1. Derive the expression for stress tensor in cylindrical coordinates (r, θ, z). Calculate the volume integral of r-1 over the sphere of radius R.
2. Find the solution u(r,t) of the heat equation with initial and boundary conditions given.
3. Find the temperature distribution inside a cylindrical rod at any time t > 0, given the initial temperature distribution and boundary conditions.
4. Find the function u(r,φ) satisfying the Laplace's equation and boundary condition on the surface of a sphere.
5. Find the solution u(r,y) of the given partial differential equation satisfying the boundary conditions.
This document appears to be a 10 question math exam in Vietnamese with the following key details:
1. The exam is 180 minutes long with no additional time for submission.
2. The questions cover topics like graphing functions, solving equations, integrals, geometry problems finding volumes of shapes, and coordinate geometry.
3. The final question asks students to find the minimum value of an expression given certain constraints on variables a, b, and c.
1. The document provides information about a math exam, including the exam time of 180 minutes and 6 questions ranging from 1 to 2 points each. The questions cover topics such as solving equations, finding roots of equations, integrals, geometry problems, and systems of equations.
2. The responses provide solutions to each question, showing the steps and reasoning for obtaining the answers. Solutions include solving equations, finding integrals, using geometry relationships, and solving a system of inequalities.
3. Diagrams and calculations are shown to visually depict the solutions to the geometry problems involving shapes, angles, and areas.
1. The document provides information about a math exam, including the duration of 180 minutes.
2. It lists 7 questions on the exam covering topics like functions, derivatives, integrals, geometry, and inequalities.
3. The questions involve solving equations, finding maximum/minimum values, determining tangent lines, proving relationships between angles and lines, and optimizing expressions.
The document contains a math test with multiple choice and free response questions. Some key points:
- It asks to find the domain and range of the function f(x) = 3x^2 - 6x + 1.
- It asks to solve the system of equations x^2 + y^2 - 4x + 2y - 5 = 0 and 2x - y = 0 to find the points A and B where the line is tangent to the circle.
- It asks to find the real root of the equation z^4 - 22z + 5 = 0.
- It provides two parts (A and B) for the free response section and asks to choose one. Part
This document contains 6 math equations:
1) yj = 0
2) x' - 14 = 0
3) r<1+l?-> l3r = c
4) xz-13>'Y[-lL
5) f7t6x-2,4 =to
6) \z-3>-sE:a
Each equation is set equal to a variable or constant with restrictions on x and r provided for some equations.
This document provides a lesson plan for teaching chemistry. It includes preliminary details like the name of the teacher, school, subject, unit, and topic. It outlines the learning outcomes which are cognitive competencies for students to recall terms, facts, and concepts, and affective competencies like willingness to participate. It lists the pre-requisites and teaching materials. The plan describes classroom activities like demonstrations and discussions. It explains how concepts will be formed and knowledge constructed through summarization and review.
This document is an edit decision list for a film or video project. It contains 16 entries with shot numbers, timecodes for shot starts and ends, and brief comments describing each shot or take. The comments indicate things like camera issues, actor performances, or desired edits. The list provides a high-level overview of the shots and edits needed to assemble the final video project.
This document appears to be a 10 question math exam in Vietnamese with the following key details:
1. The exam is 180 minutes long with no additional time for submission.
2. The questions cover topics like graphing functions, solving equations, integrals, geometry problems finding volumes of shapes, and coordinate geometry.
3. The final question asks students to find the minimum value of an expression given certain constraints on variables a, b, and c.
1. The document provides information about a math exam, including the exam time of 180 minutes and 6 questions ranging from 1 to 2 points each. The questions cover topics such as solving equations, finding roots of equations, integrals, geometry problems, and systems of equations.
2. The responses provide solutions to each question, showing the steps and reasoning for obtaining the answers. Solutions include solving equations, finding integrals, using geometry relationships, and solving a system of inequalities.
3. Diagrams and calculations are shown to visually depict the solutions to the geometry problems involving shapes, angles, and areas.
1. The document provides information about a math exam, including the duration of 180 minutes.
2. It lists 7 questions on the exam covering topics like functions, derivatives, integrals, geometry, and inequalities.
3. The questions involve solving equations, finding maximum/minimum values, determining tangent lines, proving relationships between angles and lines, and optimizing expressions.
The document contains a math test with multiple choice and free response questions. Some key points:
- It asks to find the domain and range of the function f(x) = 3x^2 - 6x + 1.
- It asks to solve the system of equations x^2 + y^2 - 4x + 2y - 5 = 0 and 2x - y = 0 to find the points A and B where the line is tangent to the circle.
- It asks to find the real root of the equation z^4 - 22z + 5 = 0.
- It provides two parts (A and B) for the free response section and asks to choose one. Part
This document contains 6 math equations:
1) yj = 0
2) x' - 14 = 0
3) r<1+l?-> l3r = c
4) xz-13>'Y[-lL
5) f7t6x-2,4 =to
6) \z-3>-sE:a
Each equation is set equal to a variable or constant with restrictions on x and r provided for some equations.
This document provides a lesson plan for teaching chemistry. It includes preliminary details like the name of the teacher, school, subject, unit, and topic. It outlines the learning outcomes which are cognitive competencies for students to recall terms, facts, and concepts, and affective competencies like willingness to participate. It lists the pre-requisites and teaching materials. The plan describes classroom activities like demonstrations and discussions. It explains how concepts will be formed and knowledge constructed through summarization and review.
This document is an edit decision list for a film or video project. It contains 16 entries with shot numbers, timecodes for shot starts and ends, and brief comments describing each shot or take. The comments indicate things like camera issues, actor performances, or desired edits. The list provides a high-level overview of the shots and edits needed to assemble the final video project.
1. The document is a practice test for a Japanese language exam containing 40 multiple choice questions testing reading comprehension and grammar.
2. The test has two sections - a multiple choice section worth 8 points and an essay section worth 2 points.
3. Test takers are not allowed to use any reference materials and must submit both the answer sheet and test paper after completion.
Đại lý dây điện Cadivi 3.5 tại Tphcm chiết khấu caoVõ Thành Tiến
Đại lý dây điện Cadivi 3.5 tại Tphcm chiết khấu cao
Bảng giá dây điện cadivi mới nhất
Chiết khấu dâ điện Cadivi 2018 mới nhất tại Tphcm
https://thietbidandung.vn/day-cap-dien-cadivi
1) The function y = 2x3 + 3x2 - 12x - 13 has two extreme points when m = 3.
2) The quadratic equation y" = 0 √6x2 + 2mx + 12 = 0 has both a maximum point and a minimum point.
3) Solving the system of equations x' - 3x = 1, y' + 4y = 3 gives the solutions (-1, -4) and (2, 0).
1. The document is a math exam with 7 questions in Vietnamese.
2. Question 1 involves analyzing the behavior and limits of the function y = -x^2 - 4x + 1.
3. Question 2 involves solving two equations for the intersection points of lines and finding the minimum length between two points.
4. The remaining questions involve additional math problems like solving equations, finding limits, calculating areas, and expansions of functions.
Đề Kiểm Tra Chất Lượng Môn Toán Trường Chuyên Hà Nội AmsterdamMathX Thích Học Toán
1. The document provides 4 math problems involving solving equations and inequalities for unknown variables x and y.
2. Problem 1 involves solving a quadratic equation for x. Problem 2 involves solving a linear equation for x.
3. Problem 3 finds values of x and y that satisfy two simultaneous equations.
4. The final problem involves using given values to solve two equations for the unknowns x and y.
This document contains mathematical calculations and derivations involving parameters such as s, K, and z. It determines that certain expressions equal zero, finds limits, and identifies poles and zeros of transfer functions. The document also contains comments on closed-loop stability analysis and indicates that the poles are real when K is less than one.
This document is an edit decision list containing information about shots in a video including the in and out times of each shot, and comments about takes and the quality of the shots. It contains over 30 entries with details about multiple takes of various shots. The goal seems to be to choose the best takes to construct the final video.
1. The document discusses theories of comminution, which is the process of reducing solid materials to smaller sizes.
2. The oldest theory from 1867 states that work input is directly proportional to the new surface area produced by crushing. However, measurements show the energy required is much greater than needed to create the new surface area.
3. A 1885 theory states work required is proportional to the reduction in volume of particles. Neither of these theories accurately predict results from commercial crushing and grinding.
4. The author developed a third theory in 1951 stating work input is proportional to something other than new surface area or volume reduction. However, the summary does not provide details on what the third theory states.
The document discusses five electrical circuit problems:
1. Calculating the power consumed by a circuit operating at 120V.
2. Determining the current in a circuit with a 120V-300W heater.
3. Calculating the resistance in a circuit with a 2.5W lamp.
4. Identifying components in a circuit diagram, including resistors, capacitors, inductors.
5. Analyzing a series circuit with a 50W bulb and variable resistor to determine how resistance affects bulb brightness.
This document discusses several manufacturing and production related concepts. It defines dog as an animal that uses its sense of smell to detect smells. It explains that a CAPP system automatically generates optimal manufacturing sequences based on the design of a given part. It describes MRP as a component of production planning that determines material and component requirements. The benefits of FMS include reduced manufacturing costs, higher productivity, and improved quality.
Haloalkanes and Haloarenes notes(complete).pdfsk4829362
The document discusses various halogenated organic compounds including haloalkanes, haloalkenes, and aromatic halides. It provides their systematic IUPAC names and common names, and describes their physical properties and reactivity patterns based on the type and position of halogen substituents. Common reaction types covered include nucleophilic substitution, elimination, and addition reactions involving halogenated compounds.
Db2 Warehouseを理由するユーザー及び、構築、運用管理を行うユーザー向けに作成したガイドです。Db2 Warehouseの構築、運用管理の際に必要に応じて参照ください。本ドキュメントはDb2 Warehouse v3.0をベースに作成されています。
It is a guide created for users who reason for Db2 Warehouse, and for users who conduct construction and operation management. Please refer to Db 2 Warehouse as necessary for construction and operation management. This document is based on Db 2 Warehouse v 3.0.
1. The question asks to analyze the function y=x3+3x2-4 and find the point of inflection of the equation (x+2)'=4cos(x).
2. For the function y=x3+3x2-4, the point of inflection is (-1,-2) and the minimum point is (0,-4).
3. The point of inflection of the equation (x+2)'=4cos(x) is (-1,0).
1. The document discusses reducing a given proposition to its minimal equivalent expression in sum of products form. It provides examples of reducing propositions such as A+BC to its minimal expression of A+B+C.
2. Methods for simplifying Boolean expressions using Boolean algebra rules are presented, including eliminating common factors, combining like terms, and removing redundant variables.
3. The process of obtaining the minimum equivalent expression for circuits and logic gates such as AND, OR, and NAND is explained step-by-step with examples.
The document appears to be an exam question paper that covers various topics related to advanced mathematics, digital VLSI design, embedded systems, ASIC design, VLSI process technology, and related subjects. It contains 10 questions with varying point values and instructs students to answer any 5 full questions. The questions cover technical topics such as matrix operations, MOS transistor modeling, logic design, processor architecture, ASIC design flows, silicon crystal growth, and more.
This document is unintelligible as it contains no actual words, only symbols and characters. It does not provide any information that can be summarized.
This math test contains 6 questions about calculus, geometry, and equations. Question 1 involves finding the derivative of a function and finding critical points. Question 2 involves solving equations. Question 3 involves finding integrals and values that satisfy an equation. Question 4 is about finding properties of a square pyramid. Question 5 involves finding points on lines and writing equations of circles. Question 6 is about finding the minimum value of an expression involving integrals.
1. The document contains questions about electrical circuits and concepts such as resistance, capacitance, current, and voltage.
2. Multiple choice questions are asked about series and parallel circuits, Kirchhoff's laws, RC circuits, inductors, and the relationship between various circuit elements.
3. Correct answers are provided for each question in the form of letters A through D. The document acts as a quiz or test of electrical circuit knowledge.
1. The document is a practice test for a Japanese language exam containing 40 multiple choice questions testing reading comprehension and grammar.
2. The test has two sections - a multiple choice section worth 8 points and an essay section worth 2 points.
3. Test takers are not allowed to use any reference materials and must submit both the answer sheet and test paper after completion.
Đại lý dây điện Cadivi 3.5 tại Tphcm chiết khấu caoVõ Thành Tiến
Đại lý dây điện Cadivi 3.5 tại Tphcm chiết khấu cao
Bảng giá dây điện cadivi mới nhất
Chiết khấu dâ điện Cadivi 2018 mới nhất tại Tphcm
https://thietbidandung.vn/day-cap-dien-cadivi
1) The function y = 2x3 + 3x2 - 12x - 13 has two extreme points when m = 3.
2) The quadratic equation y" = 0 √6x2 + 2mx + 12 = 0 has both a maximum point and a minimum point.
3) Solving the system of equations x' - 3x = 1, y' + 4y = 3 gives the solutions (-1, -4) and (2, 0).
1. The document is a math exam with 7 questions in Vietnamese.
2. Question 1 involves analyzing the behavior and limits of the function y = -x^2 - 4x + 1.
3. Question 2 involves solving two equations for the intersection points of lines and finding the minimum length between two points.
4. The remaining questions involve additional math problems like solving equations, finding limits, calculating areas, and expansions of functions.
Đề Kiểm Tra Chất Lượng Môn Toán Trường Chuyên Hà Nội AmsterdamMathX Thích Học Toán
1. The document provides 4 math problems involving solving equations and inequalities for unknown variables x and y.
2. Problem 1 involves solving a quadratic equation for x. Problem 2 involves solving a linear equation for x.
3. Problem 3 finds values of x and y that satisfy two simultaneous equations.
4. The final problem involves using given values to solve two equations for the unknowns x and y.
This document contains mathematical calculations and derivations involving parameters such as s, K, and z. It determines that certain expressions equal zero, finds limits, and identifies poles and zeros of transfer functions. The document also contains comments on closed-loop stability analysis and indicates that the poles are real when K is less than one.
This document is an edit decision list containing information about shots in a video including the in and out times of each shot, and comments about takes and the quality of the shots. It contains over 30 entries with details about multiple takes of various shots. The goal seems to be to choose the best takes to construct the final video.
1. The document discusses theories of comminution, which is the process of reducing solid materials to smaller sizes.
2. The oldest theory from 1867 states that work input is directly proportional to the new surface area produced by crushing. However, measurements show the energy required is much greater than needed to create the new surface area.
3. A 1885 theory states work required is proportional to the reduction in volume of particles. Neither of these theories accurately predict results from commercial crushing and grinding.
4. The author developed a third theory in 1951 stating work input is proportional to something other than new surface area or volume reduction. However, the summary does not provide details on what the third theory states.
The document discusses five electrical circuit problems:
1. Calculating the power consumed by a circuit operating at 120V.
2. Determining the current in a circuit with a 120V-300W heater.
3. Calculating the resistance in a circuit with a 2.5W lamp.
4. Identifying components in a circuit diagram, including resistors, capacitors, inductors.
5. Analyzing a series circuit with a 50W bulb and variable resistor to determine how resistance affects bulb brightness.
This document discusses several manufacturing and production related concepts. It defines dog as an animal that uses its sense of smell to detect smells. It explains that a CAPP system automatically generates optimal manufacturing sequences based on the design of a given part. It describes MRP as a component of production planning that determines material and component requirements. The benefits of FMS include reduced manufacturing costs, higher productivity, and improved quality.
Haloalkanes and Haloarenes notes(complete).pdfsk4829362
The document discusses various halogenated organic compounds including haloalkanes, haloalkenes, and aromatic halides. It provides their systematic IUPAC names and common names, and describes their physical properties and reactivity patterns based on the type and position of halogen substituents. Common reaction types covered include nucleophilic substitution, elimination, and addition reactions involving halogenated compounds.
Db2 Warehouseを理由するユーザー及び、構築、運用管理を行うユーザー向けに作成したガイドです。Db2 Warehouseの構築、運用管理の際に必要に応じて参照ください。本ドキュメントはDb2 Warehouse v3.0をベースに作成されています。
It is a guide created for users who reason for Db2 Warehouse, and for users who conduct construction and operation management. Please refer to Db 2 Warehouse as necessary for construction and operation management. This document is based on Db 2 Warehouse v 3.0.
1. The question asks to analyze the function y=x3+3x2-4 and find the point of inflection of the equation (x+2)'=4cos(x).
2. For the function y=x3+3x2-4, the point of inflection is (-1,-2) and the minimum point is (0,-4).
3. The point of inflection of the equation (x+2)'=4cos(x) is (-1,0).
1. The document discusses reducing a given proposition to its minimal equivalent expression in sum of products form. It provides examples of reducing propositions such as A+BC to its minimal expression of A+B+C.
2. Methods for simplifying Boolean expressions using Boolean algebra rules are presented, including eliminating common factors, combining like terms, and removing redundant variables.
3. The process of obtaining the minimum equivalent expression for circuits and logic gates such as AND, OR, and NAND is explained step-by-step with examples.
The document appears to be an exam question paper that covers various topics related to advanced mathematics, digital VLSI design, embedded systems, ASIC design, VLSI process technology, and related subjects. It contains 10 questions with varying point values and instructs students to answer any 5 full questions. The questions cover technical topics such as matrix operations, MOS transistor modeling, logic design, processor architecture, ASIC design flows, silicon crystal growth, and more.
This document is unintelligible as it contains no actual words, only symbols and characters. It does not provide any information that can be summarized.
This math test contains 6 questions about calculus, geometry, and equations. Question 1 involves finding the derivative of a function and finding critical points. Question 2 involves solving equations. Question 3 involves finding integrals and values that satisfy an equation. Question 4 is about finding properties of a square pyramid. Question 5 involves finding points on lines and writing equations of circles. Question 6 is about finding the minimum value of an expression involving integrals.
1. The document contains questions about electrical circuits and concepts such as resistance, capacitance, current, and voltage.
2. Multiple choice questions are asked about series and parallel circuits, Kirchhoff's laws, RC circuits, inductors, and the relationship between various circuit elements.
3. Correct answers are provided for each question in the form of letters A through D. The document acts as a quiz or test of electrical circuit knowledge.
1. n0 crAo DUc VA DAo TAo Hq vd t€n thi sinh:
DAI HOC I{Ufi Sd bdo danh:
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ducycgiu crnhiet do khong doi bing 7, cbn mrit r - ( duoc giu crnhiet
khongdoi bXng U.
Cdu IV. Tim hdm u(r,g) @hotrong toa d6 cuc) diEu h6a trong hinh trdn c6 tAm d
e6c toa d6 O vd brin kinh E. th6a man dibu ki6n tr6n bi6n cria hinh trdn
u(R, P) : '4(sin(P+ 2 cos2P)'
CAu V. Tim ne.hiArntt - u(r,y) cuaphucrngtrinh
ur, - 2 sin g,'r-t,ra- .or2 fr.uaa- cosr.uo - Q
th6a min dlEu ki6n sau
u(r, cosr) - sinrr ur(r) cosr) : r * cosr.
dei
-n
+ ^
oo
cac
Ghi chri: Cdn bo coi thi khdng giAi thfch gi them.