications, and how does this probability converge to 1 as the number of repetitions increases? | 33 | math-ai/AutoMathText |
https://www.albert.io/ie/gmat/percents-of-students-playing-sports-and-failing-school | ?
Free Version
Moderate
Percents of Students Playing Sports and Failing School
GMAT-4JGYFY
There are $60$ students in a class, unfortunately, $25\%$ of these students are failing school. $30\%$ of the students in the class play basketball as their only sport while the remaining $70\%$ of the class play soccer as th... | 2016-12-06 12:20:33 | {
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"url": "https://www.albe... | In a class of 60 students, 25% are failing and 30% of the students play basketball, while 70% play soccer. If 20% of the failing students are soccer players, what percent of the basketball players are failing, rounded to the nearest whole percent? | 50 | math-ai/AutoMathText |
https://socratic.org/questions/how-do-you-simplify-4x-2-6x-8#367546 | # How do you simplify 4x-2+(-6x)+8?
Jan 21, 2017
See a solution process below for: 4x + 2 = 6x - 8
#### Explanation:
First, subtract $\textcolor{red}{4 x}$ and add $\textcolor{b l u e}{8}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:
$4 x - \textcolor{red}{4 x} + 2 + \t... | 2023-03-30 09:02:18 | {
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"url": "https://socratic... | What is the simplified form of the expression \(4x - 2 - 6x + 8\)? | 151 | math-ai/AutoMathText |
https://ai.stackexchange.com/questions/22079/continuous-state-and-continuous-action-markov-decision-process-time-complexity-e | # Continuous state and continuous action Markov decision process time complexity estimate: backward induction VS policy gradient method (RL)
Model Description: Model based(assume known of the entire model) Markov decision process.
Time($$t$$): Finite horizon discrete time with discounting factor
State($$x_t$$): Cont... | 2023-02-02 02:32:27 | {
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"url": "https://ai... | What is the worst-case computational complexity of performing backward induction on a discrete state space that results from discretizing a five-dimensional continuous state space, given that each dimension has five grid points? | 10 | math-ai/AutoMathText |
https://brilliant.org/discussions/thread/proof-of-a-chebyshev-identity/ | ×
# Proof of a Chebyshev Identity
Reference: Wiki on Chebyshev Polynomials, Proof problem 6.
$$\huge T_n(x) = \frac{ ( x - \sqrt{ x^2 - 1} )^n + ( x + \sqrt{ x^2 - 1 } ) ^ n } { 2} .$$
Solution: $$\text{From the above identity, we get}$$ $$\large{ T }_{ n }(\cos { \theta )= } \frac { { \left( \cos { \theta -\sqrt {... | 2016-12-09 00:04:11 | {
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"url": "https://brilli... | Given the identity for the Chebyshev polynomial of the first kind, \( T_n(\cos \theta) = \cos(n \theta) \), calculate \( T_5(0.5) \). What is the exact value of \( T_5(0.5) \)? | 77 | math-ai/AutoMathText |
https://undergroundmathematics.org/geometry-of-equations/r9273/solution | Review question
# Can we find the point midway between an intersection and a line? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Ref: R9273
## Solution
$P$ is the point of intersection of the lines $y+x=1$ and $3y+2x=1$. Find the co... | 2018-01-23 07:56:05 | {
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"url": "... | What are the coordinates of the point that is midway between the point of intersection \( P \) of the lines \( y + x = 1 \) and \( 3y + 2x = 1 \), and the line \( y = 2x + 8 \)? | 118 | math-ai/AutoMathText |
https://online.stat.psu.edu/stat200/lesson/12/12.6 | # 12.6 - Correlation & Regression Example
Each spring in Indianapolis, IN the National Football League (NFL) holds its annual combine. The combine is a place for college football players to perform various athletic and psycholological tests in front of NFL scouts.
Two of the most recognized tests are the forty-yard d... | 2021-07-27 14:59:12 | {
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"url": "https://online.stat.... | Given the correlation coefficient of approximately -0.73 between vertical jump height (in inches) and forty-yard dash time (in seconds) for 337 college football players, what percentage of the variance in the forty-yard dash time can be explained by the vertical jump height according to the linear regression model? | 39 | math-ai/AutoMathText |
https://www.physicsforums.com/threads/tough-integral.275432/ | # Homework Help: Tough Integral
1. Nov 27, 2008
### the.flea
1. The problem statement, all variables and given/known data
Integral of: 2x^3/(x^3-1) with respect to x.
3. The attempt at a solution
you can divide them to get sum of integrals.
=int(2,x) + 2*int(1/(x^-1),x)
=2x + 2*int(1/(x^-1),x)
Im having trouble pr... | 2018-08-14 10:52:33 | {
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"url": "https://ww... | Evaluate the integral \(\int \frac{2x^3}{x^3 - 1} \, dx\) and provide a detailed solution. | 185 | math-ai/AutoMathText |
http://openstudy.com/updates/4f37744fe4b0fc0c1a0d5156 | ## TomLikesPhysics 3 years ago If I want to integrate (sinx)^2 using the method of substitution than what are my function g and g`? x would be pointless because than I would just replace the x with a t but sinx also does not seem to work because there is no cosx.
1. NotSObright
Replace cos x by sqrt(1-t^2)
2. NotSOb... | 2015-08-31 21:46:32 | {
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"url": "http://openstu... | What is the value of the integral \(\int_0^{\frac{\pi}{2}} \sin^2 x \, dx\) using the trigonometric identity \(\sin^2 x = \frac{1}{2} - \frac{1}{2}\cos(2x)\)? | 25 | math-ai/AutoMathText |
http://openstudy.com/updates/50f8befce4b027eb5d9a4d24 | mlk913 Group Title find all values of Θ for which sinΘ = -sqrt (1-cos^2Θ) on (0,2pi) one year ago one year ago
• This Question is Open
1. seidi.yamauti Group Title
the fundamental law that is [sin²x + cos²x = 1] will help you that is the same as sin²x=1-cos²x
2. seidi.yamauti Group Title
$\sin ^{2}\theta + \cos ^{2... | 2014-07-28 08:24:59 | {
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"url": "http://openstudy... | Find all values of \( \theta \) in the interval \( (0, 2\pi) \) for which \( \sin \theta = -\sqrt{1 - \cos^2 \theta} \). | 152 | math-ai/AutoMathText |
https://www.cymath.com/blog/2013-09-09 | # Problem of the Week
## Updated at Sep 9, 2013 8:53 AM
This week we have another calculus problem:
How can we solve for the integral of $$\tan^{3}x$$?
Let's start!
$\int \tan^{3}x \, dx$
1 Use Pythagorean Identities: $$\tan^{2}x=\sec^{2}x-1$$.$\int (\sec^{2}x-1)\tan{x} \, dx$2 Expand.$\int \tan{x}\sec^{2}x-\tan... | 2021-09-16 11:03:57 | {
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"url": "https://www.cymat... | Evaluate the integral $$\int \tan^{3}x \, dx$$ and express your answer in terms of $x$ and any necessary constants. | 142 | math-ai/AutoMathText |
https://physics.stackexchange.com/questions/266061/why-does-the-amount-of-my-mouthwash-influence-the-colour/266112 | # Why does the amount of my mouthwash influence the colour?
When I only have a little mouthwash left, it's more of an aqua/baby blue colour. When it's full, it's a much more deep blue. Why does the amount of the liquid determine the colour? Doesn't seem like it would be an issue of concentration.
• Is it a different ... | 2022-06-26 21:28:46 | {
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"url": "https://ph... | If a bottle of mouthwash and a clear glass both contain the same volume of liquid, but the mouthwash appears significantly darker in color due to its higher optical density, how would you calculate the minimum length of the path the light travels through the mouthwash that results in an optical density greater than 1? ... | 38 | math-ai/AutoMathText |
http://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-4-exponential-and-logarithmic-functions-section-4-2-the-natural-exponential-function-4-2-exercises-page-379/30 | ## College Algebra 7th Edition
Published by Brooks Cole
# Chapter 4, Exponential and Logarithmic Functions - Section 4.2 - The Natural Exponential Function - 4.2 Exercises: 30
#### Answer
$D(20)\approx 1.6$ ft
#### Work Step by Step
We are given: $D(t)=\frac{5.4}{1+2.9e^{-0.01t}}$ We plug in $t=20$ years: $D(20)=... | 2018-04-19 13:41:01 | {
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"url": "http://ww... | Given the function \( D(t) = \frac{5.4}{1 + 2.9 e^{-0.01t}} \), determine the value of \( D(20) \) and round your answer to two decimal places. | 158 | math-ai/AutoMathText |
https://www.maa.org/programs/faculty-and-departments/course-communities/browse?term_node_tid_depth=40572&page=5 | # Browse Course Communities
Displaying 51 - 60 of 235
This applet allows the user to enter values for $n$ and $p$.
This interactive resource allows the user to enter $p$ and $n$. It gives the probability distribution, graphs it, and can also calculate probabilities between two given values.
This article gives a descr... | 2022-08-08 05:20:46 | {
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"url": "https://www.maa.org/p... | In the context of the St. Petersburg paradox, what is the expected value of the game where the player receives $2^n$ dollars if a fair coin lands heads on the $n$th toss, and how does this lead to the paradox regarding infinite expected value? | 6 | math-ai/AutoMathText |
https://reference.digilentinc.com/learn/fundamentals/circuits/ohms-law/start | # Ohm's Law
## Introduction
Ohm's Law states that the voltage difference across a resistor is proportional to the current through the resistor. The constant of proportionality is the resistance, R. The governing equation is shown to the left below, while a typical symbolic representation of a resistor is shown to the... | 2020-08-06 18:42:07 | {
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"url": "https://refer... | A 2 MΩ resistor is connected to a current source supplying 7 μA of current. What is the voltage across the resistor, and what are the polarities of its terminals? | 72 | math-ai/AutoMathText |
https://en.m.wikibooks.org/wiki/Computability_and_Complexity/Complexity/Time_Complexity/P | # P
We can classify all the computational problems into 2 categories, that can be solved by algorithms and that cannot be solved. Although some problems can be solved, we may not be able to solve them in reasonable amount of time. The problems which can be solved are classified in to P and NP. There are other classifi... | 2022-12-10 06:38:03 | {
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"url": "https://en.m.w... | What is the relationship between the complexity classes P and NP in terms of the solvability of problems, and can you provide an example of a problem that belongs to each class? | 202 | math-ai/AutoMathText |
http://wiki.sagemath.org/HeckeAlgebras | # Design discussion about Hecke Algebras
Quite a few people expressed interest in (affine) Iwahori-Hecke algebras, including NicolasBorie, DanBump, BrantJones, VincentFeray, FlorentHivert, MikeHansen, AndrewMathas, AnneSchilling, NicolasThiéry.
There are pieces of code for it in many different places in MuPAD-Combina... | 2015-05-29 18:01:04 | {
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"url": "http://wiki.sag... | What is the dimension of the (q_1, q_2)-Iwahori-Hecke algebra for the Weyl group of type B_3, considering a base ring that contains the parameters \( q_1 \) and \( q_2 \)? | 78 | math-ai/AutoMathText |
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=znsl&paperid=6548&option_lang=eng | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PERSONAL OFFICE
General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Zap. Nauchn. Sem. POMI: Year: Volume: Issue: Page: Find
Zap. Nauchn... | 2019-05-20 08:51:21 | {
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"openwebmath_score": 0.3033161759376526,
"url": "http://www.mathne... | What are the new sufficient conditions established by V. M. Korchevsky for the applicability of the strong law of large numbers for sequences of pairwise independent non-identically distributed random variables, and how do they generalize Etemadi's extension of Kolmogorov's strong law of large numbers? | 91 | math-ai/AutoMathText |
https://konsulting-pr.pl/3792/Sep/1599728985.html | # the significance about a cone and a cylinder
2017-05-19T21:05:55+00:00
• ## What is the difference between a cone and a cylinder
Cone and Cylinder in Math A cone is a 3dimensional solid object that has a circular base and a single vertex When the vertex is over the center of the base, it is called a right cone Whe... | 2021-12-04 07:53:25 | {
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"url": "https://ko... | Given that a cone and a cylinder have the same circular base and identical height, if the volume of the cylinder is \(84\pi\) cubic inches, what is the volume of the cone? | 100 | math-ai/AutoMathText |
https://balbhartisolutions.com/maharashtra-board-11th-maths-solutions-chapter-9-ex-9-2-part-1/ | Balbharti Maharashtra State Board Class 11 Maths Solutions Pdf Chapter 9 Probability Ex 9.2 Questions and Answers.
## Maharashtra State Board 11th Maths Solutions Chapter 9 Probability Ex 9.2
Question 1.
First, 6 faced die which is numbered 1 to 6 is thrown, then a 5 faced die which is numbered 1 to 5 is thrown. What... | 2022-11-28 21:35:53 | {
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"url": "https:/... | A bag contains 75 tickets numbered from 1 to 75. If one ticket is drawn at random, what is the probability that the number on the ticket is either a perfect square or divisible by 4? | 3 | math-ai/AutoMathText |
https://secure.cas.usf.edu/depts/mth/research/seminars/analysis/spring09/ | Research
Analysis
Friday, April 17, 2009
Title: Some Results on Unbounded Bergman Operators
Speaker: Sherwin Kouchekian
Time: 4:00pm–5:00pm
Place: PHY 109
Abstract
We will consider Bergman operators. These are operators of multiplication by the independent variable $$z$$ over the space of square integrable analyti... | 2023-04-01 08:29:41 | {
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"openwebmath_perplexity": 1414.204012089994,
"openwebmath_score": 0.5255521535873413,
"url": "https://secure.cas.u... | What is the minimum degree of a polynomial that can produce singularities outside a given domain when solving the Dirichlet Problem, considering various geometrical properties of the domain? | 56 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/3728632/on-the-equation-psi-12-psin-n-n-involving-the-dedekind-psi-function-a | # On the equation $\psi(-1+2(\psi(n)-n))=n$ involving the Dedekind psi function, as a characterization of Mersenne primes
In this post we denote the Dedekind psi function as $$\psi(m)$$ for integers $$m\geq 1$$. This is an important arithmetic fuction in several subjects of mathematics. As reference I add the Wikipedi... | 2020-08-10 11:28:00 | {
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"openwebmath_score": 0.8944151401519775,
"url": "https://ma... | Can you determine for which integers \( n \geq 2 \) the equation
\[
\psi(2(\psi(n) - n) - 1) = n
\]
holds true, specifically relating \( n-1 \) to being a Mersenne prime? In particular, if \( 2^p - 1 \) is a Mersenne prime, what specific values of \( n \) can we find that satisfy this equation? | 32 | math-ai/AutoMathText |
https://www.qb365.in/materials/stateboard/9th-maths-term-3-trigonometry-two-marks-questions-1192.html | #### Term 3 Trigonometry Two Marks Questions
9th Standard
Reg.No. :
•
•
•
•
•
•
Maths
Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. From the given figure find all the trigonometric ratios of angle B.
2. From the given figure, find the values of (i) sinB (ii) secB (iii) cot B (iv) cosC (v) tanC (vi) cosecC
... | 2022-01-26 10:35:24 | {
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"openwebmath_perplexity": 2145.4484999415736,
"openwebmath_score": 0.9010040163993835,
"url": "https://www.qb365.... | Given that \( \cos A = \frac{2x}{1+x^2} \), find \( \sin A \) and \( \tan A \) in terms of \( x \). What is the numerical value of \( \tan A \) when \( x = 1 \)? | 79 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/845243/finding-lim-x-to-infty-left-frac1-x3x2-7-x-right5 | # Finding $\lim_{x \to - \infty} \left( \frac{1 - x^{3}}{x^{2} + 7 x} \right)^{5}$.
I have to evaluate the following limit: $$\lim_{x \to - \infty} \left( \frac{1 - x^{3}}{x^{2} + 7 x} \right)^{5}.$$ What I did was to divide both the numerator and the denominator of the expression inside the parentheses by $\dfrac{1}{... | 2019-07-23 22:14:38 | {
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"openwebmath_score": 0.9904192686080933,
"url": "https://ma... | Evaluate the limit:
\[
\lim_{x \to -\infty} \left( \frac{1 - x^{3}}{x^{2} + 7x} \right)^{5}.
\]
What is the value of this limit? | 128 | math-ai/AutoMathText |
https://nforum.ncatlab.org/discussion/4587/distributivity-pullback/ | Start a new discussion
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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeDec 2nd 2012
•... | 2021-04-16 15:15:08 | {
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"url": "https://nfor... | Given the sequence of comments dated from December 2, 2012, to June 26, 2017, how many unique authors contributed to the discussion in the provided snippet? | 230 | math-ai/AutoMathText |
http://community.boredofstudies.org/12/mathematics-advanced/386521/urgent-need-help-probability-question.html | # Thread: URGENT! Need help with probability question
1. ## URGENT! Need help with probability question
Thank god if someone replies as HSC math is within a few hours
-If 3% of coins produced are faulty, what is the probability that a sample of 3 coins taken from the production line will have atleast two faulty coin... | 2019-05-19 08:58:27 | {
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"openwebmath_score": 0.6656769514083862,
"url": "http:... | If 3% of coins produced are faulty, what is the probability that a sample of 3 coins taken from the production line will contain at least 2 faulty coins? Please express your answer as a fraction in simplest form. | 29 | math-ai/AutoMathText |
https://homework.cpm.org/category/ACC/textbook/acc6/chapter/5%20Unit%205/lesson/CC1:%205.3.2/problem/5-82 | ### Home > ACC6 > Chapter 5 Unit 5 > Lesson CC1: 5.3.2 > Problem5-82
5-82.
For each of the following products, estimate the answer. Explain your reasoning. Then multiply each set of numbers to see how close you were.
To estimate the product of each expression in parts (a), (b), and (c), try rounding
the mixed number... | 2021-03-01 17:10:29 | {
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"openwebmath_score": 0.8441652655601501,
"url": "https://homework.cpm.... | Estimate the product of the mixed numbers \(2 \frac{1}{3}\) and \(1 \frac{1}{2}\), and then calculate the exact product to verify your estimation. What are the estimated and actual products? | 191 | math-ai/AutoMathText |
https://www.shaalaa.com/question-bank-solutions/applications-compound-interest-formula-the-population-place-increased-54000-2003-rate-5-annum-what-would-be-its-population-2005_15332 | CBSE Class 8CBSE
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# Solution for The Population of a Place Increased to 54000 in 2003 at a Rate of 5% per Annum What Would Be Its Population in 2005? - CBSE Class 8 - Mathematics
ConceptApplications of Compound Interest Formula
#### Question
The population of a place increased to 54000 in 2003... | 2019-05-24 12:14:23 | {
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"openwebmath_perplexity": 1758.9335402679374,
"openwebmath_score": 0.23934265971183777,
"url": "https://www... | What will the population of a place be in 2005 if it was 54,000 in 2003 and is increasing at a rate of 5% per annum? | 266 | math-ai/AutoMathText |
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