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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_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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"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_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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"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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•... | 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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"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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"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_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 |
https://en.m.wikipedia.org/wiki/Embedding | # Embedding
In mathematics, an embedding (or imbedding[1]) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map f : XY. ... | 2019-05-20 23:57:31 | {
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"openwebmath_score": 0.9348891377449036,
"url": "https://en.m.... | What is the minimum dimension \( n \) required for an embedding of a smooth manifold \( M \) of dimension \( m \) into \( \mathbb{R}^n \) according to the Whitney embedding theorem, and can you provide an example of a manifold that achieves this minimum? | 108 | math-ai/AutoMathText |
https://www.physicsforums.com/threads/find-power-series-representations-of-the-general-solution.810052/ | Find power series representations of the general solution
1. Apr 22, 2015
Shackleford
1. The problem statement, all variables and given/known data
(1+x2) y'' + 2xy' = 0 in powers of x
2. Relevant equations
$y'' = \sum_{n=2}^{\infty} (n-1)na_nx^{n-2}$
$y' = \sum_{n=1}^{\infty} na_nx^{n-1}$
3. The attempt at a so... | 2017-08-19 12:38:06 | {
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"openwebmath_score": 0.39215511083602905,
"url": "https://ww... | What is the power series representation of the general solution to the differential equation \((1+x^2)y'' + 2xy' = 0\)? Please provide the coefficients \(a_n\) for the series expansion. | 107 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/2077500/why-must-a-function-be-closed-for-descent-methods-to-work | # Why must a function be closed for descent methods to work?
At the beginning of chapter 9 of Boyd & Vandenberghe's Convex Optimization, about unconstrained minimization, it is said:
The starting point $$x^{(0)}$$ for a method must lie in $$\mathbf{dom} f$$, and in addition the sublevel set $$S = \{x \in \mbox{dom} \... | 2022-01-22 06:36:07 | {
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"openwebmath_score": 0.8123181462287903,
"url": "https://mat... | Can you provide two distinct examples of convex functions that are not closed, and explain how this lack of closedness affects the solvability of the minimization problem using descent methods? | 256 | math-ai/AutoMathText |
https://eurekamathanswers.com/compound-interest-as-repeated-simple-interest/ | Do you want to calculate Compound Interest? If so, this article is the best place for you to guide you on the concept of Compound Interest as Repeated Simple Interest. We will explain to you everything on how to calculate compound interest as repeated simple interest without using a formula. Check out the Worked-out Ex... | 2021-11-30 14:30:16 | {
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"openwebmath_score": 0.41904768347740173,
"url": "http... | What is the compound interest earned on an investment of $25,000 for 4 years at an annual interest rate of 6%, calculated using the method of repeated simple interest? | 244 | math-ai/AutoMathText |
https://qa.engineer.kmitl.ac.th/ngttmi/derivative-of-sin-18ff3a | # derivative of sin
By definition: Using the well-known angle formula tan(α+β) = (tan α + tan β) / (1 - tan α tan β), we have: Using the fact that the limit of a product is the product of the limits: Using the limit for the tangent function, and the fact that tan δ tends to 0 as δ tends to 0: One can also compute the ... | 2021-08-06 01:10:05 | {
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"url": "https://qa.engineer... | What is the derivative of the function \( f(x) = \sin^2(\ln x) \)? | 281 | math-ai/AutoMathText |
https://socratic.org/questions/what-is-the-trigonometric-form-of-7-i-1 | # What is the trigonometric form of (7-i) ?
Aug 18, 2016
$5 \sqrt{2} \left(\cos \left(0.142\right) - i \sin \left(0.142\right)\right)$
#### Explanation:
To convert from $\textcolor{b l u e}{\text{complex to trigonometric form}}$
That is $\left(x + y i\right) \to \left[r \left(\cos \theta + i \sin \theta\right)\ri... | 2020-02-23 18:04:33 | {
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"url": "https://socrati... | What is the trigonometric form of the complex number \( 7 - i \) in terms of \( r \), \( \theta \), and the expressions for \( \cos \theta \) and \( \sin \theta \)? | 67 | math-ai/AutoMathText |
http://www.jessicayung.com/what-does-the-lagrange-multiplier-mean/ | # What does the Lagrange Multiplier mean?
Note: The crux of this post really is in talking about the Lagrange Multiplier, so scroll down to ‘The Lagrange’ for that.
#### What is a constrained optimisation problem?
Suppose we want to maximise our own utility (our enjoyment) but have a limited amount of resources (tim... | 2021-10-19 11:46:02 | {
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"url": "http://www.j... | Given the utility function \( u(x) = x \) and a budget constraint of \( x \leq 10 \), what is the value of the Lagrange multiplier \(\lambda\) when maximizing utility under this constraint, assuming that the maximum utility occurs exactly at the constraint boundary? | 42 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/1283325/questions-about-p-adic-numbers/1283339 | I got two questions about $p$-adic numbers:
1. I often read that the field $\mathbb Q_p$ is much different than the field $\mathbb R$.
An element of $\mathbb Q_p$ is of the form $\sum_{i=-k}^{\infty}a_ip^i$ where $a_i\in \{0,...,p-1\}$.
But isn't this just a real number? So at least the elements of $\mathbb Q_p$ are... | 2019-10-15 13:20:01 | {
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"url": "https://ma... | Let \( p = 5 \) and consider the series
\[
S = \sum_{n=0}^{\infty} 5^{n!}.
\]
Is the series \( S \) convergent in \( \mathbb{Q}_5 \)? If so, what is its value in \( \mathbb{Q}_5 \)? | 57 | math-ai/AutoMathText |
http://atozmath.com/example/Factor.aspx?he=e | Home > Algebra calculators > Factoring Polynomials example
Factoring Polynomials example ( Enter your problem ) FormulaExamples 2. Examples Type-1 (Taking common) Examples... (1) ax + a + 2x + 2 =(ax + a) + (2x + 2) =a(x + 1) + 2(x + 1) =(x + 1)(a + 2) Type-2 (Difference of squares) Examples... (1) 25x^2 - 36 =(5x)^2... | 2019-05-19 22:29:42 | {
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"url": "http://atozma... | Given the polynomial \( p(x) = x^3 - 3x^2 - 6x + 8 \), determine the complete factorization of \( p(x) \) and find the sum of the roots of the polynomial. | 186 | math-ai/AutoMathText |
http://cms.math.ca/Events/winter12/res/gav | 2012 CMS Winter Meeting
Fairmont Queen Elizabeth (Montreal), December 7 - 10, 2012
Geometry of Algebraic Varieties
Org: Xi Chen (Alberta), Steven Lu (UQAM) and Peter Russell (McGill)
[PDF]
XI CHEN, University of Alberta
Rational self maps of Calabi-Yau manifolds [PDF]
It is expected that a very general Calabi-Yau ... | 2015-07-31 17:28:26 | {
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"url": "http://cms.math.ca/... | In the context of projective Kähler manifolds, if the holomorphic sectional curvature is negative, what positivity conditions can be stated for the canonical line bundle, and how does this relate to the uniruledness of the manifold? | 219 | math-ai/AutoMathText |
https://www.physicsforums.com/threads/why-8-gluons.59555/ | # Why 8 gluons?
1. Jan 12, 2005
### Kalimaa23
Greetings,
I found a puzzling reference in my EP-course, that basically says :
"Gluon cary a dual charge, one colour and one anticolour. This means one can have 3²=9 combinations."
So far, so good. But then :
"We have to substract one colourless combination. This lea... | 2018-11-19 23:53:59 | {
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"openwebmath_perplexity": 2109.9980845344658,
"openwebmath_score": 0.7663911581039429,
"url": "https://w... | How many independent generators does the special unitary group SU(3) have, and what is the mathematical reasoning behind this number? | 304 | math-ai/AutoMathText |
https://mathhelpboards.com/threads/number-of-groups.2716/ | # Number of groups
#### goosey00
##### Member
I am not quite sure if I am using the correct formula. The problem is -A class of 30 students(12 male and 18 female) are put into groups of 3. How many combinations can be formed if the requirement is that no group can be entirely male or female? I get 4060 since it doesn... | 2022-07-06 17:11:00 | {
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"openwebmath_score": 0.7661325931549072,
"url": "https://m... | A class of 30 students, consisting of 12 males and 18 females, is to be divided into groups of 3. What is the total number of ways to form these groups if each group must contain at least one male and one female? | 147 | math-ai/AutoMathText |
http://archives.math.utk.edu/visual.calculus/4/int_by_parts.7/ | Problem:
Evaluate the following integral:
Solution:
1. Let
and let
2. Hence,
and let
3. Using the formula for integration by parts
we get
4. Now we can use integration by parts again to compute the following integral
5. Let
and let
6. Hence,
and let
7. Finally we get
8. We can now use the above result to finis... | 2016-10-24 21:46:07 | {
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"url": "http://archives.math... | Evaluate the integral \( I = \int x e^{-x^2} \, dx \) from 0 to infinity. What is the value of this integral? | 166 | math-ai/AutoMathText |
http://adunataalpini-pordenone2014.it/prxf/ideal-gas-law-hot-air-balloon-problem.html | Types of Problems Included: Boyles' Law Charles' Law Gay-Lussac's Law Combined Gas Law Ideal Gas Law Included in This Product: ~Student Handout with problems and multiple choice answers ~Color-by-number hot air balloon handout for students to color with correct answers ~Completed color-by-number fish key ~Key with all ... | 2020-10-25 11:05:32 | {
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"u... | A hot air balloon has an envelope volume of 2,500 liters at a temperature of 20 °C and a pressure of 1 atm. If the balloon is heated to 100 °C, what will be the new volume of the air inside the balloon, assuming the pressure remains constant? Use the ideal gas law to support your calculations. | 8 | math-ai/AutoMathText |
https://bookini.ru/interdisciplinary-applied-mathematics/150/ | # Interdisciplinary Applied Mathematics
Скачать в pdf «Interdisciplinary Applied Mathematics»
a □ □ □ □
°°ooo
0 0.1 0.2 0.3 0.4 0.5
Y
FIGURE 4.11. The velocity distribution normalized with the local average velocity in half of a microchannel (left). The linearized Boltzmann solution is from (Ohwada... | 2018-05-23 23:28:41 | {
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"url": "https://bookini.... | Given the normalized velocity distribution \( U^*(y, Kn) \) from equation (4.15) and the errors associated with different slip flow models, calculate the maximum positive error in the predicted centerline velocity when using Schamberg's model if the average velocity \( U \) is 1 unit. What is the numerical value of thi... | 59 | math-ai/AutoMathText |
https://mathshistory.st-andrews.ac.uk/Extras/Gauss_Disquisitiones/ | # Gauss: Disquisitiones Arithmeticae
In 1801 Carl Friedrich Gauss published his classic work Disquisitiones Arithmeticae. He was 24 years old. A second edition of Gauss' masterpiece appeared in 1870, fifteen years after his death. This second edition was produced for the Göttingen Academy of Sciences (Königliche Gesel... | 2020-07-06 21:45:56 | {
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https://mathhelpboards.com/threads/find-minimum-a%C2%B2-b%C2%B2.28168/ | # [SOLVED]Find minimum a²+b²
#### anemone
##### MHB POTW Director
Staff member
Determine the minimum value of $a^2+b^2$ when $(a,\,b)$ traverses all the pairs of real numbers for which the equation $x^4+ax^3+bx^2+ax+1=0$ has at least one real root.
#### SquareOne
##### New member
Here's my attempt at a solution.
S... | 2021-01-24 08:53:35 | {
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"url": "https://ma... | What is the minimum value of \( a^2 + b^2 \) such that the polynomial \( x^4 + ax^3 + bx^2 + ax + 1 \) has at least one real root? | 127 | math-ai/AutoMathText |
http://openstudy.com/updates/556ddb80e4b0c4e453fa2ff5 | ## anonymous one year ago When does the double-slit interference have its first dark spot on either side of the central peak intensity? **will draw image!** A. when the paths d_1 and d_2 differ by one wavelength B. when the paths d_1 and d_2 differ by half a wavelength C. when the waves arrive in step, or "in phase" wi... | 2016-10-25 22:48:57 | {
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"url": "http://openstu... | In a double-slit interference experiment, at what path difference between the two waves will the first dark spot appear on either side of the central peak intensity? A. one wavelength B. half a wavelength C. when the waves are "in phase" D. when the paths have the same length. | 141 | math-ai/AutoMathText |
http://mathhelpforum.com/number-theory/19636-linear-congruence.html | # Math Help - Linear Congruence
1. ## Linear Congruence
The following was confusing me, so any help/explanations would be greatly appreciated!
Find all incongruent solutions to the following linear congruence:
21x ≡ 14 (mod 91)
2. Originally Posted by clockingly
The following was confusing me, so any help/explanat... | 2014-11-28 18:15:29 | {
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"url": "http://... | Find all incongruent solutions to the linear congruence \( 21x \equiv 14 \mod 91 \). How many distinct residue classes exist for this solution? | 248 | math-ai/AutoMathText |
https://spot.pcc.edu/slc/mathresources/output/html/radicals-binomial-denominators.html |
## Section11.6Rationalizing Binomial-Denominators that include Square Root expressions
The expressions $a+b$ and $a-b$ are called conjugates; collectively they form a conjugate pair. They have the special property that when you expand their product, the result is a binomial. Specifically:
\begin{equation*} (a+b)(a-b... | 2019-04-22 16:59:56 | {
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"url": "https://spot.pcc.edu/... | Rationalize the denominator and simplify the result for the expression \(\frac{12}{5-\sqrt{13}}\). What is the final simplified form of the expression? | 229 | math-ai/AutoMathText |
https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-3-differentiation-3-7-the-chain-rule-exercises-page-146/33 | # Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 33
y'=$\frac{2(4x^{3}-3x^{2})}{(x^{4}-x^{3}-1)^{1/3}}$
#### Work Step by Step
The chain rule states that if y=g(h(x)), then y'=g'(h(x))h'(x). Since y=$(x^{4}-x^{3}-1)^{2/3}$, we can set g(x)=$x^{2/3}$ (outside function) and h(x)=$x^{4}$-$x^{3... | 2019-07-15 17:56:26 | {
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"url": "https://www.... | Given the function \( y = (x^4 - x^3 - 1)^{2/3} \), compute the derivative \( y' \) and evaluate \( y' \) at \( x = 1 \). What is the value of \( y'(1) \)? | 264 | math-ai/AutoMathText |
https://socratic.org/questions/how-do-you-solve-4-x-5-1-2-28 | # How do you solve 4(x-5)^(1/2)=28?
May 27, 2017
See the solution process below:
#### Explanation:
First, divide each side of the equation by $\textcolor{red}{4}$ to isolate the term with the exponent while keeping the equation balanced:
$\frac{4 {\left(x - 5\right)}^{\frac{1}{2}}}{\textcolor{red}{4}} = \frac{28}{... | 2020-01-25 02:19:37 | {
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"url": "https://socrati... | What is the solution for \( x \) in the equation \( 4(x-5)^{1/2} = 28 \)? | 236 | math-ai/AutoMathText |
http://mathhelpforum.com/advanced-statistics/78641-computing-bell-number-set-n-elements.html | # Math Help - Computing Bell Number for set of n elements.
1. ## Computing Bell Number for set of n elements.
First of all, sorry if this is in the wrong area, if so, please move it. Anyway
suppose I have a set of 3 elements. Computing by hand it is obvious to see that the answer is 5. But what if I have 20 elements?... | 2014-03-15 14:16:09 | {
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"url": "http:/... | What is the value of the Bell number \( B(20) \), which counts the number of ways to partition a set of 20 elements? | 109 | math-ai/AutoMathText |
http://openstudy.com/updates/56189103e4b086e96bfe5b8b | ## anonymous one year ago The velocity in ft/sec of a particle is given by v(t) = −16t + 2. Find the position function s(t), of the particle if it has an initial position s(0) = 6 feet.
1. anonymous
@jim_thompson5910
2. anonymous
3. jim_thompson5910
integrate v(t) to get s(t) don't forget the +C. You'll solve for C... | 2016-10-23 18:11:34 | {
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"url": "http://openstudy... | Given the velocity function \( v(t) = -16t + 2 \) of a particle and the initial position \( s(0) = 6 \) feet, determine the position of the particle after 1 second. | 82 | math-ai/AutoMathText |
http://mathhelpforum.com/math-topics/29354-equal-resistance-print.html | # of equal resistance
• February 27th 2008, 11:35 AM
lovinhockey26
of equal resistance
What resistance must be placed in parallel with a 149 Ohm resistor to make the equivalent resistance 124 Ohm?
• February 27th 2008, 11:41 AM
Peritus
• February 27th 2008, 11:49 AM
lovinhockey26
I'm still not sure what I need to use.... | 2015-08-30 11:37:14 | {
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"url": "http:... | What resistance should be placed in parallel with a 149 Ohm resistor to achieve an equivalent resistance of 124 Ohm? | 417 | math-ai/AutoMathText |
https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-12th-edition/chapter-9-section-9-2-exponential-functions-9-2-exercises-page-597/33 | ## Intermediate Algebra (12th Edition)
$x=-3$
We are given the equation $5^{x}=\frac{1}{125}$. First, we must write both sides using the same base. $5^{x}=5^{-3}=\frac{1}{125}$ Next, we must take the natural log of both sides. $ln(5^{x})=ln(5^{-3})$ $xln(5)=-3ln(5)$ Divide both sides by $ln(5)$. $x=-3$ | 2018-07-17 10:10:51 | {
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"url": "https://www.... | If \( 5^x = \frac{1}{125} \), what is the value of \( x \)? | 398 | math-ai/AutoMathText |
https://jeremykun.com/tag/random-graph/ | # Zero-One Laws for Random Graphs
Last time we saw a number of properties of graphs, such as connectivity, where the probability that an Erdős–Rényi random graph $G(n,p)$ satisfies the property is asymptotically either zero or one. And this zero or one depends on whether the parameter $p$ is above or below a universal... | 2020-01-21 06:32:04 | {
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"url": "https://je... | In the context of Erdős–Rényi random graphs $G(n,p)$, determine the value of the threshold parameter $p$ such that with probability tending to one, the graph is connected as $n$ approaches infinity. Specifically, for what values of $p(n)$ does the graph transition from being disconnected to almost surely connected? | 5 | math-ai/AutoMathText |
https://gateoverflow.in/tag/queue | # Recent questions tagged queue
1
Which of the following is useful in traversing a given graph by breadth first search? Stack Set List Queue
2
If queue is implemented using arrays, what would be the worst run time complexity of queue and dequeue operations? $O(n),O(n)$ $O(n),O(1)$ $O(1),O(n)$ $O(1),O(1)$
1 vote
3
A __... | 2021-05-11 10:35:36 | {
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"url": "https://gate... | If a queue is implemented using a non-circular singly linked list, and the 'enqueue' operation is executed by inserting a new node at the head while the 'dequeue' operation involves deleting the node at the tail, what is the time complexity for 'enqueue' and 'dequeue' operations in this implementation? | 168 | math-ai/AutoMathText |
http://mathhelpforum.com/calculus/105735-chain-rule.html | # Math Help - Chain Rule
1. ## Chain Rule
Write absolute value(x)=sqrt(x^2) and use the chain rule to show that
(d/dx)abs(x)=x/abs(x)
could i get some help with this please?
i know the chain rule is F'(x)=f'(g(x))*g'(x) but i do not know how to apply that to this problem.
thank you
2. First you need to divide th... | 2015-08-01 23:14:58 | {
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"url": "http://... | Show that the derivative of the absolute value function can be expressed as
\[
\frac{d}{dx} |x| = \frac{x}{|x|}
\]
by using the chain rule and considering the cases for \( x > 0 \) and \( x < 0 \). What is the derivative when \( x = 0 \)? | 133 | math-ai/AutoMathText |
https://testbook.com/question-answer/the-period-of-oscillation-of-a-simple-pendulum-dep--603ddcc75d312156e5314013 | # The period of oscillation of a simple pendulum depends on
This question was previously asked in
ISRO Refrigeration and Air Conditioning 2015 Official
View all ISRO Scientist ME Papers >
1. mass of the bob
2. its effective length
4. density bob
Option 2 : its effective length
Free
ISRO Scientist ME 2020 Paper
1652
8... | 2021-12-05 20:35:50 | {
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"url": "https://testbo... | What is the relationship between the effective length of a simple pendulum and its period of oscillation, specifically expressed in terms of the formula for the time period? | 240 | math-ai/AutoMathText |
https://www.physicsforums.com/threads/a-simple-equation-with-simple-solution-how-to-solve-it.991892/ | # A simple equation with simple solution - how to solve it?
• I
## Main Question or Discussion Point
I've been trying to solve y as a function of x in the following equation.
y-x=√(1-x^2)+√(1-y^2)
The equation look pretty simple, and according to Mathematica the solution is simple too: y=√(1-x^2)
The (proposed) so... | 2020-08-12 07:27:33 | {
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"url": "https:... | Given the equation \( y - x = \sqrt{1 - x^2} + \sqrt{1 - y^2} \), determine all pairs \((x, y)\) that satisfy this equation in the range \(-1 \leq x \leq 1\) and \(-1 \leq y \leq 1\). What is the geometric interpretation of the solutions? | 117 | math-ai/AutoMathText |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-1-foundations-for-algebra-1-3-real-numbers-and-the-number-line-practice-and-problem-solving-exercises-page-21/52 | ## Algebra 1
Certain numbers are negative, but not integers. For example, the number $-\frac{1}{2}$ is a negative number, as it is less than $0$, but it is not an integer, as it is fractional. | 2018-08-16 18:49:31 | {
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"url": "https://www.... | What is the sum of all negative rational numbers that are not integers and are less than \( -\frac{1}{2} \) but greater than \( -1 \)? | 349 | math-ai/AutoMathText |
http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/statug_npar1way_details08.htm | The NPAR1WAY Procedure
Scores for Linear Rank and One-Way ANOVA Tests
For each score type that you specify, PROC NPAR1WAY computes a one-way ANOVA statistic and also a linear rank statistic for two-sample data. The following score types are used primarily to test for differences in location: Wilcoxon, median, Van der... | 2018-09-23 18:32:05 | {
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"url": "http://support.sas.co... | What are the specific score types available in PROC NPAR1WAY for testing location and scale differences, and how would you compute Wilcoxon scores for a two-sample dataset? | 299 | math-ai/AutoMathText |
https://aliquote.org/post/categorical-variables-in-mathematica/ | # aliquote.org
Until now, I was always defining a design matrix by hand to fit, say, a linear regression model with categorical covariates in Mathematica. If you know how to define a linear model in Mathematica, DesignMatrix works exactly the same. I suggested this approach to a Matlab user a long time ago. Then I rea... | 2023-03-29 19:06:46 | {
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"url": "https://aliquot... | Given the dataset "polymorphism.dta" containing participant ID, age, and genotype (which has three levels), if the genotype is recoded such that the third category becomes the baseline category, how would the coding for the genotype levels change, and what would be the ANOVA F-statistic when fitting a one-way ANOVA mod... | 7 | math-ai/AutoMathText |
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-11-data-analysis-and-statistics-11-3-use-normal-distributions-11-3-exercises-mixed-review-page-762/53 | ## Algebra 2 (1st Edition)
Published by McDougal Littell
# Chapter 11 Data Analysis and Statistics - 11.3 Use Normal Distributions - 11.3 Exercises - Mixed Review - Page 762: 53
7
#### Work Step by Step
Solving the equation for x, we find: $$\left(\sqrt{x-3}\right)^2=\left(x-5\right)^2 \\ x-3=x^2-10x+25 \\ x=7,\:x... | 2019-10-18 08:31:12 | {
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"url": "https://www... | Given the equation \(\left(\sqrt{x-3}\right)^2=\left(x-5\right)^2\), determine the sum of all valid solutions for \(x\). | 327 | math-ai/AutoMathText |
https://www.physicsforums.com/threads/quick-definition-question-dihedral-group.626435/ | # Quick definition question: Dihedral group
1. Aug 8, 2012
### srfriggen
A dihedral group of an n-gon denoted by Dn, whose corresponding group is called the Dihedral group of order 2n?
What I gather from that is a square has 8 symmetries, an octagon has 16, a hexagon 12, etc?
2. Aug 8, 2012
### marschmellow
Yep,... | 2018-06-20 19:29:18 | {
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"url": "https:... | What is the order of the dihedral group \( D_n \) for an \( n \)-gon, and can you derive the multiplication table for the dihedral group \( D_4 \) using the relations \( S^2 = 1 \), \( R^4 = 1 \), and \( SR = R^3S \)? | 176 | math-ai/AutoMathText |
http://math.stackexchange.com/questions/266762/multiplication-operator-and-trace-class | # Multiplication operator and trace class
Suppose we work in $H=l^2(\Bbb{N})$ and suppose the multiplication operator $T_f$ such that $T_f\psi=f\psi$ and $f:\Bbb{N}\rightarrow \Bbb{C}$. We denote by $B_1(H)$ the trace class of operators.
Question: I want to find a sufficient and necessary condition for $f$, such that... | 2015-07-05 00:16:56 | {
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"url": "http://mat... | What is the condition on the sequence \( \{f(n)\} \) such that the multiplication operator \( T_f \) defined on \( l^2(\mathbb{N}) \) is a trace-class operator? Specifically, express this condition in terms of the summability of the series \( \sum_{n=1}^\infty |f(n)| \). | 153 | math-ai/AutoMathText |
https://electronics.stackexchange.com/questions/347075/how-to-design-a-2nd-order-high-pass-butterworth-filter-with-a-gain-of-6-db | # How to design a 2nd Order High Pass Butterworth filter with a gain of 6 dB?
I have been trying to design a 2nd order filter with a gain of 6 dB (or 2 Av), using the following Sallen-Key Topology.
I have calculated R1 and R2 to give me a desired cut-off of 1.6kHz and this part is working fine. I am however not manag... | 2019-06-19 07:27:44 | {
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"url": "https://e... | What resistor values should I choose for a Sallen-Key 2nd Order High Pass Butterworth filter to achieve a gain of 6 dB while maintaining a cutoff frequency of 1.6 kHz? | 239 | math-ai/AutoMathText |
https://read.somethingorotherwhatever.com/entry/TheSensualquadraticForm | # Interesting Esoterica
• Published in 1997
In the collection
John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book ... | 2020-08-14 00:42:31 | {
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"url"... | What is the year in which John Horton Conway's book "The Sensual (quadratic) Form" was published, and during what event did he give the Hedrick Lectures that focused on quadratic forms? | 223 | math-ai/AutoMathText |
https://www.hackmath.net/en/math-problem/8424?tag_id=101 | # 80 students
80 students were asked what type of test they preferred. 50 students said they liked multiple choice and 42 liked true or false. If 36 liked both multiple choice and true or false types, how many students preferred multiple choice only?
Result
m = 14
#### Solution:
$m = 50-36 = 14$
Leave us a comme... | 2019-11-22 17:40:19 | {
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"url": "https://www.ha... | In a survey of 80 students regarding their test preferences, 50 students indicated they preferred multiple choice tests, while 42 preferred true/false tests. Additionally, 36 students liked both types of tests. How many students preferred only multiple choice tests? | 226 | math-ai/AutoMathText |
https://socratic.org/questions/what-is-the-polar-form-of-3-4 | # What is the polar form of (-3,4)?
Jan 6, 2016
$\left(5 , {126.87}^{0}\right)$
#### Explanation:
If $\left(a , b\right)$ is a are the coordinates of a point in Cartesian Plane, $u$ is its magnitude and $\alpha$ is its angle then $\left(a , b\right)$ in Polar Form is written as $\left(u , \alpha\right)$.
Magnitude ... | 2022-07-03 02:45:10 | {
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"openwebmath_perplexity": 213.9894813504459,
"openwebmath_score": 0.9756544232368469,
"url": "https://socratic... | What is the angle in degrees for the polar form of the point (-3, 4), expressed in the standard range [0°, 360°)? | 257 | math-ai/AutoMathText |
https://testbook.com/question-answer/an-e-mail-password-must-contain-three-characters--5cda74affdb8bb05bf0d3946 | # An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?
This question was previously asked in
GATE EE 2018 Official Paper
View all GATE EE Papers >
1. 6,760
... | 2021-10-24 22:06:39 | {
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"url": "https://testboo... | How many distinct three-character passwords can be formed using one numeral (0-9), one upper case letter (A-Z), and one lower case letter (a-z), taking into account the different arrangements of these characters? | 170 | math-ai/AutoMathText |
https://math.stackexchange.com/questions/2170670/probability-involving-two-independent-uniform-random-variables | # Probability involving two independent uniform random variables
Suppose $U$ and $V$ are independent, standard uniforms random variables. Suppose I want to calculate the probability $P(U^2 > 4V)$. I would like to use some intelligent method like starting from a joint density of (U, V), then transform the problem into ... | 2019-05-19 09:08:36 | {
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"openwebmath_perplexity": 85.92094951077907,
"openwebmath_score": 0.8623508810997009,
"url": "https://ma... | What is the probability \( P(U^2 > 4V) \) where \( U \) and \( V \) are independent uniform random variables on the interval \([0, 1]\)? | 189 | math-ai/AutoMathText |
https://mathoverflow.net/questions/325566/have-the-tides-ever-turned-twice-on-any-open-problem | # Have the tides ever turned twice on any open problem?
Oftentimes open problems will have some evidence which leads to a prevailing opinion that a certain proposition, $$P$$, is true. However, more evidence is discovered, which might lead to a consensus that $$\neg P$$ is true. In both cases the evidence is not simpl... | 2021-07-28 10:10:18 | {
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"openwebmath_perplexity": 685.3941114343984,
"openwebmath_score": 0.7249188423156738,
"url": "https://mat... | What is an example of a mathematical problem that has had at least three distinct prevailing opinions over time regarding its truth (from believing it true, to believing it false, and back to true), and what were the reasons for these shifts in consensus? | 242 | math-ai/AutoMathText |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/6/lesson/6.2.2/problem/6-93 | ### Home > PC3 > Chapter 6 > Lesson 6.2.2 > Problem6-93
6-93.
Determine all of the roots of $p(x)=x^4−x^3−11x^2−x−12$. Then sketch a graph of the function. Check your sketch on a graphing calculator.
The possible rational roots are factors of $12$.
One of the roots is $x = −3$. Divide out the factor $\left(x + 3\ri... | 2022-05-17 04:37:25 | {
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"url": "https://homework.cpm.o... | Determine all the roots of the polynomial \( p(x) = x^4 - x^3 - 11x^2 - x - 12 \) and calculate the values of these roots. Additionally, verify the presence of any rational roots using the Rational Root Theorem. What are the exact values of all roots, and how many real roots does the polynomial have? | 76 | math-ai/AutoMathText |
https://engineeringprep.com/problems/018 | ## A Pebble on a Mountain
You are at the top of a mountain, and the mountain slopes down below you at a 45° angle below the horizontal. You throw a pebble over the slope, at an angle of 40° above the horizontal. The pebble travels in free-fall for 4 seconds before landing on the slope of the mountain. Its trajectory i... | 2022-08-14 19:00:50 | {
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"url": "https:/... | What is the initial velocity of a pebble thrown at a 40° angle above the horizontal from the top of a mountain, which slopes down at a 45° angle, if it travels for 4 seconds in free-fall before landing on the slope? | 184 | math-ai/AutoMathText |
https://socratic.org/questions/a-100-0-ml-sample-of-0-10-m-nh-3-is-titrated-with-0-10-m-hno-3-how-do-you-determ | # A 100.0 mL sample of 0.10 M NH_3 is titrated with 0.10 M HNO_3. How do you determine the pH of the solution after the addition of 40.0 mL of HNO_3?. The Kb of NH3 is 1.8 × 10-5.?
Dec 29, 2016
You can do it like this:
#### Explanation:
As the acid is added to the base the following neutralisation takes place:
$\t... | 2020-02-28 09:35:41 | {
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"url": "https://socrati... | What is the pH of a solution after adding 40.0 mL of 0.10 M HNO₃ to 100.0 mL of 0.10 M NH₃, given that the Kb of NH₃ is 1.8 × 10⁻⁵? | 201 | math-ai/AutoMathText |
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