This document discusses using multi-step word problems and equations to model real-world situations involving two variables. It provides examples of identifying independent and dependent variables, writing equations to represent relationships, making tables of ordered pairs, and plotting graphs. Students are given practice writing equations, identifying variables, making tables and graphs for problems involving money saved, books collected, cost of rides, and more. The document emphasizes using graphs to show how the dependent variable changes as the independent variable changes.
Finding the Extreme Values with some Application of Derivativesijtsrd
There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint
Math 251, 2014, Summer 2 QUIZ 10 Grade_____20 From 11..docxandreecapon
Math 251, 2014, Summer 2 QUIZ 10 Grade_____/20
From 11.1 to 11.4 Name_______________________________________________
Work individually
Show all work.
No calculators.
__________________________________________________________________________________________________
1
1. If , , , where , , , , , , , , u u x y z x x r s t y y r s t z z r s t
Follow the questions below to find an expression for .
) In the equation above, what is the dependent variable, what are the intermediate variables and
what are the independent variables?
) There
u
s
a
b
are three intermediate variables and three independent variables. Each intermediate variable has a partial derivative
with repect to each of the three independent variables. Give the three partial derivatives of each of the three
intermediate variables (9 in total). Hint: one if them is .
) Each of these partial derivatives is a function of the three dependent variables. What are they
y
t
c
?
Hint: , , so must also be a function of , , and .
) If was simply a function of its intermediate variables , and , the dependent variable would
have three partial derivativ
y
y y r s t r s t
t
d u x y z
es. What are these 3 partial derivatives? Hint: one of them would be .
) Consider the partial derivatives in ( ). They are all functions of three variables.
What are they? Hint: ,
u
y
e d
u u x
, so must also be a function of , and .
u
y z x y z
y
Math 261, 2014, Summer 2 QUIZ 10
2 of 3
) There are three dependent variables and one independent variable. The dependent variable therefore has a
partial derivative with respect to the each of the independent varibles. What are those par
f
tial derivatives?
Hint: one of them is .
) We want to find where is the dependent variable we have selected.
is constructed by applying the chain rule three times, once to each
u
t
u
g s
s
u
s
derivative of with respect to
each of the intermediate variables. What are the three chain rules that sum to make up ?
Hint: for , the three chain rules are . . .
u
u
s
u u u x u y u
t t x t y t z
z
t
) Each partial derivative can be espressed as the dot product of two vectors.
What is the dot product representation of ?
Hint, . . . , , , ,
)
h
u
s
u u x u y u z u u u x y z
t x t y t z t x y z t t t
i
Notice that , , is common to all the partial derivatives of the dependent variable
with respect to the independent variable. What do we call , , ?
u u u
x y z
u u u
x y z
Math 261, 2014, Summer 2 QUIZ 10
3 of 3
2.
4 2 3 2
2
If , where , , sin ,
t t
u x y y z x rse y rs e z r s t
...
Word embeddings have received a lot of attention since some Tomas Mikolov published word2vec in 2013 and showed that the embeddings that the neural network learned by “reading” a large corpus of text preserved semantic relations between words. As a result, this type of embedding started being studied in more detail and applied to more serious NLP and IR tasks such as summarization, query expansion, etc… More recently, researchers and practitioners alike have come to appreciate the power of this type of approach and have started a cottage industry of modifying Mikolov’s original approach to many different areas.
In this talk we will cover the implementation and mathematical details underlying tools like word2vec and some of the applications word embeddings have found in various areas. Starting from an intuitive overview of the main concepts and algorithms underlying the neural network architecture used in word2vec we will proceed to discussing the implementation details of the word2vec reference implementation in tensorflow. Finally, we will provide a birds eye view of the emerging field of “2vec" (dna2vec, node2vec, etc...) methods that use variations of the word2vec neural network architecture.
This (long) version of the Tutorial was presented at #O'Reilly AI 2017 in San Francisco. See https://bmtgoncalves.github.io/word2vec-and-friends/ for further details.
Finding the Extreme Values with some Application of Derivativesijtsrd
There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint
Math 251, 2014, Summer 2 QUIZ 10 Grade_____20 From 11..docxandreecapon
Math 251, 2014, Summer 2 QUIZ 10 Grade_____/20
From 11.1 to 11.4 Name_______________________________________________
Work individually
Show all work.
No calculators.
__________________________________________________________________________________________________
1
1. If , , , where , , , , , , , , u u x y z x x r s t y y r s t z z r s t
Follow the questions below to find an expression for .
) In the equation above, what is the dependent variable, what are the intermediate variables and
what are the independent variables?
) There
u
s
a
b
are three intermediate variables and three independent variables. Each intermediate variable has a partial derivative
with repect to each of the three independent variables. Give the three partial derivatives of each of the three
intermediate variables (9 in total). Hint: one if them is .
) Each of these partial derivatives is a function of the three dependent variables. What are they
y
t
c
?
Hint: , , so must also be a function of , , and .
) If was simply a function of its intermediate variables , and , the dependent variable would
have three partial derivativ
y
y y r s t r s t
t
d u x y z
es. What are these 3 partial derivatives? Hint: one of them would be .
) Consider the partial derivatives in ( ). They are all functions of three variables.
What are they? Hint: ,
u
y
e d
u u x
, so must also be a function of , and .
u
y z x y z
y
Math 261, 2014, Summer 2 QUIZ 10
2 of 3
) There are three dependent variables and one independent variable. The dependent variable therefore has a
partial derivative with respect to the each of the independent varibles. What are those par
f
tial derivatives?
Hint: one of them is .
) We want to find where is the dependent variable we have selected.
is constructed by applying the chain rule three times, once to each
u
t
u
g s
s
u
s
derivative of with respect to
each of the intermediate variables. What are the three chain rules that sum to make up ?
Hint: for , the three chain rules are . . .
u
u
s
u u u x u y u
t t x t y t z
z
t
) Each partial derivative can be espressed as the dot product of two vectors.
What is the dot product representation of ?
Hint, . . . , , , ,
)
h
u
s
u u x u y u z u u u x y z
t x t y t z t x y z t t t
i
Notice that , , is common to all the partial derivatives of the dependent variable
with respect to the independent variable. What do we call , , ?
u u u
x y z
u u u
x y z
Math 261, 2014, Summer 2 QUIZ 10
3 of 3
2.
4 2 3 2
2
If , where , , sin ,
t t
u x y y z x rse y rs e z r s t
...
Word embeddings have received a lot of attention since some Tomas Mikolov published word2vec in 2013 and showed that the embeddings that the neural network learned by “reading” a large corpus of text preserved semantic relations between words. As a result, this type of embedding started being studied in more detail and applied to more serious NLP and IR tasks such as summarization, query expansion, etc… More recently, researchers and practitioners alike have come to appreciate the power of this type of approach and have started a cottage industry of modifying Mikolov’s original approach to many different areas.
In this talk we will cover the implementation and mathematical details underlying tools like word2vec and some of the applications word embeddings have found in various areas. Starting from an intuitive overview of the main concepts and algorithms underlying the neural network architecture used in word2vec we will proceed to discussing the implementation details of the word2vec reference implementation in tensorflow. Finally, we will provide a birds eye view of the emerging field of “2vec" (dna2vec, node2vec, etc...) methods that use variations of the word2vec neural network architecture.
This (long) version of the Tutorial was presented at #O'Reilly AI 2017 in San Francisco. See https://bmtgoncalves.github.io/word2vec-and-friends/ for further details.