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A mathematical explanation of a simple trick that shows how to quickly calculate the cube root of a maximally 6-digit number that was given by a spectator. The spectator chooses a natural two-digit number, keeps it in secret and only information he/she gives publicly is its cube. Conjurer's task is to quickly guess the original number.

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2period review andanswers

2period review andanswers

Bazinga game

Bazinga game

Math hssc-i-bc

Math hssc-i-bc

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2period review andanswers

The document contains a math review with examples of different techniques for counting combinations and permutations, as well as examples involving polynomials, solid geometry, and volume. It provides the steps to solve problems involving multiplication to find combinations, factoring polynomials, finding volumes of geometric shapes, and determining angle measures using parallel lines and a transversal.

Bazinga game

True or False: x=14 is a solution to x+8=23. True or False: x=14 is a solution to x-10=4. Evaluate the expression x^3-5x for x= -2. If a state’s income tax is 4.3% of taxable income, how much will be owed in tax if your taxable income is $51,000? Solve the following equation: X+2.29=8.27.

Math hssc-i-bc

This document contains a mathematics exam for HSSC-I (Higher Secondary School Certificate Part 1) with questions covering various topics:
1) Simplifying expressions involving complex numbers, trigonometric functions, and logarithms.
2) Evaluating trigonometric functions for given angles.
3) Proving trigonometric, logarithmic, and angle identity equations.
4) Solving triangles using trigonometric functions, laws of sines and cosines.
5) Solving systems of linear equations using Cramer's rule.
The exam is divided into two sections with a total of 80 marks and includes questions requiring graphing, truth tables, and solving trigonometric, exponential,

IIT JEE - Mathematics 2009 i

This document contains an unsolved mathematics paper from 2009 containing multiple choice and paragraph style questions testing concepts in complex numbers, trigonometry, probability, matrices, conic sections, and differential equations. There are 4 sections with a total of 20 questions covering topics such as the area of a rectangle defined by complex number roots, properties of unit vectors, loci of points in triangles and ellipses, conditional probabilities of die rolls, the number of possible symmetric matrices meeting certain criteria, matching conic sections to defining expressions, and matching intervals to differential equations and integrals.

Advanced Trigonometry

- The document discusses various trigonometric identities and formulae, including basic identities, compound angles, double angles, and their applications.
- It provides examples of using trigonometric formulae to find unknown sides and angles, including solving trigonometric equations involving double angles.
- Three-dimensional trigonometry is also introduced, defining the angle between two planes and an example problem of finding unknown angles and lengths in a pyramid.

New ways of multiplying numbers

Man has hitherto devised several manual methods to solve the problems of multiplying numbers. The
Egyptians and the Russians methods are part of the several ways. In this research some of the old methods of
multiplications were analyzed and some new ones were discovered, developed and formulated by the author.
This paper presents to the world, new manual ways of multiplying numbers.

Integration

This document provides information about integration in higher mathematics. It begins with an overview of integration as the opposite of differentiation. It then discusses using antidifferentiation to find integrals by reversing the power rule for differentiation. Several examples are provided to illustrate integrating polynomials. The document also discusses using integrals to find the area under a curve or between two curves. It provides examples of calculating areas bounded by graphs and the x-axis. Finally, it presents some exam-style integration questions for practice.

Complex nos demo 2

(1) This document provides an introduction to complex numbers, including: defining complex numbers using i as the square root of -1, addition and multiplication of complex numbers, expressing complex numbers in polar form, and De Moivre's theorem.
(2) De Moivre's theorem states that for a complex number r(cosθ + i sinθ) and integer n, (r(cosθ + i sinθ))n = rn(cos(nθ) + i sin(nθ)). It allows taking complex numbers to any power and finding roots of complex numbers.
(3) The document provides examples of using De Moivre's theorem to find powers and roots of complex numbers in both

5.4 Complex Numbers

This document introduces complex numbers. It defines the imaginary unit i as the square root of -1, which allows quadratic equations with no real solutions, like x^2=-1, to be solved. Complex numbers have both a real part and an imaginary part in the form a + bi. They can be added, subtracted, multiplied, and divided by distributing terms and using properties of i such as i^2 = -1. Complex numbers are plotted on a plane with real numbers on the x-axis and imaginary numbers on the y-axis.

Examen du premier semestre g9

This document contains a multi-part math exam with questions involving:
1) Proving statements about numbers, writing fractions in simplest form, and identifying decimal and scientific notation.
2) Modeling price discount information as a system of equations and solving to find original prices.
3) Comparing the advantages of two meal subscription offers based on number of meals per month.
4) Calculating lengths and angles in a rectangle problem, and proving properties of isosceles triangles.
5) Plotting points, lines, determining equations, perpendicularity, and circle properties involving tangents, radii, and circumscribed triangles.

Chapter 6 exponents and surds

This document discusses exponents and surds. It covers exponent or index notation, exponent or index laws, zero and negative indices, standard form, properties of surds, multiplication of surds, and division by surds. Examples are provided to illustrate exponent notation, evaluating exponents, writing numbers as products of prime factors, the laws of exponents, evaluating expressions with negative bases, and using a calculator to evaluate exponents.

ACT MATH PREPARATION

This document provides 50 math questions related to ACT preparation. The questions cover a variety of math topics including geometry, algebra, statistics, and word problems. They are multiple choice questions with 5 possible answer choices for each question. The questions range in difficulty from basic calculations and operations to more complex multi-step word problems.

Lesson5.1 complexnumbers demo

This document provides an introduction to complex numbers. It discusses:
1) The definition of the imaginary number i and its powers.
2) How complex numbers combine real and imaginary numbers in the form of a + bi.
3) The four basic operations that can be performed on complex numbers: addition, subtraction, multiplication, and division.

Chapter 31 logarithms

This document provides an introduction to logarithms, including:
- Logarithms are the inverse of exponential functions and can be used to solve exponential equations without graphing.
- If y = ax, then x = loga y, where loga y is the logarithm of y in base a.
- Rules for logarithms include: loga(xy) = loga x + loga y and loga(xn) = n loga x.
- Logarithms in base 10 are called common logarithms and are often written as log x, assuming base 10. Calculators have a log key for base 10 logarithms.

How to test

To solve a quadratic equation by completing the square, rewrite the left side in the form of x^2 + bx, add (b/2)^2 to both sides to create a perfect square on the left, then take the square root of both sides. To solve by the quadratic formula, identify the coefficients a, b, and c and plug them into the formula x = (-b ± √(b^2 - 4ac)) / 2a to find the solutions.

Final Project

The document compares and contrasts multiple methods for multiplying multi-digit numbers - the traditional method, distributive law, Chinese method, Egyptian method, and lattice method. All the methods are based on the distributive law and break the multiplication into a series of addition steps. The Chinese method uses place value and counting line intersections. The Egyptian method uses doubling and powers of two. The lattice method uses a grid layout to show the place value and distributive steps.

How To Multiply

M.O.4.1.8:
solve multi-digit whole number multiplication problems using a variety of strategies, including the standard algorithm, justify methods used

Higher Maths 1.2.3 - Trigonometric Functions

The document contains notes on trigonometric graphs and functions. It discusses the amplitude and period of trigonometric graphs, defines radians and relates them to degrees, provides exact values of trigonometric functions at common angles, explains the four quadrants used to measure angles, and gives examples of solving trigonometric equations both graphically and algebraically using properties of the quadrants.

2period review andanswers

2period review andanswers

Bazinga game

Bazinga game

Math hssc-i-bc

Math hssc-i-bc

IIT JEE - Mathematics 2009 i

IIT JEE - Mathematics 2009 i

Advanced Trigonometry

Advanced Trigonometry

New ways of multiplying numbers

New ways of multiplying numbers

Integration

Integration

Complex nos demo 2

Complex nos demo 2

5.4 Complex Numbers

5.4 Complex Numbers

Examen du premier semestre g9

Examen du premier semestre g9

Chapter 6 exponents and surds

Chapter 6 exponents and surds

ACT MATH PREPARATION

ACT MATH PREPARATION

Lesson5.1 complexnumbers demo

Lesson5.1 complexnumbers demo

Chapter 31 logarithms

Chapter 31 logarithms

How to test

How to test

Final Project

Final Project

How To Multiply

How To Multiply

Higher Maths 1.2.3 - Trigonometric Functions

Higher Maths 1.2.3 - Trigonometric Functions

Mock cat solutions paper no 1

This document contains a mock CAT exam with multiple choice questions and explanations. It consists of two pages. The first page lists 60 multiple choice questions with answer options A-D. The second page provides explanations for the questions and solutions to problems. It discusses topics like probability, ratios, geometry, time/speed/distance word problems, and data interpretation from graphs.

1.1 Math Quiz

1. The document contains 21 multiple choice math questions covering topics like area, perimeter, volume, coordinate geometry, factoring, and algebraic equations.
2. For each question, the question stem and possible multiple choice answers are provided, along with the correct answer and an explanation of the mathematical steps taken to arrive at the solution.
3. The questions progress from easier concepts involving basic formulas to more complex problems requiring multiple steps of algebraic manipulation or geometric reasoning.

235806093 matematik-pt3

This document contains a 10 question mathematics exam with multiple parts to each question. The exam covers topics such as number lines, percentages, geometry, algebra, graphs, and trigonometry. It provides diagrams, tables and questions for students to solve problems and show their work. The exam is designed to test students' understanding of essential mathematics concepts.

Problemas resueltos de matemática_ preuniversitario

1. The maximum value of n is 3 based on the equations: m -2 = n +5 and n2 +5 = m+4.
2. The polynomial is reducible to a single term with coefficient 48.
3. Based on the equation 1239=1.92 +2.9+3, the value of a×b is 4×2=8.

10 Mathematics Standard.pdf

This document provides instructions for a mathematics exam for Class X. It has the following key details:
- The exam has 4 sections (A, B, C, D) with a total of 40 questions. All questions are compulsory.
- Section A has 20 one-mark multiple choice questions. Section B has 6 two-mark questions. Section C has 8 three-mark questions. Section D has 6 four-mark questions.
- There is no overall choice but some questions provide an internal choice between alternatives. Students must attempt only one of the choices for those questions.
- Calculators are not permitted. The instructions provide details about the number and type of questions in each section and remind students

Math magic

This document contains instructions for 3 magic tricks:
1. Have an audience member choose a number in a box, then use a "trik" of adding and subtracting digits to reveal the number.
2. Instruct a participant to multiply a chosen number by 3, add 1, then multiply by 3 again. The secret is that the number is actually multiplied by 10 with 3 added.
3. Tell a participant to multiply their number by 2, add 5, multiply the result by 5, and add 4. The last digit will always be 9, and the original number is the front digits minus 2.

magic of math

This document contains instructions for 3 magic tricks:
1. Have an audience member choose a number in a box, then use a "trik" of adding and subtracting digits to reveal the number.
2. Instruct a participant to multiply a chosen number by 3, add 1, then multiply by 3 again. The secret is that the number is actually multiplied by 10 with 3 added.
3. Tell a participant to multiply their number by 2, add 5, multiply the result by 5, and add 4. The last digit will always be 9, and the original number is the front digits minus 2.

Guess paper x

The document provides 20 multiple choice questions testing mathematics objectives related to topics like sets, algebra, trigonometry, and geometry. It then lists 18 additional practice problems involving algebraic expressions, logarithms, geometry constructions, data analysis, and solving equations both algebraically and graphically. The objectives and practice problems cover a wide range of foundational mathematics skills.

Indices

This document provides examples and exercises on working with indices. It introduces index notation for exponents, such as 52 = 5 × 5. The key rules for manipulating indices are presented: when multiplying terms with the same base, add the indices; when dividing terms, subtract the indices; and when raising a term to a power, multiply the indices. Negative indices produce fractional results, with the negative index representing the denominator. Worked examples demonstrate simplifying expressions using these index rules.

3rd Semester Mechanical Engineering (2013-December) Question Papers

3rd Semester Mechanical Engineering (2013-December) Question PapersBGS Institute of Technology, Adichunchanagiri University (ACU)

- Heat transfer does not inevitably cause a temperature rise. An increase in internal energy can also cause a temperature rise without heat transfer.
- For a non-flow system, the heat transferred is equal to the change in enthalpy of the system.
- Enthalpy is a property that depends on the temperature and pressure of a system. An increase in enthalpy means the system has gained heat at constant pressure.Summative Assessment Paper-4

APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.

How You Can Read ISIN_

The International Securities Identification Number (ISIN) code provides a unique identification for securities. It is composed of 12 alphanumeric characters broken into sections that identify the country of issuance, security type, and check digit. The first two characters identify the country. The next nine characters provide information on the issuer and security type. The final character is a check digit calculated using the preceding characters to validate the number. The ISIN allows unambiguous identification of any traded security globally.

imc-2018-s.pdf

- The document is the solutions leaflet for the UK Intermediate Mathematical Challenge with 25 math problems and their brief solutions.
- It provides alternative solutions for students to compare with their own work and encourages students to submit additional solutions.
- The UKMT (United Kingdom Mathematics Trust) organizes the challenge to promote mathematical problem solving among students.

IME 2020 - fechada

The document contains a mathematics exam with 15 multiple choice questions. It covers topics such as geometric and arithmetic progressions, combinations, trigonometry, complex numbers, polynomials, and sets. The questions involve calculating values, identifying geometric objects, solving systems of equations, and finding cardinalities of sets.

Summative Assessment Paper-2

APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.

Fuvest 2020 - aberta

The document contains 6 questions regarding mathematics and geometry problems. Some key details:
- Question 1 involves analyzing properties of numbers in a 3x3 square and finding the minimum number in a 16 number square.
- Question 2 describes the construction of the Koch snowflake and calculates properties like the number of sides and perimeter at different steps.
- Question 3 provides information about a game with 16 shaped pieces in 4 colors and calculates possible collections and probabilities.
- The remaining questions involve calculating lengths, areas, complex numbers, and values of a function over an interval.

PNEB - MATHEMATICS 2013

This document contains instructions for a mathematics exam consisting of 12 questions worth 100 marks total. It provides details on the exam format, instructions for candidates, and sample exam questions in both multiple choice and structured formats. The questions cover topics in algebra, geometry, trigonometry, calculus, probability, and statistics. Candidates are instructed to show all work, use the space provided below each question, and not use additional paper or calculators during the exam.

Matlab level 1.pptx

Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems.

Cat 2005-solutions

The document provides solutions to 15 problems from a CAT exam. Here are summaries of 3 of the problems:
1) The problem involves finding the remainder when a sum of terms of the form (163 + 173 + ...) is divided by 70. The solution shows the sum can be written as 70k, so the remainder is 0.
2) The problem involves 4 tanks losing chemical at different rates per minute. It is found that tank D loses chemical the fastest, at 50 units per minute, and will empty first after 20 minutes, when its initial 1000 units are completely lost.
3) The problem involves two circles intersecting at two points to form a square. It is noted that the area common to

PEA 305.pdf

The document provides information on various number system concepts in Vedic maths including:
1. Methods for multiplying numbers with 11, 9, 99, and 999 using place value concepts.
2. Methods for multiplying two-digit and three-digit numbers using the "criss-cross" method.
3. Shortcuts for finding squares and square roots of numbers.
4. Divisibility rules and their applications.
5. Concepts like remainder theorem, power cycles, and unit digit patterns that are useful for solving problems involving remainders and exponents.
6. Information on factors, multiples, and their properties like total number of factors and sum of factors.

Mock cat solutions paper no 1

Mock cat solutions paper no 1

1.1 Math Quiz

1.1 Math Quiz

235806093 matematik-pt3

235806093 matematik-pt3

Problemas resueltos de matemática_ preuniversitario

Problemas resueltos de matemática_ preuniversitario

10 Mathematics Standard.pdf

10 Mathematics Standard.pdf

Math magic

Math magic

magic of math

magic of math

Guess paper x

Guess paper x

Indices

Indices

3rd Semester Mechanical Engineering (2013-December) Question Papers

3rd Semester Mechanical Engineering (2013-December) Question Papers

Summative Assessment Paper-4

Summative Assessment Paper-4

How You Can Read ISIN_

How You Can Read ISIN_

imc-2018-s.pdf

imc-2018-s.pdf

IME 2020 - fechada

IME 2020 - fechada

Summative Assessment Paper-2

Summative Assessment Paper-2

Fuvest 2020 - aberta

Fuvest 2020 - aberta

PNEB - MATHEMATICS 2013

PNEB - MATHEMATICS 2013

Matlab level 1.pptx

Matlab level 1.pptx

Cat 2005-solutions

Cat 2005-solutions

PEA 305.pdf

PEA 305.pdf

Ptolemy's theorem visualisation. 3D graphics.

Ptolemy's theorem states the following: a convex quadrilateral can be inscribed in a circle if and only if the product of the lengths of one pair of opposite sides added to the product of the lengths of the other pair is equal to the product of the lengths of the diagonals. Thus, in a cyclic quadrilateral ABCD we have
AB*DC + AD*BC = AC*BD

An inequality painted on the vase body.

The 3D picture shows an attempt at combining applied art with pure mathematics. The vase shown in the picture is an example of ceramic vessel that could exist in real world.

Still life with vases - a 3D visualisation.

The picture presenting a still life with two vases made of black polished ceramics, standing on blocks of granite and limestone, placed in an empty room illuminated by sunlight going through a big window.

How to draw arcs of huge circles - usage of the "drawing tool".

The slide explaining visually the procedure of drawing huge circles. A theoretical background of the method has been described in another slide.

How to draw arcs of huge circles - description.

In case you are interested in drawing circles with a huge diameter (by "huge" I mean here really big ones, measured in kilometers or so) there is a tricky idea needed because the rope-and-the-stick method won't work for circles with a diameter bigger than several dozen meters. Here you can use a method based on the well known fact from geometry stating that all angles inscribed in a circle and subtended by the same chord (lying on the same side of the chord) are equal.

Calculation of the volume of a bottle partially filled with a fluid.

How to calculate the volume of a flat-bottomed, corked bottle, partially filled with a fluid having only the ruler as a measuring tool?
The 3D graphics made by me and presented below gives an answer to this question.

Permutation theorem and its use to proving inequalities.

The permutation theorem is very useful when dealing with inequalities between sums of products of the two real number sequences. In numerous cases inequalities otherwise difficult to prove can be proven almost automatically.

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

Proof of the inequality between the sum of the reciprocals of a triangle sides lengths and a cyclic sum of a specific form. Use of a transformed inequality between the arithmetic mean and the harmonic mean.

Complex Integral

Evaluation of integrals of the given functions along the unit circle on the complex plane. Application of the parametrization method. Evaluation of the integral of an odd function.

Indescribable numbers

1) There are a finite number of possible symbol sets that could be used to describe numbers, as the set of all symbols used by humans is finite.
2) While new symbols can be invented, the set of all possible symbol combinations remains finite.
3) Any description system based on a finite set of symbols can only describe countably many numbers, whereas the set of all real numbers is uncountably large. Therefore, there will always be real numbers that cannot be described.

Late Spring 2015 Photos

Photos taken in May and June 2015.

Ptolemy's theorem visualisation. 3D graphics.

Ptolemy's theorem visualisation. 3D graphics.

An inequality painted on the vase body.

An inequality painted on the vase body.

Still life with vases - a 3D visualisation.

Still life with vases - a 3D visualisation.

How to draw arcs of huge circles - usage of the "drawing tool".

How to draw arcs of huge circles - usage of the "drawing tool".

How to draw arcs of huge circles - description.

How to draw arcs of huge circles - description.

Calculation of the volume of a bottle partially filled with a fluid.

Calculation of the volume of a bottle partially filled with a fluid.

Permutation theorem and its use to proving inequalities.

Permutation theorem and its use to proving inequalities.

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

Complex Integral

Complex Integral

Indescribable numbers

Indescribable numbers

Late Spring 2015 Photos

Late Spring 2015 Photos

Properties of virus(Ultrastructure and types of virus)

It is obligate type of parasite which affect living organism.

Science-Technology Quiz (School Quiz 2024)

Science-Technology Quiz (School Quiz 2024)

A mature quasar at cosmic dawn revealed by JWST rest-frame infrared spectroscopy

The rapid assembly of the first supermassive black holes is an enduring mystery. Until now, it was not known whether quasar ‘feeding’ structures (the ‘hot torus’) could assemble as fast as the smaller-scale quasar structures. We present JWST/MRS (rest-frame infrared) spectroscopic observations of the quasar J1120+0641 at z = 7.0848 (well within the epoch of reionization). The hot torus dust was clearly detected at λrest ≃ 1.3 μm, with a black-body temperature of
K, slightly elevated compared to similarly luminous quasars at lower redshifts. Importantly, the supermassive black hole mass of J1120+0641 based on the Hα line (accessible only with JWST), MBH = 1.52 ± 0.17 × 109 M⊙, is in good agreement with previous ground-based rest-frame ultraviolet Mg II measurements. Comparing the ratios of the Hα, Paα and Paβ emission lines to predictions from a simple one-phase Cloudy model, we find that they are consistent with originating from a common broad-line region with physical parameters that are consistent with lower-redshift quasars. Together, this implies that J1120+0641’s accretion structures must have assembled very quickly, as they appear fully ‘mature’ less than 760 Myr after the Big Bang.

The Dynamical Origins of the Dark Comets and a Proposed Evolutionary Track

So-called ‘dark comets’ are small, morphologically inactive near-Earth objects
(NEOs) that exhibit nongravitational accelerations inconsistent with radiative
effects. These objects exhibit short rotational periods (minutes to hours), where
measured. We find that the strengths required to prevent catastrophic disintegration are consistent with those measured in cometary nuclei and expected in
rubble pile objects. We hypothesize that these dark comets are the end result
of a rotational fragmentation cascade, which is consistent with their measured
physical properties. We calculate the predicted size-frequency distribution for
objects evolving under this model. Using dynamical simulations, we further
demonstrate that the majority of these bodies originated from the 𝜈6
resonance,
implying the existence of volatiles in the current inner main belt. Moreover, one of
the dark comets, (523599) 2003 RM, likely originated from the outer main belt,
although a JFC origin is also plausible. These results provide strong evidence
that volatiles from a reservoir in the inner main belt are present in the near-Earth
environment.

Lunar Mobility Drivers and Needs - Artemis

NASA’s new campaign of lunar exploration will see astronauts visiting sites of scientific or strategic
interest across the lunar surface, with a particular focus on the lunar South Pole region.[1] After landing
crew and cargo at these destinations, local mobility around landing sites will be key to movement of
cargo, logistics, science payloads, and more to maximize exploration returns.
NASA’s Moon to Mars Architecture Definition Document (ADD)[2] articulates the work needed to achieve
the agency’s human lunar exploration objectives by decomposing needs into use cases and functions.
Ongoing analysis of lunar exploration needs reveals demands that will drive future concepts and elements.
Recent analysis of integrated surface operations has shown that the transportation of cargo on the
surface from points of delivery to points of use will be particularly important. Exploration systems will
often need to support deployment of cargo in close proximity to other surface infrastructure. This cargo
can range from the crew logistics and consumables described in the 2023 “Lunar Logistics Drivers and
Needs” white paper,[3] to science and technology demonstrations, to large-scale infrastructure that
requires precision relocation.

The cryptoterrestrial hypothesis: A case for scientific openness to a conceal...

Recent years have seen increasing public attention and indeed concern regarding Unidentified
Anomalous Phenomena (UAP). Hypotheses for such phenomena tend to fall into two classes: a
conventional terrestrial explanation (e.g., human-made technology), or an extraterrestrial explanation
(i.e., advanced civilizations from elsewhere in the cosmos). However, there is also a third minority
class of hypothesis: an unconventional terrestrial explanation, outside the prevailing consensus view of
the universe. This is the ultraterrestrial hypothesis, which includes as a subset the “cryptoterrestrial”
hypothesis, namely the notion that UAP may reflect activities of intelligent beings concealed in stealth
here on Earth (e.g., underground), and/or its near environs (e.g., the moon), and/or even “walking
among us” (e.g., passing as humans). Although this idea is likely to be regarded sceptically by most
scientists, such is the nature of some UAP that we argue this possibility should not be summarily
dismissed, and instead deserves genuine consideration in a spirit of epistemic humility and openness.

SDG (sustainable development goal) of government

Helping in finding out the goal of sustainable development

degree Certificate of Aston University

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二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(aston毕业证书)英国阿斯顿大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(aston毕业证书)英国阿斯顿大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(aston毕业证书)英国阿斯顿大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(aston毕业证书)英国阿斯顿大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

Gasification and Pyrolyssis of plastic Waste under a Circular Economy perpective

Review on Gasification LCA. Presentation given by Cecilia Hofmann at Advanced Recycling Conference in Cologne, 2023.

Testing the Son of God Hypothesis (Jesus Christ)

Instead of answering the God hypothesis, we investigate the Son of God hypothesis. We developed our own methodology to deal with existential statements instead of universal statements unlike science. We discuss the existence of the supernaturals and found that there are strong evidence for it. Given that supernatural exists, we report on miracles investigated in the past related to the Son of God. A Bayesian methodology is used to calculate the combined degree of belief of the Son of God Hypothesis. We also report the testing of occurrences of words/numbers in the Bible to suggest the likelihood of some special numbers occurring, supporting the Son of God Hypothesis. We also have a table showing the past occurrences of miracles in hundred year periods for about 1000 years. Miracles that we have looked at include Shroud of Turin, Eucharistic Miracles, Marian Apparitions, Incorruptible Corpses, etc.

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Identifying Indian wood involves recognizing key characteristics such as grain patterns, color, texture, hardness, and specific anatomical features. These identification keys include observing the wood's pores, growth rings, and resin canals, as well as its scent and weight. Understanding these features is essential for accurate wood identification, which is crucial for various applications in carpentry, furniture making, and conservation.
Additionally, the application of Convolutional Neural Networks (CNN) in wood identification has revolutionized this field. CNNs can analyze images of wood samples to identify species with high accuracy by learning and recognizing intricate patterns and features. This technological advancement not only enhances the precision of wood identification but also accelerates the process, making it more efficient for industry professionals and researchers alike.

Summer program introduction in Yunnan university

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SCIENTIFIC INVESTIGATIONS – THE IMPORTANCE OF FAIR TESTING.pptx

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Bragg Brentano Alignment for D4 with LynxEye Rev3.pptx

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TOPIC: INTRODUCTION TO FORENSIC SCIENCE.pptx

This presentation, "Introduction to Forensic Science," offers a basic understanding of forensic science, including its history, why it's needed, and its main goals. It covers how forensic science helps solve crimes and its importance in the justice system. By the end, you'll have a clear idea of what forensic science is and why it's essential.

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For more details visit on YouTube; @SELF-EXPLANATORY; https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
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- 1. Given a number (ab)3 , 1 a 9, 0 b 9. Find without use of calculator the number ab. Solution by Mikolaj Hajduk: The aforementioned math problem is a symbolic description of the following game: an illusion- ist asks a randomly chosen spectator to pick (secretly) one of the natural numbers smaller than 100 and calculate its cube and give the result speaking it aloud. The illusionist imme- diately gives an answer, i.e. the original number chosen by the spectator. This trick doesn’t require the magician to know all cubes of the numbers between 1 and 100. It’s enough to remember only cubes of the ﬁrst ten numbers from 1 to 10 because the method of determination of the original number is based on this information as it will be shown in the further parts of this paper. The cube of any two-digit number and the cube of the last digit of the original number are congruent modulo 10, more precisely (ab)3 ≡ b3 (mod 10) indeed, we have (ab)3 = (10a + b)3 = (10a)3 + 3(10a)2 b + 3(10a)b2 + b3 = = 1000a3 + 300a2 b + 30ab2 + b3 = = 10(100a3 + 30a2 b + 3ab2 ) + b3 So the last digit of the cube of the original number gives us a way to determine the second digit of the original number. Let’s take a look at the following array: c 2015/04/28 22:18:03, Mikolaj Hajduk 1 / 3 next
- 2. a 1 2 3 4 5 6 7 8 9 10 a3 1 8 27 64 125 216 343 512 729 1000 a3 mod 10 1 8 7 4 5 6 3 2 9 0 The ﬁrst digit of the original number chosen by the spectator may be determined as follows: we discard the last three digits of the cube and take the integer part of the cube root from the number that has left, in other words we get that a = 3 (ab)3 1000 and we will show below how we can explain this result. At ﬁrst, from the deﬁnition of the ﬂoor function we get the following useful feature: A x ∈ R A m ∈ Z (m x =⇒ m x ) (∗) now, bearing in mind the feature (∗), we can prove correctness of the formula for the ﬁrst digit of the guessed number: 10a 10a + b = ab < 10a + 10 = 10(a + 1) ⇐⇒ 1000a3 (ab)3 < 1000(a + 1)3 ⇐⇒ a3 (ab)3 1000 < (a + 1)3 =⇒ (∗) c 2015/04/28 22:18:03, Mikolaj Hajduk 2 / 3 next
- 3. a3 (ab)3 1000 < (a + 1)3 ⇐⇒ a 3 (ab)3 1000 < a + 1 =⇒ (∗) a 3 (ab)3 1000 < a + 1 Because the number 3 (ab)3 1000 is integer, greater than or equal to a and less than a + 1, then it has to be equal to a (the is no integer n such that a < n < a + 1). Finally we get the postulated formula for the ﬁrst digit of the guessed number. Example of use Let (ab)3 = 250047. The second number of the guessed number ab is 3 as it corresponds in our array to 7 = (ab)3 mod 10. The ﬁrst digit of the original number is equal to 3 (ab)3 1000 = 3 √ 250 = 6 so the original number is equal to 63. Let’s check it out. Indeed 633 = 250047. c 2015/04/28 22:18:03, Mikolaj Hajduk 3 / 3