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MHB Deriving the first and second order Newton-Cotes formulas

MHB Math Problem of the Week

POTW Sum of an Alternating Series
B How long will it take to reach 1000ppm CO2 from 2000ppm
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MHB Computing projectile's maximum height and range.
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MHB Is Theorem 5.2 in SET THEORY AND LOGIC True or False?
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MHB LU decomposition: With or without pivoting?
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B Principal square root of a complex number, why is it unique?
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MHB Summation Challenge: Evaluate $\sum_{k=1}^{2014}\frac{1}{1-x_k}$
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MHB Gre.al.13 sum of even and odd numbers
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I Is ##\delta##-steady needed in this proof, given ##\epsilon##-steady
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MHB Degree of Freedom: Maths Definition & Differential Equations
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I Heat Wave Equations: Explaining Delta t & x Approach to Zero
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B Adding random noise to a gradient
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I Calculating the digits of pi by colliding boxes
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MHB Act.ge.5 third angle of triangle
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Curse of dimensionality - what is it that grows?
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MHB Proving Angles in Triangle ABC < 120° & Cos + Sin > -√3/3
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I Cartesian to Polar form.... Is it just a transformation of the plane?
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B The same inequality, but two equivalent ways to express it
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MHB Proving $x-1$ is a Factor of $P(x)$ with Polynomials
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MHB Efficiency of Sieve vs. Derivative Method for Primality Testing
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I Position of a point as a function of angular position
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MHB Basic Inequality Prove: $A\leq B\wedge B\leq A \Rightarrow A=B$
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MHB Solving Trig Identity: Sin[1/2 sin^−1 (x)] = 1/2 X (sqr(1+x) –sqr(1-x))
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MHB Proof of Inequality: $|a+b| \leq |a| + |b|$
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MHB Counting Multiples of 2012 in Combination Numbers
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MHB Does Increasing Mass Reduce the Amplitude of a Forced SDOF Oscillator?
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MHB Proving Orthogonal Projection of Triangle V, v'_{1}
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MHB Calculating Distance Traveled: Solving for the Unknown in a Multi-Unit Problem
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MHB Expanding and simplifying brackets
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B Reconciling different ways to define an ellipse
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MHB Angle at Y-axis Crossing of y=sin(1/x) Graph
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B Why do we call function a Rule
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I About divergence, gradient and thermodynamics
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MHB Act.al.4 What is the 50th term
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A Ramanujan Summation, Variations of
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I Proving an identity for a free variable
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B Question about Notation of Function
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MHB Gre.al.12 transformationof a function
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MHB Calculating Integral with Simpson's Rule for Error < $0.5\cdot 10^{-3}$
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MHB B=Q^TAQ has a LU decomposition
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MHB How Does Modifying Numerator and Denominator Affect the Value of a Fraction?
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What is the meaning of 'exp' in this math expression?
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MHB Can Urgent Math Help Be Effective in Just 3 Hours?
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MHB Find Polynomials Fulfilling Real Coefficient Equation
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MHB -act.63 cost per game with season pass
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MHB For j >1 the first 2^j digits are correct
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I Is it possible to solve for “t?”
2
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MHB Find Cubic Function & Polynomial of Degree 3
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MHB Calculate Gaussian Quadrature: x1, x2 & w1, w2
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MHB For which values of a can we solve it iteratively?
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I What type is a polynomial function?
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MHB Orthonormal basis for the poynomials of degree maximum 2
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MHB What is the form of that matrix?
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MHB COVID-19 in a Small Town: Probability of Infection
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MHB Prove 9999999+1999000 is Composite Number
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I Using recurrence formula to solve Legendre polynomial integral
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MHB Uncovering the Hidden Simplicity of Similar Triangles
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MHB How to solve sqrt(x + 15) + sqrt(x) = 15 ?
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MHB Real Roots of Composite Polynomials: Solving P(Q(x))=0
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MHB Can You Meet the Sine Function Challenge?
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MHB Find a,b,c,d for Max $a+b-c+d$
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B Why are imaginary numbers called "imaginary"? If they really exist
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I Definiteness of a nonsymmetric matrix
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MHB Min Value of $\dfrac{a+3c}{a+2b+c}$+$\dfrac{4b}{a+b+2c}$+$\dfrac{8c}{a+b+3c}$
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MHB Proving Series Inequality: $\sqrt[3]{\frac{2}{1}}$ to $\frac{1}{8961}$
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MHB Determine its image point after the transformation
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MHB Does Q have at least one element that is not in P?Which quantity is greater?
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MHB Finding $k$ for 2 Non-Negative Roots of $x^2-2x\lfloor x \rfloor +x-k=0$
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MHB Real Roots of Cubic Equation: $x^3+a^3x^2+b^3x+c^3=0$
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MHB Roots of Cubic Equation: Finding $x_1,\,x_2$, and $x_3$
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I Closest point on a plane to a point near the plane
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MHB Maximum and minimum of a function
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MHB What conditions guarantee convergence of Newton's method for approximating pi/2?
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MHB Uniqueness of Cubic Spline Interpolation: How Can We Prove It?
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B What is the Difference between imaginary part and imaginary number?
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MHB -gre.qu.10 quantity on 2 means
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B Super silly question about a polynomial identity
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MHB How to Cook the Perfect Steak"Cook Perfect Steak: Step-by-Step Guide
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B Is 0^0 indefinite in Von Neuman Entropy?
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B Understanding Absolute Value and the Symbol ||: What Does it Mean?
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MHB What are the values of n and k in n+8=2^k when n!+8 = 2^k?
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A Name for a subset of real space being nowhere a manifold with boundary
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MHB Min Value of $a^2+b^2$ in Quadratic Equation
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MHB Compose Functions: True/False?
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I Solving congruences and diophantine equations in number theory
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MHB Prove Triangle Inequality: $\sqrt{2}\sin A-2\sin B+\sin C=0$
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MHB Help? Algebra 2 Math - Solve X,Y,Z
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MHB Prove $\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}\le 10$ w/ $a,b,c,d>0$
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MHB What are some questions about thermodynamics and their potential answers?
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MHB Can Exponent Values Be Determined with One Equation and Two Variables?
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MHB Prove Centroid Goes Through It
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Making, testing and proving conjectures
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MHB Is Every Statement Correct in Defining an Onto Function?
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MHB -gre.ge.2 distance by similiar triangles
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MHB -gre.ge.04 intersection of parabola and line
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MHB Centripetal acceleration of viking ship in the amusement park.
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A Partition function in number theory and statistical mechanics
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MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
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B Can You Solve This Exercise on Arithmetic-Geometric Series?
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A Frequency estimation - Minimising the number of samples
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MHB [ASK] Seemingly Simple Limit Question but I have no Idea
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Mathematics

Mathematics, often referred to as the language of the universe, is the systematic study of patterns, structures, and relationships using numbers, quantities, shapes, and symbols.

It is a fundamental discipline that provides tools for logical reasoning, problem-solving, and quantitative analysis. Math is divided into various branches, including algebra, geometry, calculus, statistics, and more, each serving unique purposes across diverse fields.

Whether applied in science, engineering, economics, or everyday life, mathematics offers a universal framework for understanding and modeling the intricacies of the world around us, making it an essential and foundational element of human knowledge and intellectual inquiry.

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