11 x1 t14 03 arithmetic & geometric means (2013)
•
2 likes•5,375 views
The document discusses arithmetic mean and geometric mean. It provides the formulas for calculating arithmetic mean and geometric mean. It then works through an example of finding the arithmetic mean and geometric mean of the numbers 25, 4, and 10. The arithmetic mean is calculated as 29/3 = 9.667 and the geometric mean is calculated as 10 * sqrt(25 * 4) = 10 * 5 = 50.
Report
Share
Report
Share
Download to read offline
Recommended
Glioma markers in neurosurgery
The document discusses various molecular markers for gliomas, including IDH1/2 mutations, MGMT promoter methylation, 1p/19q co-deletion, EGFR amplification, and other markers. It summarizes that the 2016 WHO classification of brain tumors now incorporates molecular parameters in addition to histology. Only IDH mutation status, MGMT methylation status, and 1p/19q co-deletion are routinely used clinically for prognostication and prediction of glioma patient outcomes and treatment responses.
Monitoring of Minimal Residual Disease Principles and Applications
This document discusses methods for monitoring minimal residual disease (MRD) in acute myeloid leukemia (AML) patients, including polymerase chain reaction (PCR) to detect leukemic fusion genes or mutations, and multiparameter flow cytometry (FCM) to identify aberrant myeloid precursors. MRD detection can provide prognostic information, help evaluate treatment effectiveness, guide risk-adjusted therapy, and predict relapse. Both methods have advantages and limitations, and more standardization is needed. MRD remains a promising tool to improve AML patient outcomes by guiding personalized therapy.
Tailoring Therapy for Follicular Lymphoma Based on the Latest Evidence
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This live or zoom broadcasted hematology/oncology fellowship program will bring an expert faculty member to your institution to discuss the latest developments and expert perspectives in the treatment of follicular lymphoma.
Molecular BIOLOGY OF RENAL CELL CARCINOMA BY DR.PRASHANT KUMBHAJ
Renal cell carcinoma is not a single disease but has several histologic subtypes. Studies over the past two decades have identified five inherited renal cancer syndromes caused by mutations in specific genes. These include von Hippel-Lindau syndrome, hereditary papillary renal carcinoma, Birt-Hogg-Dubé syndrome, tuberous sclerosis, and mutations in tricarboxylic acid cycle enzyme genes. Identification of the mutated genes in familial forms of renal cell carcinoma has provided insights into renal carcinogenesis and helped guide clinical management.
NEOPLASIA MCQs & USMLE Style case based study by Dr. ROOPAM JAIN
This document contains 16 multiple choice questions about neoplasia and cancer. The questions cover topics like immune system response to cancer cells, common diagnoses for lumps or masses found in different body areas, identifying the most likely diagnosis for biopsy results, genetic mutations that can cause cancer susceptibility, mechanisms of chemotherapy drug action and side effects, distinguishing between benign and pre-cancerous polyps, identifying the likely viral cause of symptoms, identifying the most common molecular abnormality seen in a case, identifying the most likely mechanism causing cancer in children, identifying the gene mutation mechanism causing a cancer, and characteristics of an aggressive neck mass cancer.
Adjuvant treatment in low grade glioma
This document discusses the treatment of low-grade gliomas. It notes that maximal surgical resection is generally recommended when feasible and associated with more favorable outcomes. For pilocytic astrocytomas, no adjuvant therapy is necessary after complete resection. Postoperative radiotherapy may be considered for incompletely resected or higher risk nonpilocytic gliomas. Recent trials found no survival advantage from higher radiation doses compared to 45-54 Gy or from early radiotherapy versus delayed radiotherapy. Temozolomide is being tested in clinical trials for nonpilocytic gliomas.
Conformational_Analysis.pptx
Conformational analysis, molecular modelling technique, b.pharm 8th semester, unit 5, computer aided drug design
Enhancing MRD Testing in Hematologic Malignancies: When Negativity is a Posit...
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This expert CME-approved slide deck, presented by Noopur Raje, MD, Director of the Center for Multiple Myeloma at Massachusetts General Cancer Center, will explore the current and emerging roles of MRD testing in hematologic malignancies. She presents the ongoing questions and latest data regarding the clinical utility of MRD testing in prognosis and treatment.
STATEMENT OF NEED
Measurable residual disease (MRD) is defined as the persistence of cancer cells at levels below morphologic detection after treatment. For patients with hematologic malignancies, MRD testing is increasingly being used to predict disease progression, monitor disease status, and evaluate treatment options (Dekker et al, 2023). Questions about current and future roles of MRD testing abound, including validation of assays, such as next-generation sequencing, machine learning, and flow cytometry; standardization of collection methods and modalities; considerations for clinical trial design and statistical analyses; and improved understanding of the roles of MRD status and depth of response across hematologic malignancies (Dekker et al, 2023; Baines et al, 2023). It is critical for members of the multidisciplinary cancer care team to stay up-to-date on the latest data regarding the clinical utility of MRD testing in prognosis and treatment. In this CME-approved activity, Noopur Raje, MD, Director of the Center for Multiple Myeloma at Massachusetts General Cancer Center, will explore the current and emerging roles of MRD testing in hematologic malignancies.
TARGET AUDIENCE
Medical oncologists, hematologists, pathologists, and other health care professionals involved in the treatment of patients with hematologic malignancies.
LEARNING OBJECTIVES
Upon completion of this activity, participants should be able to:
Distinguish the advantages and limitations of current MRD detection methods
Evaluate consensus recommendations on indications for MRD testing in hematologic malignancies
Explain the current and potential roles of MRD status and depth of response as a biomarker in clinical trials
Describe mechanisms of drug resistance/loss of response to BCMA-directed therapies
Assess the clinical utility of MRD in prognosis and treatment of selected hematologic malignancies, including acute lymphoblastic leukemia, chronic lymphocytic leukemia, and multiple myeloma
Recommended
Glioma markers in neurosurgery
The document discusses various molecular markers for gliomas, including IDH1/2 mutations, MGMT promoter methylation, 1p/19q co-deletion, EGFR amplification, and other markers. It summarizes that the 2016 WHO classification of brain tumors now incorporates molecular parameters in addition to histology. Only IDH mutation status, MGMT methylation status, and 1p/19q co-deletion are routinely used clinically for prognostication and prediction of glioma patient outcomes and treatment responses.
Monitoring of Minimal Residual Disease Principles and Applications
This document discusses methods for monitoring minimal residual disease (MRD) in acute myeloid leukemia (AML) patients, including polymerase chain reaction (PCR) to detect leukemic fusion genes or mutations, and multiparameter flow cytometry (FCM) to identify aberrant myeloid precursors. MRD detection can provide prognostic information, help evaluate treatment effectiveness, guide risk-adjusted therapy, and predict relapse. Both methods have advantages and limitations, and more standardization is needed. MRD remains a promising tool to improve AML patient outcomes by guiding personalized therapy.
Tailoring Therapy for Follicular Lymphoma Based on the Latest Evidence
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This live or zoom broadcasted hematology/oncology fellowship program will bring an expert faculty member to your institution to discuss the latest developments and expert perspectives in the treatment of follicular lymphoma.
Molecular BIOLOGY OF RENAL CELL CARCINOMA BY DR.PRASHANT KUMBHAJ
Renal cell carcinoma is not a single disease but has several histologic subtypes. Studies over the past two decades have identified five inherited renal cancer syndromes caused by mutations in specific genes. These include von Hippel-Lindau syndrome, hereditary papillary renal carcinoma, Birt-Hogg-Dubé syndrome, tuberous sclerosis, and mutations in tricarboxylic acid cycle enzyme genes. Identification of the mutated genes in familial forms of renal cell carcinoma has provided insights into renal carcinogenesis and helped guide clinical management.
NEOPLASIA MCQs & USMLE Style case based study by Dr. ROOPAM JAIN
This document contains 16 multiple choice questions about neoplasia and cancer. The questions cover topics like immune system response to cancer cells, common diagnoses for lumps or masses found in different body areas, identifying the most likely diagnosis for biopsy results, genetic mutations that can cause cancer susceptibility, mechanisms of chemotherapy drug action and side effects, distinguishing between benign and pre-cancerous polyps, identifying the likely viral cause of symptoms, identifying the most common molecular abnormality seen in a case, identifying the most likely mechanism causing cancer in children, identifying the gene mutation mechanism causing a cancer, and characteristics of an aggressive neck mass cancer.
Adjuvant treatment in low grade glioma
This document discusses the treatment of low-grade gliomas. It notes that maximal surgical resection is generally recommended when feasible and associated with more favorable outcomes. For pilocytic astrocytomas, no adjuvant therapy is necessary after complete resection. Postoperative radiotherapy may be considered for incompletely resected or higher risk nonpilocytic gliomas. Recent trials found no survival advantage from higher radiation doses compared to 45-54 Gy or from early radiotherapy versus delayed radiotherapy. Temozolomide is being tested in clinical trials for nonpilocytic gliomas.
Conformational_Analysis.pptx
Conformational analysis, molecular modelling technique, b.pharm 8th semester, unit 5, computer aided drug design
Enhancing MRD Testing in Hematologic Malignancies: When Negativity is a Posit...
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This expert CME-approved slide deck, presented by Noopur Raje, MD, Director of the Center for Multiple Myeloma at Massachusetts General Cancer Center, will explore the current and emerging roles of MRD testing in hematologic malignancies. She presents the ongoing questions and latest data regarding the clinical utility of MRD testing in prognosis and treatment.
STATEMENT OF NEED
Measurable residual disease (MRD) is defined as the persistence of cancer cells at levels below morphologic detection after treatment. For patients with hematologic malignancies, MRD testing is increasingly being used to predict disease progression, monitor disease status, and evaluate treatment options (Dekker et al, 2023). Questions about current and future roles of MRD testing abound, including validation of assays, such as next-generation sequencing, machine learning, and flow cytometry; standardization of collection methods and modalities; considerations for clinical trial design and statistical analyses; and improved understanding of the roles of MRD status and depth of response across hematologic malignancies (Dekker et al, 2023; Baines et al, 2023). It is critical for members of the multidisciplinary cancer care team to stay up-to-date on the latest data regarding the clinical utility of MRD testing in prognosis and treatment. In this CME-approved activity, Noopur Raje, MD, Director of the Center for Multiple Myeloma at Massachusetts General Cancer Center, will explore the current and emerging roles of MRD testing in hematologic malignancies.
TARGET AUDIENCE
Medical oncologists, hematologists, pathologists, and other health care professionals involved in the treatment of patients with hematologic malignancies.
LEARNING OBJECTIVES
Upon completion of this activity, participants should be able to:
Distinguish the advantages and limitations of current MRD detection methods
Evaluate consensus recommendations on indications for MRD testing in hematologic malignancies
Explain the current and potential roles of MRD status and depth of response as a biomarker in clinical trials
Describe mechanisms of drug resistance/loss of response to BCMA-directed therapies
Assess the clinical utility of MRD in prognosis and treatment of selected hematologic malignancies, including acute lymphoblastic leukemia, chronic lymphocytic leukemia, and multiple myeloma
11X1 T10 03 arithmetic & geometric means
This document discusses arithmetic and geometric means. It introduces the arithmetic mean, which is also known as the average, and the geometric mean. It provides examples of calculating the arithmetic and geometric means for various data sets and numbers. The document concludes with exercises involving computing means for different values.
Math (geometric mean)
The document defines geometric sequences as patterns of numbers where each term is determined by multiplying the previous term by a common factor. It provides examples of geometric sequences and explains how to find the geometric mean between two terms of a geometric sequence by setting up a proportion. The geometric mean of two numbers a and b is the number x such that a/x = x/b. It also relates the geometric mean to proportions in a geometric figure with three lengths, where each mean length is the geometric mean of the other two lengths in that proportion.
Geometric Mean
The geometric mean is a type of average that indicates the central tendency of a set of numbers using their product, as opposed to the arithmetic mean which uses their sum, and it is calculated by taking the nth root of the product of the numbers. The geometric mean is more appropriate than the arithmetic mean for describing proportional growth and ratios, and it has various applications in fields like optics, signal processing, geometry, and finance.
Geometric Sequence and Mean
Group Members:
Shemm Madrid
Marx Del Mundo
Angel Mae Ruiz
Reenie Trisha Vergara
Richelle Mae Padilla
11 x1 t14 01 definitions & arithmetic series (2013)
This document defines arithmetic series and provides examples of solving problems related to arithmetic series. It begins by defining an arithmetic series as a sequence where each term is found by adding a constant amount to the previous term. It then gives the general formula for finding the nth term and provides examples of using the formula to find specific terms and solve other problems such as determining the first term greater than a given value.
11 x1 t14 05 sum of an arithmetic series (2012)
The document discusses the formula for calculating the sum of an arithmetic series. It provides the general formula as Sn = (a + l)n/2 if the last term (l) is known, and as Sn = (2a + (n-1)d)/2 otherwise. It also gives examples of using the formula to calculate specific sums.
11 x1 t14 09 mathematical induction 2 (2012)
The document discusses mathematical induction and provides two examples of using it to prove statements. It first proves that the expression nn+1nn+2 is divisible by 3 for all positive integers n. It shows the basis step for n=1 and inductive step, assuming true for n=k and proving for n+1. Secondly, it proves 33n+2n+2 is divisible by 5 for all n, again using a basis step and inductive step. The document demonstrates the key steps of mathematical induction.
11 x1 t14 10 mathematical induction 3 (2012)
The document uses mathematical induction to prove that 2n is greater than n^2 for all n greater than 4. It shows that the statement holds for n=5. It then assumes the statement is true for some integer k greater than 4, and proves that it must also be true for k+1. Therefore, by the principle of mathematical induction, the statement is true for all integers n greater than 4.
11 x1 t14 08 mathematical induction 1 (2012)
Mathematical induction has the following steps:
1) Prove that the statement is true for the base case (usually n=1).
2) Assume the statement is true for some integer k.
3) Using the assumption from step 2, prove the statement is true for k+1.
4) By proving the statement true for n=1 and showing that if it is true for k then it is true for k+1, the statement is true for all positive integers n.
11 x1 t14 02 geometric series (13)
The document defines a geometric series as a sequence of numbers where each subsequent term is found by multiplying the previous term by a constant ratio. The constant ratio is called the common ratio and is represented by r. Examples are provided to demonstrate calculating terms of a geometric series given the first term and common ratio. The concept of finding the first term greater than a given value is also illustrated.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each measure, along with examples to illustrate how to calculate the median, mode, geometric mean, and harmonic mean. The document is intended as a guide for understanding and calculating different types of averages and measures of central tendency.
Business Finance Chapter 10
This document summarizes key lessons from analyzing historical capital market returns between 1926-2008:
1. There is typically a reward for bearing more risk, as seen by higher average returns for asset classes like stocks compared to less risky treasury bills. However, riskier assets also experience greater variability in returns.
2. Variability, or volatility, in returns is a measure of risk. Greater variability is seen in scatter plots and frequency distributions that show a wider spread of returns for riskier assets like stocks versus less variable returns for treasury bills.
3. While history shows average returns that reward risk, the future is unpredictable and past performance does not guarantee future results, as seen from periods like 2000-2002
Geometric sequences and geometric means
This document discusses geometric sequences and geometric means. It defines a geometric sequence as a sequence where each term after the first is the product of the preceding term and a fixed number called the common ratio. It provides the formula for calculating the nth term and the sum of the first n terms of a geometric sequence. The terms between the first and last term of a geometric sequence are called the geometric means. It includes sample problems demonstrating how to find specific terms, the common ratio, the first term, geometric means, and the sum of terms for various geometric sequences.
Geometric Sequence and Geometric Mean
Members:
Shemm Madrid
Marx Chryz Del Mundo
Reenie Trisha Vergara
Angel Mae Ruiz
Richelle Mae Padilla
Grade 10 Math Module (1st Quarter)
This document provides an introduction to and overview of a learning module on sequences. It outlines two main lessons that will be covered:
1) Arithmetic Sequences - including finding the nth term, next terms, means, and sums of terms
2) Geometric and Other Sequences - including finding the nth term, means, and sums of terms for geometric sequences as well as exploring other types of sequences like harmonic and Fibonacci sequences.
A pre-assessment with 24 multiple choice questions is also provided to gauge students' prior knowledge on topics related to sequences before beginning the lessons.
Risk, return, and portfolio theory
The document discusses risk and return in investments. It defines key concepts such as realized and expected return, ex-ante and ex-post returns, sources and measurements of risk including standard deviation and coefficient of variation. It also discusses the risk-return tradeoff and how higher risk investments require higher potential returns to compensate for additional risk.
Presentation of data
Here are the class widths, marks and boundaries for the given class intervals:
a. Class interval (ci): 4 – 8
Class Width: 4
Class Mark: 6
Class Boundary: 3.5 – 8.5
b. Class interval (ci): 35 – 44
Class Width: 9
Class Mark: 39.5
Class Boundary: 34.5 – 43.5
c. Class interval (ci): 17 – 21
Class Width: 4
Class Mark: 19
Class Boundary: 16.5 – 20.5
d. Class interval (ci): 53 – 57
Class Width: 4
Class Mark: 55
Class Boundary: 52.5 –
Goodbye slideshare UPDATE
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
Goodbye slideshare
NOTE: there is no sound, i.e. it is not a slidecast, as slideshare are going to get rid of this feature.
More Related Content
Viewers also liked
11X1 T10 03 arithmetic & geometric means
This document discusses arithmetic and geometric means. It introduces the arithmetic mean, which is also known as the average, and the geometric mean. It provides examples of calculating the arithmetic and geometric means for various data sets and numbers. The document concludes with exercises involving computing means for different values.
Math (geometric mean)
The document defines geometric sequences as patterns of numbers where each term is determined by multiplying the previous term by a common factor. It provides examples of geometric sequences and explains how to find the geometric mean between two terms of a geometric sequence by setting up a proportion. The geometric mean of two numbers a and b is the number x such that a/x = x/b. It also relates the geometric mean to proportions in a geometric figure with three lengths, where each mean length is the geometric mean of the other two lengths in that proportion.
Geometric Mean
The geometric mean is a type of average that indicates the central tendency of a set of numbers using their product, as opposed to the arithmetic mean which uses their sum, and it is calculated by taking the nth root of the product of the numbers. The geometric mean is more appropriate than the arithmetic mean for describing proportional growth and ratios, and it has various applications in fields like optics, signal processing, geometry, and finance.
Geometric Sequence and Mean
Group Members:
Shemm Madrid
Marx Del Mundo
Angel Mae Ruiz
Reenie Trisha Vergara
Richelle Mae Padilla
11 x1 t14 01 definitions & arithmetic series (2013)
This document defines arithmetic series and provides examples of solving problems related to arithmetic series. It begins by defining an arithmetic series as a sequence where each term is found by adding a constant amount to the previous term. It then gives the general formula for finding the nth term and provides examples of using the formula to find specific terms and solve other problems such as determining the first term greater than a given value.
11 x1 t14 05 sum of an arithmetic series (2012)
The document discusses the formula for calculating the sum of an arithmetic series. It provides the general formula as Sn = (a + l)n/2 if the last term (l) is known, and as Sn = (2a + (n-1)d)/2 otherwise. It also gives examples of using the formula to calculate specific sums.
11 x1 t14 09 mathematical induction 2 (2012)
The document discusses mathematical induction and provides two examples of using it to prove statements. It first proves that the expression nn+1nn+2 is divisible by 3 for all positive integers n. It shows the basis step for n=1 and inductive step, assuming true for n=k and proving for n+1. Secondly, it proves 33n+2n+2 is divisible by 5 for all n, again using a basis step and inductive step. The document demonstrates the key steps of mathematical induction.
11 x1 t14 10 mathematical induction 3 (2012)
The document uses mathematical induction to prove that 2n is greater than n^2 for all n greater than 4. It shows that the statement holds for n=5. It then assumes the statement is true for some integer k greater than 4, and proves that it must also be true for k+1. Therefore, by the principle of mathematical induction, the statement is true for all integers n greater than 4.
11 x1 t14 08 mathematical induction 1 (2012)
Mathematical induction has the following steps:
1) Prove that the statement is true for the base case (usually n=1).
2) Assume the statement is true for some integer k.
3) Using the assumption from step 2, prove the statement is true for k+1.
4) By proving the statement true for n=1 and showing that if it is true for k then it is true for k+1, the statement is true for all positive integers n.
11 x1 t14 02 geometric series (13)
The document defines a geometric series as a sequence of numbers where each subsequent term is found by multiplying the previous term by a constant ratio. The constant ratio is called the common ratio and is represented by r. Examples are provided to demonstrate calculating terms of a geometric series given the first term and common ratio. The concept of finding the first term greater than a given value is also illustrated.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each measure, along with examples to illustrate how to calculate the median, mode, geometric mean, and harmonic mean. The document is intended as a guide for understanding and calculating different types of averages and measures of central tendency.
Business Finance Chapter 10
This document summarizes key lessons from analyzing historical capital market returns between 1926-2008:
1. There is typically a reward for bearing more risk, as seen by higher average returns for asset classes like stocks compared to less risky treasury bills. However, riskier assets also experience greater variability in returns.
2. Variability, or volatility, in returns is a measure of risk. Greater variability is seen in scatter plots and frequency distributions that show a wider spread of returns for riskier assets like stocks versus less variable returns for treasury bills.
3. While history shows average returns that reward risk, the future is unpredictable and past performance does not guarantee future results, as seen from periods like 2000-2002
Geometric sequences and geometric means
This document discusses geometric sequences and geometric means. It defines a geometric sequence as a sequence where each term after the first is the product of the preceding term and a fixed number called the common ratio. It provides the formula for calculating the nth term and the sum of the first n terms of a geometric sequence. The terms between the first and last term of a geometric sequence are called the geometric means. It includes sample problems demonstrating how to find specific terms, the common ratio, the first term, geometric means, and the sum of terms for various geometric sequences.
Geometric Sequence and Geometric Mean
Members:
Shemm Madrid
Marx Chryz Del Mundo
Reenie Trisha Vergara
Angel Mae Ruiz
Richelle Mae Padilla
Grade 10 Math Module (1st Quarter)
This document provides an introduction to and overview of a learning module on sequences. It outlines two main lessons that will be covered:
1) Arithmetic Sequences - including finding the nth term, next terms, means, and sums of terms
2) Geometric and Other Sequences - including finding the nth term, means, and sums of terms for geometric sequences as well as exploring other types of sequences like harmonic and Fibonacci sequences.
A pre-assessment with 24 multiple choice questions is also provided to gauge students' prior knowledge on topics related to sequences before beginning the lessons.
Risk, return, and portfolio theory
The document discusses risk and return in investments. It defines key concepts such as realized and expected return, ex-ante and ex-post returns, sources and measurements of risk including standard deviation and coefficient of variation. It also discusses the risk-return tradeoff and how higher risk investments require higher potential returns to compensate for additional risk.
Presentation of data
Here are the class widths, marks and boundaries for the given class intervals:
a. Class interval (ci): 4 – 8
Class Width: 4
Class Mark: 6
Class Boundary: 3.5 – 8.5
b. Class interval (ci): 35 – 44
Class Width: 9
Class Mark: 39.5
Class Boundary: 34.5 – 43.5
c. Class interval (ci): 17 – 21
Class Width: 4
Class Mark: 19
Class Boundary: 16.5 – 20.5
d. Class interval (ci): 53 – 57
Class Width: 4
Class Mark: 55
Class Boundary: 52.5 –
Viewers also liked (20)
11 x1 t14 01 definitions & arithmetic series (2013)
11 x1 t14 01 definitions & arithmetic series (2013)
More from Nigel Simmons
Goodbye slideshare UPDATE
Slideshare is discontinuing its Slidecast feature as of February 28, 2014. Existing Slidecasts will be converted to static presentations without audio by April 30, 2014. The document informs users that new slidecasts can be found on myPlick.com or the author's blog starting in 2014. However, myPlick proved unreliable, so future slidecasts will instead be hosted on the author's YouTube channel.
Goodbye slideshare
NOTE: there is no sound, i.e. it is not a slidecast, as slideshare are going to get rid of this feature.
11 x1 t01 03 factorising (2014)
The document discusses different methods for factorising expressions:
1) Looking for a common factor and dividing it out of all terms
2) Using the difference of two squares formula (a2 - b2 = (a - b)(a + b))
3) Factorising quadratic trinomials into two binomial factors by identifying the values that multiply to give the constant term and sum to give the coefficient of the linear term.
11 x1 t01 01 algebra & indices (2014)
The document provides information on index laws and the meaning of indices in algebra:
- Index laws state that am × an = am+n, am ÷ an = am-n, and (am)n = amn. Exponents can be added or subtracted when multiplying or dividing terms with the same base.
- Positive exponents indicate a term is raised to a power. Negative exponents indicate a root is being taken. Terms with exponents are evaluated from left to right.
- Examples demonstrate how to simplify expressions using index laws and interpret different types of indices.
12 x1 t01 03 integrating derivative on function (2013)
The document discusses integrating derivatives of functions. It states that the integral of the derivative of a function f(x) is equal to the natural log of f(x) plus a constant. It then provides examples of integrating several derivatives: (i) ∫(1/(7-3x)) dx = -1/3 log(7-3x) + c, (ii) ∫(1/(8x+5)) dx = 1/8 log(8x+5) + c, and (iii) ∫(x5/(x-2)) dx = 1/6 log(x6-2) + c. It also discusses techniques for integrating fractions by polynomial long division and finds
12 x1 t01 01 log laws (2013)
The document discusses logarithms and their properties. Logarithms are defined as the inverse of exponentials. If y = ax, then x = loga y. The natural logarithm is log base e, written as ln. Properties of logarithms include: loga m + loga n = loga mn; loga m - loga n = loga(m/n); loga mn = n loga m; loga 1 = 0; loga a = 1. Examples of evaluating logarithmic expressions are provided.
X2 t02 03 roots & coefficients (2013)
The document discusses relationships between the coefficients and roots of polynomials. It states that for a polynomial P(x) = axn + bxn-1 + cxn-2 + ..., the sum of the roots equals -b/a, the sum of the roots taken two at a time equals c/a, and so on for higher order terms. It also provides examples of using these relationships to find the sums of roots for a given polynomial.
X2 t02 02 multiple roots (2013)
P
4
3
2
The document discusses properties of polynomials with multiple roots. It first proves that if a polynomial P(x) has a root x = a of multiplicity m, then the derivative of P(x), P'(x), will have a root x = a of multiplicity m-1. It then provides an example of solving a cubic equation given it has a double root. Finally, it examines a quartic polynomial and shows that its root α cannot be 0, 1, or -1, and that 1/
X2 t02 01 factorising complex expressions (2013)
The document discusses factorizing complex expressions. The main points are:
- If a polynomial's coefficients are real, its roots will appear in complex conjugate pairs.
- Any polynomial of degree n can be factorized into a mixture of quadratic and linear factors over real numbers, or into n linear factors over complex numbers.
- Odd degree polynomials must have at least one real root.
- Examples of factorizing polynomials over both real and complex numbers are provided.
11 x1 t16 07 approximations (2013)
The document describes the Trapezoidal Rule for approximating the area under a curve between two points. It shows that the area A is estimated by dividing the region into trapezoids with height equal to the function values at the interval endpoints and bases equal to the intervals. In general, the area is approximated as the sum of the areas of each trapezoid, which is equal to the average of the endpoint function values multiplied by the interval length.
11 x1 t16 05 volumes (2013)
The document discusses methods for calculating the volumes of solids of revolution. It provides formulas for finding volumes when an area is revolved around either the x-axis or y-axis. Examples are given for finding volumes of common solids like cones, spheres, and others. Steps are shown for using the formulas to calculate volumes based on given functions and limits of revolution.
11 x1 t16 04 areas (2013)
The document discusses different methods for calculating the area under a curve or between curves.
(1) The area below the x-axis is given by the integral of the function between the bounds, which can be positive or negative depending on whether the area is above or below the x-axis.
(2) To calculate the area on the y-axis, the function is solved for x in terms of y, then the bounds are substituted into the integral of this new function with respect to y.
(3) The area between two curves is calculated by taking the integral of the upper curve minus the integral of the lower curve, both between the same bounds on the x-axis.
11 x1 t16 02 definite integral (2013)
The document discusses 8 properties of definite integrals:
1) Integrating polynomials results in a fraction.
2) Constants can be factored out of integrals.
3) Integrals of sums are equal to the sum of integrals.
4) Splitting an integral range results in the sum of the integrals.
5) Integrals of positive functions over a range are positive, and negative if the function is negative.
6) Integrals can be compared based on the relative values of the integrands.
7) Changing the limits of integration flips the sign of the integral.
8) Integrals of odd functions over a symmetric range are zero, and integrals of even functions are twice the integral over
More from Nigel Simmons (20)
12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)
Recently uploaded
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
PCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
Recently uploaded (20)
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
11 x1 t14 03 arithmetic & geometric means (2013)
- 2. Arithmetic & Geometric Means n aaaa AM n 321 Arithmetic Mean(average)
- 3. Arithmetic & Geometric Means n aaaa AM n 321 Arithmetic Mean(average) n naaaaGM 321 Geometric Mean
- 4. Arithmetic & Geometric Means n aaaa AM n 321 25and4ofandtheFind.. GMAMge Arithmetic Mean(average) n naaaaGM 321 Geometric Mean
- 5. Arithmetic & Geometric Means n aaaa AM n 321 25and4ofandtheFind.. GMAMge Arithmetic Mean(average) 2 29 2 425 AM n naaaaGM 321 Geometric Mean
- 6. Arithmetic & Geometric Means n aaaa AM n 321 25and4ofandtheFind.. GMAMge Arithmetic Mean(average) 2 29 2 425 AM n naaaaGM 321 Geometric Mean 10 100 425 GM
- 7. Exercise 6F; 1ace etc, 2bd, 4, 7, 8ade, 10, 13, 19*