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1. The document discusses four mathematics word problems involving quadratic equations. 2. The first problem involves finding the length of one side of a rectangular field given the total area. The second finds the height of a water tank given its base dimensions. 3. The third determines the radius of a cone given its volume. 4. The fourth finds the printing time of two printers given their total time and one printer's time.
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tugas 2
1. The document is a mathematics assignment in Indonesian that contains 4 word problems involving quadratic equations.
2. The first problem involves finding the width of a rectangular plot of land given the total area and dimensions of the land. The second problem involves finding the height of a water tank given its base dimensions and volume.
3. The third problem involves finding the radius of a cone given its volume. The fourth problem involves finding the printing time of two printers given their total printing time and one printer's time.
Tugas matematika kelompok_b (2)
This document contains a summary of 4 math problems solved by a group for their assignment. It lists the group members and their tasks which include:
1) Solving a quadratic equation problem to find the equation x^2 - 90x + 800.
2) Finding the volume of a block using the formula Volume = length x width x height, resulting in a volume of 3000cm^3.
3) Finding the original radius of a cone after increases to its radius and height, determining the radius was originally 12cm.
4) Solving two time equations to find the time a second printer takes is 3 hours.
Persamaan kuadrat
The document summarizes three word problems involving quadratic equations and their solutions:
1) A problem about the area of a rectangle with length p=60m and width l=30m having area L=1000m^2. The solutions are x=80m or x=10m.
2) A problem about the area of a trapezoid with bases of 50-2x cm and 40-2x cm and height x cm having area of 200 cm^2. The solutions are x=30 cm or x=15 cm.
3) A problem about the volume of a cylinder with radius r and height t=3cm having volume V=27. The solutions are r=12
Tugas matek pertaama
The document contains a list of 4 names and student numbers that make up a study group for the 2013/2014 school year at SMK N 1 Tabanan. It also contains 4 math problems with solutions:
1) Solving a quadratic equation to find the values of X. The solutions are X = 80 and X = 10.
2) Finding the volume of a shape given measurements that vary with X. The volume is 3000 cm^3.
3) Solving an equation involving radicals to find original radii of a cone. The radii are 12 and 6.
4) Solving an equation involving fractions to find the values of X. The only positive solution is X = 2.
Tugas matik i
1. The first problem involves solving a quadratic equation (x2 - 90x + 800 = 0) to find the length (x) of one side of a square field with an area of 1000 square meters.
2. The second problem involves solving another quadratic equation (4x2 - 180x + 1800 = 0) to find the length (x) of one side of a rectangular field with an area of 3000 cubic centimeters.
3. The third problem involves setting up and solving two equations relating the original radius (r) and height of a cone to the increased radius and volume after increases of 24 units to find that the original radius was 12 centimeters.
4. The fourth problem uses a system
Mat. persamaan kuadrat
The document contains mathematical word problems and their step-by-step solutions. The problems involve setting up and solving equations to find unknown values like x, r, or t. The equations relate variables like length, width, area, and volume. The solutions show the work of setting up the equations based on the given information and algebraic manipulations to solve for the unknowns.
Tugas matematika kelompok_b (2)
This document contains information about a group assignment in Indonesian. It lists the group name, leader, and members. It then provides 3 math problems and solutions. The problems involve quadratic equations, volume of a shape, and time to print with two printers. The document solves for unknown values x, r, and time x in each problem step-by-step.
Tugas matematika menemukan konsep persamaan kuadrat
1. The document describes solving several quadratic equations by factoring, completing the square, and using the quadratic formula. It provides examples of finding the roots of quadratic equations in various forms.
2. Methods for solving quadratic equations discussed include factoring, completing the square to convert it into the standard form of a quadratic equation, and using the quadratic formula.
3. Several examples are worked through step-by-step to demonstrate these different methods of solving quadratic equations algebraically.
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tugas 2
1. The document is a mathematics assignment in Indonesian that contains 4 word problems involving quadratic equations.
2. The first problem involves finding the width of a rectangular plot of land given the total area and dimensions of the land. The second problem involves finding the height of a water tank given its base dimensions and volume.
3. The third problem involves finding the radius of a cone given its volume. The fourth problem involves finding the printing time of two printers given their total printing time and one printer's time.
Tugas matematika kelompok_b (2)
This document contains a summary of 4 math problems solved by a group for their assignment. It lists the group members and their tasks which include:
1) Solving a quadratic equation problem to find the equation x^2 - 90x + 800.
2) Finding the volume of a block using the formula Volume = length x width x height, resulting in a volume of 3000cm^3.
3) Finding the original radius of a cone after increases to its radius and height, determining the radius was originally 12cm.
4) Solving two time equations to find the time a second printer takes is 3 hours.
Persamaan kuadrat
The document summarizes three word problems involving quadratic equations and their solutions:
1) A problem about the area of a rectangle with length p=60m and width l=30m having area L=1000m^2. The solutions are x=80m or x=10m.
2) A problem about the area of a trapezoid with bases of 50-2x cm and 40-2x cm and height x cm having area of 200 cm^2. The solutions are x=30 cm or x=15 cm.
3) A problem about the volume of a cylinder with radius r and height t=3cm having volume V=27. The solutions are r=12
Tugas matek pertaama
The document contains a list of 4 names and student numbers that make up a study group for the 2013/2014 school year at SMK N 1 Tabanan. It also contains 4 math problems with solutions:
1) Solving a quadratic equation to find the values of X. The solutions are X = 80 and X = 10.
2) Finding the volume of a shape given measurements that vary with X. The volume is 3000 cm^3.
3) Solving an equation involving radicals to find original radii of a cone. The radii are 12 and 6.
4) Solving an equation involving fractions to find the values of X. The only positive solution is X = 2.
Tugas matik i
1. The first problem involves solving a quadratic equation (x2 - 90x + 800 = 0) to find the length (x) of one side of a square field with an area of 1000 square meters.
2. The second problem involves solving another quadratic equation (4x2 - 180x + 1800 = 0) to find the length (x) of one side of a rectangular field with an area of 3000 cubic centimeters.
3. The third problem involves setting up and solving two equations relating the original radius (r) and height of a cone to the increased radius and volume after increases of 24 units to find that the original radius was 12 centimeters.
4. The fourth problem uses a system
Mat. persamaan kuadrat
The document contains mathematical word problems and their step-by-step solutions. The problems involve setting up and solving equations to find unknown values like x, r, or t. The equations relate variables like length, width, area, and volume. The solutions show the work of setting up the equations based on the given information and algebraic manipulations to solve for the unknowns.
Tugas matematika kelompok_b (2)
This document contains information about a group assignment in Indonesian. It lists the group name, leader, and members. It then provides 3 math problems and solutions. The problems involve quadratic equations, volume of a shape, and time to print with two printers. The document solves for unknown values x, r, and time x in each problem step-by-step.
Tugas matematika menemukan konsep persamaan kuadrat
1. The document describes solving several quadratic equations by factoring, completing the square, and using the quadratic formula. It provides examples of finding the roots of quadratic equations in various forms.
2. Methods for solving quadratic equations discussed include factoring, completing the square to convert it into the standard form of a quadratic equation, and using the quadratic formula.
3. Several examples are worked through step-by-step to demonstrate these different methods of solving quadratic equations algebraically.
SIT292 Linear Algebra 2013
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MATHS
This document provides methods for calculating the square of various types of numbers:
1) For numbers ending in 5, add 1 to the digit before 5 and multiply it by that digit. Then write 25 after it (e.g. 225 for 15x15).
2) For numbers with all the same digit, write the digits in ascending then descending order (e.g. 12321 for 111x111).
3) For two-digit numbers starting with 5, take the square of the first digit and second digit separately and concatenate them (e.g. 2704 for 52x52).
4) For two-digit numbers starting with 9, subtract from 100, take the square of
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This document introduces four mathematical identities:
1) (x+y)z = xz + yz, which explains how to multiply the sum of two numbers by a third number
2) (x+y)(u+v) = xu + xv + yu + yv, which explains how to multiply the sum of two numbers by the sum of two other numbers
3) (x-y)2 = x2 - 2xy + y2
4) (X+Y)(X-Y) = X2 - Y2
It provides examples of applying each identity to demonstrate how to use algebra to simplify expressions.
Algebra
This document contains 3 identities related to multiplication and addition of numbers:
1) To multiply the sum of two numbers by a third number, we multiply each number in the sum separately and add the results, following the identity (x+y)z = xz + yz.
2) To multiply the sum of two numbers by the sum of two other numbers, we multiply each number in the first sum by each number in the second sum and add the results, as expressed by the identity (x+y)(u+v) = xu + xv + yu + yv.
3) The document presents the identities (x-y)2 = x2 - 2xy +
Quadratic equations 5
The document discusses solving a quadratic equation. It is given that the quadratic equation x^2 - 8x + 12 = 0 has roots p and q. Using the roots, it is determined that the quadratic equation x^2 + ax + b = 0 has roots of p^2 + q^2 and 2pq. The sum of the coefficients a and b is then calculated to be 896.
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Ejercicios de verano para primero de eso
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Tugas matik ii
The document provides examples of factorizing quadratic equations and completing the square to solve quadratic equations. It discusses:
1) Factoring quadratic expressions like x2 + 5x - 50, x2 + 3x, and 2x2 + 3x + 1.
2) Completing the square to solve equations like x2 + 5x + 4 = 0 and 2x2 - 14x + 12 = 0.
3) Using the quadratic formula to solve equations like x2 - 15x + 30 = 0, x2 + 8x - 20 = 0, and x2 + 3x = 0.
4) Setting the discriminant equal to 0 to find the value of p that makes the equation
【演習】Re：ゲーム理論入門 第14回 -仁-
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https://www.youtube.com/channel/UCEr2VZ6DI4gATRtVJw49ZFw
Math Studies Calculus Application
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Math is fun!
The document provides steps for finding the inverse of the function f(x) = 12x-4/x-7. It works through rearranging the equation by switching x and y values, distributing terms, and factoring to arrive at the inverse function f-1(x)=7x-4/(x-12). A second example shows how to find the maximum area of a playground given its perimeter of 18600 feet by setting up equations for perimeter and area and solving.
Alg1 lesson 9-5
1) The document provides examples of factoring quadratic expressions using the difference of squares formula.
2) It shows how to factor expressions of the form (ax + b)(ax - b) = a^2x^2 - b^2.
3) Examples are given of solving equations by setting factored expressions equal to 0 and solving for the variables.
Tarea de Matematicas
The document provides examples of mathematical exercises involving factoring polynomials and binomial expressions. Some examples include factoring the difference of squares, perfect square trinomials, and perfect cube binomials. Standard factoring techniques are demonstrated such as grouping like terms, finding common factors, and using the difference and sum of cubes identities.
Integral
The document contains 10 math problems involving integration. For each problem, the question, workings, and answer are provided. The problems cover a range of integration techniques including substitution, partial fractions, and trigonometric identities.
Day 4 evaluating with add and subtract
The document provides examples of evaluating expressions involving integers. It begins with the expression -3 - 5 + (-4) - (-2). It then introduces a flow chart for adding and subtracting integers based on rules for using a number line. The flow chart shows that when adding, the value increases, and when subtracting, the value decreases. Several practice problems with solutions are provided. It concludes with homework assignments and prompts for creating a practice problem with mistakes.
Answer Key Period Exam
Here are the solutions to the exponent problems:
27) 32 = 9 (because 3 x 3 = 9)
28) (y + 3)2 = 25, when y = 2
(2 + 3)2 = (5)2 = 25
29) x2 + 8 = 12, when x = 2
(2)2 + 8 = 4 + 8 = 12
30) x3 = 64, when x = 4
43 = 64
So in summary:
27) 9
28) y = 2
29) x = 2
30) x = 4
Sim k-01
Dokumen tersebut merupakan materi perkuliahan Sistem Informasi Manajemen yang membahas konsep dasar SIM, termasuk sistem, informasi, dan manajemen. Dokumen ini juga menjelaskan karakteristik sistem, klasifikasi sistem, faktor-faktor informasi, dan pengaruh pengelolaan SIM dalam organisasi.
Tips menjawab pengajian am kertas 2
Dokumen memberikan panduan untuk menjawab soalan esei secara efektif dengan menekankan perlunya memahami soalan secara mendalam, mengenalpasti kata kunci, merangka jawapan, mengemukakan idea dengan menjelaskan isu secara objektif dari pelbagai pendekatan, menyokong idea dengan alasan kukuh, dan memberikan penjelasan yang jelas.
Gerbang logika dasar fi
Dokumen ini membahas tentang gerbang logika XOR (Exclusive OR). Gerbang XOR akan memberikan output 1 jika masukan-masukannya berbeda, yaitu salah satu masukan bernilai 1 tetapi tidak kedua-duanya. Dokumen ini juga menjelaskan tabel kebenaran, persamaan, dan penggunaan gerbang XOR untuk lebih dari dua masukan.
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This document provides methods for calculating the square of various types of numbers:
1) For numbers ending in 5, add 1 to the digit before 5 and multiply it by that digit. Then write 25 after it (e.g. 225 for 15x15).
2) For numbers with all the same digit, write the digits in ascending then descending order (e.g. 12321 for 111x111).
3) For two-digit numbers starting with 5, take the square of the first digit and second digit separately and concatenate them (e.g. 2704 for 52x52).
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This document introduces four mathematical identities:
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2) (x+y)(u+v) = xu + xv + yu + yv, which explains how to multiply the sum of two numbers by the sum of two other numbers
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It provides examples of applying each identity to demonstrate how to use algebra to simplify expressions.
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This document contains 3 identities related to multiplication and addition of numbers:
1) To multiply the sum of two numbers by a third number, we multiply each number in the sum separately and add the results, following the identity (x+y)z = xz + yz.
2) To multiply the sum of two numbers by the sum of two other numbers, we multiply each number in the first sum by each number in the second sum and add the results, as expressed by the identity (x+y)(u+v) = xu + xv + yu + yv.
3) The document presents the identities (x-y)2 = x2 - 2xy +
Quadratic equations 5
The document discusses solving a quadratic equation. It is given that the quadratic equation x^2 - 8x + 12 = 0 has roots p and q. Using the roots, it is determined that the quadratic equation x^2 + ax + b = 0 has roots of p^2 + q^2 and 2pq. The sum of the coefficients a and b is then calculated to be 896.
ℤₙ* The Multiplicative group for ℤₙ modulo n
This document discusses the multiplicative group Zn* modulo n. Zn* is the set of integers from 1 to n that are relatively prime to n, meaning they do not share any factors. It provides examples of Zn* for different values of n, such as Z9* = {1, 2, 4, 5, 7, 8} and Z97* containing all integers from 1 to 97 that are relatively prime to 97. The document also discusses cyclic groups and using a generator g to generate the elements of a cyclic group modulo n.
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This document discusses finding the maximum and minimum values of trigonometric functions and when they occur. It provides reminders of the max and min values of sin(x) and cos(x) and examples of finding the max and min of more complex trig functions including composite functions with added or subtracted constants or variables. The examples become increasingly complex, adding angles to the trig functions inside and outside parentheses. The key question asks the reader to find the max value and corresponding x-value of the function 2cos(x + π/4).
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The document provides examples of factorizing quadratic equations and completing the square to solve quadratic equations. It discusses:
1) Factoring quadratic expressions like x2 + 5x - 50, x2 + 3x, and 2x2 + 3x + 1.
2) Completing the square to solve equations like x2 + 5x + 4 = 0 and 2x2 - 14x + 12 = 0.
3) Using the quadratic formula to solve equations like x2 - 15x + 30 = 0, x2 + 8x - 20 = 0, and x2 + 3x = 0.
4) Setting the discriminant equal to 0 to find the value of p that makes the equation
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https://www.nicovideo.jp/watch/sm37233994
https://www.youtube.com/watch?v=d3Ze6tuA1Qc&t=301s
https://www.youtube.com/channel/UCEr2VZ6DI4gATRtVJw49ZFw
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Math is fun!
The document provides steps for finding the inverse of the function f(x) = 12x-4/x-7. It works through rearranging the equation by switching x and y values, distributing terms, and factoring to arrive at the inverse function f-1(x)=7x-4/(x-12). A second example shows how to find the maximum area of a playground given its perimeter of 18600 feet by setting up equations for perimeter and area and solving.
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The document provides examples of evaluating expressions involving integers. It begins with the expression -3 - 5 + (-4) - (-2). It then introduces a flow chart for adding and subtracting integers based on rules for using a number line. The flow chart shows that when adding, the value increases, and when subtracting, the value decreases. Several practice problems with solutions are provided. It concludes with homework assignments and prompts for creating a practice problem with mistakes.
Answer Key Period Exam
Here are the solutions to the exponent problems:
27) 32 = 9 (because 3 x 3 = 9)
28) (y + 3)2 = 25, when y = 2
(2 + 3)2 = (5)2 = 25
29) x2 + 8 = 12, when x = 2
(2)2 + 8 = 4 + 8 = 12
30) x3 = 64, when x = 4
43 = 64
So in summary:
27) 9
28) y = 2
29) x = 2
30) x = 4
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3. The key steps shown are factorizing, completing the square, setting the discriminant equal to zero, and using the quadratic formula to solve for the roots of the equations.
Jawaban matematika persamaan kuadrat
1. The document contains 4 word problems with algebraic solutions.
2. The first problem involves finding the unknown side length of a rectangular field given other dimensions. The second finds the volume of a block given its base area and heights.
3. The third problem involves setting up two equations relating the volume, radius, and height of two cones to solve for the radius.
4. The fourth problem involves finding the time taken by one printer given the total time for two printers.
Matematika kelompok
1. The document contains 4 word problems with algebraic solutions.
2. The first problem involves finding the unknown side length of a rectangular field given other dimensions. The second finds volumes using geometric formulas.
3. The third equalizes the volumes of two cones with different radii and heights.
4. The fourth determines the time one printer takes to print a book set given the total time for two printers.
Tugas 1
1. The document contains 4 math word problems. The first problem involves finding the width of a field given the total land area and required field area. The second finds the base area and dimensions of a prism. The third equates volumes before and after increasing a radius. The fourth finds the time to print a document using two printers.
2. The second problem involves finding the base area and dimensions of a prism given its total volume. It is solved by setting up and solving two equations for the base length and width in terms of the unknown dimension X.
3. The third problem equates the volumes of a cylinder before and after increasing its radius by 24. It sets up and solves the equation relating the
Fismat chapter 4
The document provides solutions to physics problems for chapter 4 of mathematics 2. It includes solutions for determining derivatives and differentials of various functions with respect to variables like x, y, r, and θ. The highest level of mathematics involved includes taking second order derivatives and solving simultaneous equations. Sample problems include determining derivatives of functions that define relationships between polar and Cartesian coordinates.
Presentation on calculus
This document provides information about an upcoming mathematics presentation including:
- A list of 12 group members presenting with their names and student IDs
- 16 topics that will be covered in the presentation ranging from distance between points and planes to surface integrals
- Sample problems and solutions for several topics like finding the distance between a point and plane, parallel planes, a point and line in space, and vector valued functions. Formulas and definitions are provided for concepts like velocity, acceleration, tangent vectors, arc length, and curvature.
ArithmeticProgression
1. The document contains examples of arithmetic progressions and their properties. It includes problems involving finding terms, common differences, and sums of APs.
2. One problem involves two APs where the ratio of the sum of the first n terms is 7n+1:4n+27. It is shown that the ratio of the 11th terms is 4:3.
3. Another problem proves that if an AP has (2n+1) terms, the ratio of the sum of odd terms to the sum of even terms is (n+1):n.
Tugas blog-matematika
The document provides exercises on calculating derivatives using various rules including the sum and difference rule, product rule, and quotient rule. It includes 15 problems calculating derivatives of given functions and finding numerical derivatives at given values. The answers provide the step-by-step work to arrive at the derivatives using the appropriate rules.
Quadratic equation by four different methods
1. The document provides examples of solving quadratic equations using different methods.
2. Various word problems involving quadratic equations are presented, such as finding unknown lengths, areas, and numbers that satisfy given conditions.
3. The examples are solved step-by-step showing the calculations and reasoning involved in arriving at the solutions.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and the dimensions of a tennis table.
Copia de derivadas tablas
This document defines derivatives of various trigonometric, hyperbolic, exponential, and logarithmic functions. It provides formulas for derivatives of sums, products, compositions, and inverse functions. Some key formulas include:
- The derivative of f(g(x)) is f'(g(x))g'(x)
- The derivative of sin(u) is cos(u)u'
- The derivative of cosh(u) is sinh(u)u'
- Trigonometric identities like sin^2(x) + cos^2(x) = 1
Maths 301 key_sem_1_2007_2008
The document contains the solutions to several calculus problems:
1) Finding the total amount spent in an economy where dollars recirculate at 90% each time.
2) Calculating the speed needed to shoot a basketball into a hoop from a given distance and height.
3) Taking derivatives and integrals to solve optimization problems.
Maieee04
The document provides instructions for a mathematics test that is 1 1/2 hours long and consists of 75 questions worth a total of 225 marks. For each correct answer, 3 marks are awarded, and for each wrong answer, 1 mark is deducted. It then lists 34 math problems as sample questions on topics including relations, functions, complex numbers, matrices, series, and calculus.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and dimensions of a tennis table.
Tugas 1 (xak2f)
This document contains 4 math word problems with their step-by-step solutions:
1) A word problem about finding the area of a rectangle given its length and width. The solution is that x = 10 or x = 80.
2) A word problem about finding the area of a triangle given its base, height, and one side length variable. The solution is that x = 15 or x = 30.
3) A word problem about setting two volume formulas equal to each other to solve for the radius of a sphere. The solution is that r = 3.
4) A multi-step word problem about calculating percentages. The final solution is 2.6.
Re：ゲーム理論入門 第14回 - 仁 -
The document describes an optimization problem to allocate resources among a set of items in a way that minimizes excess amounts above predefined valuations for different combinations of items. The problem is formulated as linear constraints with a variable M representing the maximum excess. Solutions are obtained by solving the linear program for different valuations scenarios. The optimal allocation balances minimizing M while satisfying all constraints.
Interpolation
This document discusses different interpolation methods:
- Interpolation finds values of a function between known x-values where the function values are given.
- Newton's forward and backward interpolation formulas are presented along with examples.
- Newton's divided difference interpolation uses a formula involving differences to find interpolating polynomials.
- Langrange's interpolation formula expresses the interpolating polynomial as a linear combination of basis polynomials defined in terms of the x-values. An example computing an interpolated value is shown.
3c. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.3)
Pedagogy of Mathematics (Part II) - Algebra, Algebra, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, Polynomials, Constants, variables, algebraic
Class 11 Cbse Maths Sample Paper 2012
This document provides a model test paper for mathematics with 3 sections - Section A having 1 mark questions, Section B having 4 mark questions, and Section C having 6 mark questions. The document provides instructions for the test, the questions under each section, and worked out solutions for some questions in Section A. It tests concepts in mathematics like sets, algebra, trigonometry, calculus, probability, etc. through multiple choice and long answer questions.
Similar to Klmpk matik (20)
Tugas matematika menemukan konsep persamaan kuadrat
Tugas matematika menemukan konsep persamaan kuadrat
3c. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.3)
3c. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.3)
Klmpk matik
- 1. MATEMATIKA PERSAMAAN KUADRAT NAMA KELOMPOK : A ( KLS X AK 1 ) 1. 2. 3. 4. 5. NI PUTU NIA ANDRIANI NI LUH PUTU EKA ANGGRENI NI PUTU AYU PURNAMA YANTI NI MADE HERLIANA KRISNANDA NI LUH GEDE TIA YUNIKA SARI ( 01 ) ( 04 ) ( 19 ) ( 26 ) ( 27 ) SMK N 1 TABANAN TH. PEL. 2013/2014
- 2. p 1. Diket : p = 60 m l = 30 m Lrencana = 1000 m Tanah kosong berukuran 60 m x 30 m l Dit : persamaan kuadrat…? Rumus : ( p – x )( l – x ) = Lrencana Jawab : ( p – x )( l – x ) ( 60 – x )(30 – x ) 1800 – 60x – 30x + x2 1800 – 90x + x2 1800 – 1000 – 90x + x2 800 – 90x + x2 800 – 80x – 10x + x2 80 ( 10 – x ) – x ( 10 – x ) ( 80 – x )(10 – x ) = Lrencana = 1000 = 1000 = 1000 =0 =0 =0 =0 =0 x = 80 atau x = 10 Diuji : Yang digunakan adalah x = 10 ( p – x )( l – x ) 60 – 10 . 30 – 10 50 . 20 2. Diket : ps ls t pa la = 50 cm = 40 cm =x =50 – 2x = 40 – 2x = Lrencana = 1000 = 1000 x ls x pp pa la ps
- 3. Dit : Persamaan kuadrat…? Volume tempat air/balok…? Keterangan : ps = panjang seng Rumus : pa . la = La ls Jawab : pa . la = lebar seng t V =p.l.t = tinggi pa = panjang alas = La la = lebar alas ( 50 – 2x ) ( 40 – 2x ) = 200 2000 – 100x – 80x + 4x2 = 200 2000 – 180x + 4x2 = 200 2000 – 200 – 180x + 4x2 =0 1800 – 180x + 4x2 =0 450 – 45x + x2 =0 450 – 30x – 15x + x2 =0 30 ( 15 – x ) – x ( 15 – x ) =0 ( 30 – x ) ( 15 – x ) =0 La = luas alas x = 30 atau x = 15 Diuji : Yang digunakan adalah x = 15 pa = 50 – 2x la = 40 – 2 x = 50 – 2 . 15 = 50 – 30 = 40 – 30 = 20 cm t = 40 – 2 . 15 = 10 cm =x = 15 cm V =p .l .t = 20 . 10 . 15 = 3000 cm3
- 4. 3. Diket : t = 3 cm Dit : jari-jari kerucut…? Rumus : V = V1 = V2 = Jawab t ( r + 242 ) 3 r2( 3 + 24 ) : V1 = ( r + 242 ) . 3 ( r + 242 ) . 3 3 ( r2+ 48r + 242 ) 3r2 + 3 . 48r + 3 . 24 .24 r2 + 48r + 24 . 24 0 0 0 0 r = 12 = V2 r2( 3 + 24 ) = r2 ( 3 + 24 ) = 27r2 = 27r2 = 9 r2 = 8 r2 - 48r - 24 . 24 = r2 - 6r - 24 . 3 = r2 - 6r - 72 = ( r – 12 ) ( r + 6 ) atau r = - 6 Jadi , jari – jari kerucut semula adalah 12 4. Diket : Dit : p1 = x jam P2 = x + 1 jam t1 + t2 = 1,2 jam t2 untuk mencetak 1 buku…? Keterangan : p1 : printer satu p2 : printer dua t1 : waktu printer satu t2 : waktu printer dua
- 5. Jawab : = 1,2 = 1,2 = 1,2 = 1,2 x2 + x = 1,2 ( 2x + 1 ) x2 + x = 2,4x + 1,2 x2 + x – 2,4x – 1,2 =0 x2 – 1,4x – 1,2 =0 10x2 – 14x – 12x =0 10x2 – 20x + 6x – 12x = 0 10x ( x – 2 ) + 6 ( x – 2 ) = 0 ( 10x + 6 )( x – 2 ) =0 10x + 6 = 0 x–2=0 10x = -6 x x = -6 : 10 x = - 0,6 Yang digunakan adalah x = 2 p1 = x jam = 2 jam =2
- 6. p2 = x jam + 1 jam = 2 jam + 1 jam = 3 jam Jadi , waktu yang diperlukan printer ke-dua untuk mencetak satu set buku adaah 3 jam.