Indices examples and solutions. Understanding Match Type Argument in MATCH Function.
31. Flip and change the power -2 to +2. This index includes 225 stocks listed on the Tokyo Stock Exchange and is considered a benchmark for the Japanese stock market. PI Formula = 1 + NPV / Initial Investment Required. = INDEX (E1:E10, MATCH (. So if we can write the two bases, 2 and 4, with the same base, the only difference in the two sides will be their powers. Indices - ExamSolutions %. Apr 6, 2020 · Another example of a price-weighted index is the Nikkei 225 in Japan. Textbook page references. A typical response is 4 = 2 2. 71−x = 43x+1 7 1 − x = 4 3 x + 1 Solution. Selina solutions for Mathematics Concise Mathematics Class 9 ICSE CISCE 7 (Indices (Exponents)) include all questions with answers and detailed explanations. or indicial or subscript or suffix notation. Join this channel to get access to perks:→ htt Worked Examples 7. The unit vectors are called base vectors when used for. Determine the intercepts of the plane intersecting the xyz coordinate. TeeJay Maths Book Indices GCSE Maths revision worked exam questions (include fractional and negative powers) Solving equations in which the power is to be found. For example, for 3 2, 2 is the index and 3 is the base. The index only applies to the variable b and not the coefficient 3. Next, ask the class if there is a way to write 2 and 4 with the same base. Selina Solutions for Class 9 Maths Chapter 7- Indices [Exponents] The Chapter 7 of class 9 takes the students to a new topic Indices[exponents]. This tutorial will show you how this is done Nov 16, 2022 · 23x = 10 2 3 x = 10 Solution. pdf. This coordinate system can indicate directions or planes, and are often written as (hkl). 564 nm. 32. The relationship between P p and P pk is similar to that between C p and C pk. In this course, we are going to learn through worked out examples. Show Video Lesson. Finding rate of change. = 1/a1, l = 1/a2, and m = 1/a3. A-Level Maths Edexcel C1 June 2009 Q9b. The exponent of a number says how many times to use the number in a multiplication. × ×. Download Chapter-wise NCERT Solutions for Class 12 Chemistry. Our consistent goal has been to present the chapters, examples, and questions in a clear and engaging way so that students will be motivated to “learn” and “understand” math. In reality, the two questions have answers, which are complex numbers. Class 9 Chapter 8 Indices ML Aggarwal Solutions for ICSE is one of the most important chapter for the board exams which is based on simplyfying equations and finding values. Jan 22, 2020 · Solution of Ch-Test Questions on Indices of ML Aggarwal for ICSE Class 9 Mathematics Ch-8. For example, if , then , where index 4 becomes the logarithms and 2 as the base. For example, is it much easier to write 3 5 than 3 × 3 × 3 × 3 × 3. For example, 1 0 = 1, 7 0 = 1. For example: in 5 3, 5 is the "base" and 3 is the "index". Hence compute the value of 3x. For instance, in the expression 3 5, 5 is the index, indicating that 3 is multiplied by itself five times. Given below is the representation of the index of a number. On completion of this TLP you should: Understand the concept of a lattice plane; Be able to determine the Miller indices of a plane from its intercepts with the edges of the unit cell; Be able to visualise and draw a plane when given its Miller indices; Be aware of how knowledge of lattice planes and their Miller indices Jul 31, 2023 · What does Index mean in Mathematics? In the realm of mathematics, an index is a figure that signifies the number of times a particular number is multiplied by itself. 1. e. The base is 3, so rearrange both sides as powers of 3. where a and n are non zero constants. The page below will explain why. Similar to the DJIA, the Nikkei 225 is calculated by adding up the prices of all 225 stocks and dividing the total by a divisor. (b) 24 × (1 8) − 1 × 40. The CPI might overstate changes in the cost of living because it doesn't always account for how people 4 3 is the index form (or power form) of 64; 4 × 4 × 4 is the expanded form of 64; For 64 = 4 × 4 × 4 = 4 3, the base number 4 appears three times as a factor of the basic numeral (or number) 64; 4 3 is read as '4 to the power 3' or simply '4 cubed' Example 2. Indices Examples | Questions on Laws of Indices. This is a very basic intro to ensure fraction work is fully fluent and moves on with some algebraic fractions. We use the index form usually with 10 as the base for every large numbers or very small numbers e. The notes and questions for Surds & Indices - Introduction and Examples (with Solutions) have been prepared according to the Banking Exams exam syllabus. Example: 2 3 ×2 4 = 2 3+4 = 2 7 =128. Geometric Progression; Binomial Theorem & Pascal's Triangle The ML Aggarwal Solutions Class 11 Maths has been made to be user-friendly in an effort to lessen student stress and give the ML Aggarwal Solutions a clean appearance. The above example will give us, ( from this value, 4 will cut the fourth root) Or we can solve the above simply making have the same power with the given root (which in this case is 4). Thus, if the index of any number is negative, then the value Indices Question 4 with Fully Worked Answer. Sequences & Series. Multiplying and dividing indices, raising indices to a power and using standard form are Mar 22, 2024 · Figure 22. Practise. Show Step-by-step Solutions. 4 4 4 = 43. Maths : Indices : Multiplication Rule In this tutorial you are shown the multiplication rule for indices. e7+2x−3 =0 e 7 + 2 x − 3 = 0 Solution. Indices - Simplifying Negative Powers. = a 5. Try the free Mathway calculator and problem solver below to practice various math topics. Surds and Indices. 64 Angstroms = 0. Example 1: Find the numerical value for each of the following (not containing exponents): (i) 8 0 (ii)5-10 (iii)27 2/3. Example 3: Two Way Lookup. Lessons ( 99 ) SHARE. the bases of these two numbers are equal. Solution: Indices. Simplify \(p^3 \div p^{6}\) Solution. x m × x n = x m+n The word "index" means "power". It helps students understand uniform and non-uniform motion. this purpose. Some of them are broad based indices, which attempt to replicate a market, and some are more specialised ones, which attempt to capture an individual segment of the market. In this example: 82 = 8 × 8 = 64. Combine it with the MATCH function. arr[i] = iX, where X is a non negative number. Jul 8, 2024 · Binomial Surd: when two surds give rise to one single surd, the resultant surd is known as binomial surds. Some of the most common are: Air (gas on gas). Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target. Here we need to note, If the powers are odd numbers then the bases will Example: Hyperlipidemia and Leukocytosis. Mar 20, 2021 · Solutions of the second chapter has been provided in detail. √20 = 22 ∗ 5. Let’s Combine Them to Create a Powerhouse (INDEX + MATCH) Example 1: A simple Lookup Using INDEX MATCH Combo. mc-TY-indicespowers-2009-1. Apr 15, 2024 · By using the NPV method, we would now calculate profitability index (PI) –. In this case the numerator is 1 so the answer stays the same. NCERT Solutions for Class 12 Chemistry are drafted by the faculty at BYJU’S to help students learn all the complex concepts efficiently. Definitions. This is the first law of Any number with an exponent of 0 is 1. Here you will find video tutorials on powers and indices. Examples of solutions in everyday life. But, remember that 0 0 ≠ 1. Write 1/27 in the index forms. In general, , we call them as common logarithms (base 10). Solutions. For example: a 3 is a number with an index of 3 and base ‘a’. a = 7 , n = 2. If (p + q)-1 (p-1 + q-1) = paqb, prove that a + b + 2 = 0, where p and q are different positive primes. Links to other subjects. We have, Indices - ExamSolutions %. Aug 14, 2021 · This will help us to solve the problems of indices. The [log] where you can find from calculator is the common NCERT Class 9 Science Chapter 8 explains the concept of motion, and types of motion with relevant examples for a clear understanding of the concept. All of the other index laws are based on the simple facts above. Leaving Certificate Points. So. Apr 21, 2021 · Profitability Index Calculation Example #1 Let’s stick with the same Projects A and B that we saw earlier in this article, with the NPV of £10,000 for Project A, and £100,000 for Project B. Simplify and leave your answer in index form. The first argument is the reference against which it will find the lookup value. 1 22. Dec 18, 2023 · Here are the main laws of indices with examples: Product Law: a m × a n = a m+n. Introduction. Rule 1: = √rxs = √r x √s. The reciprocals of 1 and ∞ are 1 and 0 respectively, thus yielding. The calculation is done by separating the formula into two halves. PI = 1 + 1277. 3m 11s. The index represents the number of times a number has to be multiplied by itself. Example : If d³ = 5³ then as powers are equal , d = 5. ML Aggarwal Solutions for Class 9 Maths Chapter 8 Indices is designed by individual subject experts at BYJU’S, to help students solve the exercise problems of the chapter. Show step. Laws of Indices and Indices problems examples. Notice how the index only affects the variable b. Because of the redundancy, and to be consistent with other crystal systems, many crystallographers today use only three indices for hexagonal minerals. Indices or Powers. From the above computation, we can come to the conclusion that ABC Company should invest in the project as PI is more than 1. Example 1: The process capability index of P p and P pk are sometimes referred to as long-term capability or performance indices. Example 1: Determine if $$5^4\times 5^3$$ has a positive, negative or zero index. Once index notation is introduced the index laws arise naturally when simplifying numerical and algebraic expressions. Rewrite 8√x6y2 as a reduced radical with root 4. It is called as “a to the power of 3”. Here, you have to apply the basic division law. ( hkl) – for single plane and {hkl} for a group of planes. 5. Autoagglutination → ↓ RBC and Hct → It primarily affects the RBC and Hct (falsely decrease). The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Find the value of a and the value of n . Example: (2 3) 4 = 2 12 . Miller Indices: (100) So the surface/plane illustrated is the (100) plane of the cubic crystal. Evaluate the following indicial expressions, giving the final answers as exact simplified fractions. Let us solve some examples here: Example 1: Selina Concise Mathematics - Part I Solutions for Class 9 Maths ICSE Chapter 7: Get free access to Indices (Exponents) Class 9 Solutions which includes all the exercises with solved solutions. This video teaches you How to solve Indices and properties of indices. Example: Input: arr = [1, 1, 4, 17]Output: 2Explanation: The element 1 at index 0, is a power of 0The element Aug 21, 2023 · Worked Examples. Simplify. 4) The following diagram shows how to divide exponents by subtracting indices. 1 day ago · Given an array arr[] with N non-negative integers, find the maximum number of elements that are the same non-negative powers of their indices. Simplify the following (i) 6 4a ÷ 6 a (ii) 4 3 ÷ 4 (iii) 5 3 – 5 2. Consider: a 2 × a 3 = (a × a) × (a × a × a) = a 2 + 3. Negative Indices 6. 8√x6y2 Rewrite the root 8 as a rational exponent (x6y2)1 8 Multiply exponents x6 8y2 8 Reduce each exponent fraction x3 4y1 4 All exponents have denominator 4, rewrite in The following diagrams show the rules of indices or laws of indices. How to simplify negative powers? Indices - Fractional Powers. So, suppose we have We write this as ‘4 to the power 3’: 4 4 4 × × 43. Here are the solutions: Figure 22. 9 = 104+6x 9 = 10 4 + 6 x Solution. Example: Simplifying √20. 3. Checking if a function is increasing or decreasing in an interval. find roots using indices. So, a 0 = 1, for a ≠ 0. 5-z. Some common examples of Miller Indices on a cube include [111], the body diagonal; [110], the face diagonal; and (100), the face plane. Sep 2, 2019 · Previous: Distance Time Graphs Practice Questions Next: Negative Indices Practice Questions GCSE Revision Cards Indices - The basics (Laws) Indices - Examples. An index in the form of a fraction can be represented as the radical 3 days ago · The index of a number can also be zero or negative. A-Level Maths Edexcel C1 June 2009 Q9a. The index P p represents the allowable tolerance spread relative to the actual spread of the data when the data follow a normal distribution. University of New South Wales. Here, 4 is the greatest perfect square factor of 20. 5z = 2160, find the value of x, y, z. Here is a set of practice problems to accompany the Solving Exponential Equations section of the Exponential and Logarithm Functions chapter Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths learn how to simplify negative indices and fractional indices. \[a^{n}\] = \[a \ast a \ast a \ast a\cdot \cdot \cdot \cdot\] (n times) Here, Examples, solutions and videos to help GCSE Maths students learn about the multiplication and division rules of indices. Question 1: If 2x. Solution: Let us first do the general case: what is the greatest term in the expansion of \({(1 + x)^n}\) , where n is an arbitrary rational number. Calculating Consumer Price Indices in Practice. PI = 1 + 0. Apr 9, 2024 · The profitability index would not work if funds are also insufficient beyond the period of initial investment. Get NCERT solutions for Class 12 Maths free with videos. Sep 2, 2021 · Example 1: Simplify. In order to master the techniques explained here it is . 63 / 5000. Feb 22, 2022 · The Miller Indices are also enclosed within standard brackets (…. 10 8 instead of Question 15 (***) The points ( 2,14 ) and ( 6,126 ) lie on the curve with equation. = INDEX (E1:E10. 2. Nov 26, 2020 · Learning Objectives. This In the section we will be looking at indices or powers. Statistics. To solve this, you must recall: X 1 = X (any number raised to the power of one is that same number) Therefore 4 = 4 1. So . It is a solution formed by gases, among which nitrogen and oxygen stand out, which are present in the atmosphere. Mathematics Solutions Solutions for Class 8 Math Chapter 3 Indices And Cube Root are provided here with simple step-by-step explanations. Try it yourself: For example: `2^3 xx 2^4` `= (2xx2xx2) xx (2xx2xx2xx2) = 2^7` which is the same as adding the indices. These numbers are governed by several indices rules that we will discuss here. HOW TO FIND MILLER INDICES. 6 4a ÷ 6 a. • Negative index rule: a − n = 1 a n. Suppose, we have a value √3 3. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. This law states that when you multiply two terms with the same base, you add the exponents. If we calculated the profitability index using the NPV / I approach, then you take the £10,000 NPV for A and divide it by the initial investment in A Math Worksheets. The law for multiplying is `2^m xx 2^n = 2^((m+n))` There is a similar law for dividing: `4^5 ÷ 4^3` `= frac(4xx4xx4xx4xx4)(4xx4xx4)` `= 4 xx4 = 4^2` and in this case the same answer is obtained by subtracting the indices. Leaving Cert Exam solutions; Fermat's Last Theorem. Use the denominator to find the root of the number or letter. What was the inflation rate between 2016 and 2017? MATCH Function: Finds the Position baed on a Lookup Value. It involves using the rules of indices. Solutions of all exercise questions, examples, miscellaneous exercise, supplementary exercise are given in an easy to understand wayThe chapters and the topics in them areChapter 1 Relation and Functions– Types of Relation - Reflexive, Symmetr. 1)View SolutionHelpful TutorialsRational (fractional) indicesSummary of indices 2)View SolutionHelpful TutorialsRational […] 8. If m is a positive integer, then axaxaxa—- upto m terms, is written as a m ; where ‘a’ is called the base and m is called the power (or exponent or index). For further details on complex numbers, kindly refer to ‘Complex Numbers Explained with Worked Examples’ by Shefiu S. If then . The Consumer Price Index (CPI) is a measure of the average change in prices of a typical basket of goods and services over time. Reduce the result to the smallest integer. You are viewing an excerpt of this Topic. When dividing numbers in exponent notation with the same base, we subtract the exponents. Quotient Law: a m / a n =a m−n. GCSE Maths made easy Algeba covering Foundation and Higher level. Question 2: Oct 25, 2021 · The list of important index laws is given here in the shareable image format, kindly make use of it for quick reference before exams and memorize the laws frequently. 6 4a ÷ 6 a = 6 4a – a = 6 3a. Checking if a function is increasing or decreasing in whole domain. This will clear students' doubts about questions and improve their application Click on a Chapter below to begin. After studying this section, you will be able to: divide and multiply algebraic expressions using indices. Often, more than one rule has to be used when simplifying expressions with indices. Subscribe Now to get Full Access to ALL this Subject's Topics and Quizzes for this Term! Click on the button "Subscribe Now" below for Full Access! Dec 12, 2018 · Explanation of Miller indices problems #solidstate #Rqphysics Miller Indices - Illinois Institute of Technology We learned Derivatives in the last chapter, in Chapter 5 Class 12. For further discussion of Miller indices with examples, watch the videos linked here: Video 11-5: Miller indices example (2 minutes) Video 11-6: Miller indices of 0 (5 minutes) Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths to help students learn the multiplication rule, division rule and power rule of indices. These solutions for Indices And Cube Root are extremely popular among class 8 students for Math Indices And Cube Root Solutions come handy for quickly completing your homework and preparing for exams. Surds are the root values that cannot be written as whole numbers. 2: The three blue columns show the steps to calculate D for Lake A, while the three gray columns show the steps to calculate D for Lake B. 5 3 = 5 \(\times\) 5 \(\times\) 5. Indices provide a compact algebraic notation for repeated multiplication. Aug 11, 2023 · An index is a tool used to track the performance of a group of financial assets. Jun 1, 2022 · To solve the equation, we need to remember that the equal sign means the two sides of the equation are equal. g. Scroll down the page for more examples and solutions for dividing exponents. Examples. 8. Also, read: Index Document Description: Surds & Indices - Introduction and Examples (with Solutions) for Banking Exams 2024 is part of Quantitative Aptitude for Competitive Examinations preparation. PI = 1. Example question calculating CPI and inflation. Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths. Fraction Indices 7. This and others are 26) Without using a calculator simplify (√ ) freely available online. View Solution. Other Examples. Geometric Progression; Binomial Theorem & Pascal's Triangle Enter the formula as: = INDEX (. Consider: This is the second law of exponents: Simplify the following expressions, giving your answers Aug 11, 2023 · An index is a tool used to track the performance of a group of financial assets. MATH 2901. Get access to thousands of educational resources. Example 1: fractional Indices where the numerator is 1. This value can be written as: √3 3 = (3 3) ½ = 3 3/2 Where 3/2 is the index. Example 3: with a coefficient in front of base. You can return the answer in any order. Enter the reference containing the lookup value to be returned. The Consumer Price Index (CPI) The country of Ambrosia calculates inflation using a consumer price index (CPI). Keep track of what you've done and what you still need to cover for free! Create an Account. Solutions are mixtures that are present in several areas, both in nature and in the home and in industries. 1 The purpose of this chapter is to provide a general description of the ways in which consumer price indices (CPIs) are calculated in practice. Take the reciprocals of the intercepts. You are given a short test at the end. This will help the students in understanding the chapter more clearly. This video shows a guide to indices and powers. Scroll down the page for more examples and solutions on how to use the rules of indices. Some concepts appear at the lower end of GCSE higher papers and should only serve as a brief recap. Example 2: Simplify. Indices show repeated multiplication, eg. 1/27 = 1/3 x 1/3 x 1/3 = (1/3) 3 this is an index form for the number 1/27 which can also be written as 27-1. Find the atomic density (atoms/cm3) and the spacing between nearest-‐neighbor atoms in Ge. Either name can be used, and both names mean the same thing. Thus the simplificiation 2 5 × 2 3 = 2 8 quickly leads Nov 24, 2022 · Triclinic. This section covers Indices and the uses of Indices in algebra. The task is to return the maximum frequency of X. (7. We know that, √20 = 2*2*5. 1) Ge has the same crystal structure (diamond) as Si, with a lattice constant of a = 5. Write each of the following expanded forms in index form: Solution: Example 3 Laws of Exponents. If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable. 26. It explains the causes of phenomena like sunrise, sunset, and changing of the seasons. Now, we need to add the arguments of the MATCH function. need to multiply both indices together and raise it to the same base (a m) n = a mn. Solution. e4−7x+11 = 20 e 4 − 7 x + 11 = 20 Solution. Indices are the power or exponent of a value. The methods used in different countries are not exactly the same, but they have much in common. 2 Raise the answer to the power of the numerator. It decides how consistent we are to our average performance. Recall the formula for MCH and MCHC – the RBC and Hct are the denominator; so, they are inversely proportional to MCH and MCHC respectively. Laws of Indices. Example 1: Example 2: Example 3: Logarithms. The (110) surface Nov 17, 2016 · Indices can be integral or fractional, positive or negative. Example. Example – 12. Six Rules of Surds. Each and every question from the NCERT Textbook is answered in a systematic format to help students learn in a shorter duration. In this Chapter we will learn the applications of those derivatives. This law states that when you divide two terms with the same base, you subtract the exponents. 4 3 ÷ 4. 3 are scalars, called the Cartesian components or coordinates of a. 1) x m × x n = a m+n. Nov 14, 2021 · Example 10. Laws of indices Simplify 1) (5p 2 × 4p 3 × 5p 5) 3 2) MATH2901 2018 Midsession Exam with solutions. The plural of "index" is "indices". From the above, Hence, for roots, we divide the indices, while for powers we multiply the indices. Process Capability Index shows how closely a process is able to produce the output to its overall specifications. a1 – x direction, a2 – y direction, and a3 – z direction. Solve for x in: 9x + 32x - 1 = 53. Example 2: Lookup to the Left. . Miller Indices are a 3-dimensional coordinate system for crystals, based on the unit cell. along the given three directions. How we work with fractional indices. (Consider d,h, n denote numbers ) 1 ) If there are two numbers with exponential values and these two powers are equal then both. Indices are designed to represent, or track, a particular industry or market. y = n ax , x ∈. 2. Maths : Indices - Introduction Indices or powers are used to write statements involving repeated multiplication in shorthand. A collection of videos, activities and worksheets that are suitable for A Level Maths. Mar 22, 2023 · column_num - is the column number from which to return a value. If column_num is omitted, row_num is required. 2) (x m) n = x mn. 3) (xy) n = x n y n. Worked solution to the above core 1 question on indices and differentiation. Answers are in video format. Laws of indices, examples and solutions. Form 2 Questions and Answers on Indices and logarithms. For example, the formula =INDEX(A1:D6, 4, 3) returns the value at the intersection of the 4 th row and 3 rd column in range A1:D6, which is the value in cell C4. 4) where a 1, a 2 and a. A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. 2 22. Very basic rules of indices in this video. 1: Evaluate the following: (a) 5x − 2y × 2x − 5y2. Between 2016 and 2017 the CPI increased from 200 to 220 . 3y. Zakariyah. Members can access additional questions on this topic, including exam style Sep 24, 2021 · Worked examples of algebraic indices. Indices Fractional Indices: Law of Indices: How to simplify algebraic expressions. Test your knowledge by diving into some example questions. SOLUTIONS: ECE 305 Homework 1: Week 1. The number 3 is called the power or index. • Zero index rule: a 0 = 1. Exponents are also called Powers or Indices. 3. Quick Tips and Tricks. 2-y. For example, the solution to (c) are and , i. Find the magnitude of the greatest term in the expansion of \({\left( {1 - 5y} \right)^{ - 2/7}}\) for \(y = \begin{align}\frac{1}{8}\end{align}\) . 9 x + 3 2 x − 1 = 53. You may assume that each input would have exactly one solution, and you may not use the same element twice. For example, we can see that the project 3 in above example has a negative cash flow of $10,000 on date 1 (C 1). In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Thus, if the index of any non-zero number is 0, then the value will be 1. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Mark Lundstrom Purdue University. The topics in the chapter include. We can rewrite the radical in its rational exponent form, then reduce each exponent fraction. Simplifying expressions using the laws of indices Simplifying indices Indices show where a number has been multiplied by itself, eg squared or cubed, or to show roots of numbers, eg square root. ) when one is specifying a unique surface such as that being considered here. Note 0 0 is meaningless. We've selected the essential questions on Laws of Indices so you can identify difficulties and work on them. Basically, they are a shorthand way of writing multiplications of the same number. Math. Smoke (solid in gas). Put the term over 1. Introduction To Exponents (Indices) Examples of positive exponents and zero exponent. 1. If , find x and y, where a, b are different positive primes. When multiplying numbers in exponent notation with the same base, we can add the exponents. If another significant cash outflow occurs elsewhere in the company at date 1, the project 3 may have to be rejected. Solving equations where the power is to be found by expressing each term in the same base. Understanding Match Type Argument in MATCH Function. 1) The laws of indices and surds are to be remembered to solve problems on surds and indices. It is used to gauge inflation and changes in the cost of living. It is a Indices Question 1 with Fully Worked Answer. or absolute or invariant or direct or vector notation. 1: Though both Lakes A and B have the same amount of birds and the same number of different species, their diversity is different. iv sv av kh uv hp ty gj up po
