R
Resume
Luis portillo
7866180939
[email protected]
mail.com
Portfoliogen.com
Objectives
To attend a college and decide what career to do.
Education
Gateway Environmental K8
Miami, FL
Cutler Bay Senior High
Miami, FL
Awards
Science award

All gra
Triple Integrals in Spherical Coordinates  (13.7)
1. Spherical Coordinates x ! ! cos " sin # Consider spherical coordinates: y ! ! sin " sin # where z ! ! cos # x2 " y2 " z2 y tan " ! x z cos # ! ! !
" is counterclockwise from the positive side of the x
Triple Integrals in Cylindrical Coordinates  (13.6)
Cylindrical Coordinates x ! r cos ! Consider !x, y" in polar coordinates: y ! r sin ! , z!z x2 " y2 y tan ! ! x r!
Triple Integrals in Cylindrical Coordinates Let Q be a solid in space and f!x, y, z" be
Triple Integrals  (13.5)
1. Triple Integrals Let Q be a solid in space and f!x, y, z" be defined on Q. Then lim ! ! !Q f!x, y, z"dV ! #V " " " f
k!1 j!1 i!1 l m n
x # , y # , z # #V i j k
provided the limit exists. If Q! then !x, y, z" g 1 !x, y" $ z
Area, Volume and Center of Mass  (13.2)
1. Areas and Volumes Recall: For a given region R !
!x, y"  a ! x ! b, g 1 !x" ! y ! g 2 !x" ,
" "R f!x, y"dA ! " a " g !x" f!x, y"dydx.
1
b
g 2 !x"
For a given region R !
!x, y"  h 1 !y" ! x ! h 2 !y", c ! y ! d
Extrema of Functions of Several Variables  (12.7)
1. Local Extremes and Critical Points Definition: Definition: The point !a, b" is a critical point of a function f!x, y" if !a, b" is in the domain of f and either !f!a, b" ! " or !f!a, b" DNE !one or bot
The Gradient and Directional Derivative  (12.6)
1. Directional Derivatives Definition: The directional derivative of f!x, y" at the point !a, b" and in the direction of the unit vector ! "# u 1 , u 2 $, denoted as D ! f!a, b", is defined by u u f!a & hu
Chain Rule  (12.5)
1. Chain Rule Let z ! f!x, y" and x ! x!t" and y ! y!t". So implicitly z is a function of t, z ! g!t". What is dz ? dt g!t # h" ! g!t" f!x!t # h", y!t # h" ! f!x!t", y!t" ! lim lim h"0 h"0 h h f!x!t # h", y!t # h" ! z!x!t # h", y!t" #
Partial Derivatives  (12.3)
1. Partial Derivatives Recall f!x $ h" ! f!x" provided the limit exists. h#0 h The derivative of f describes the rate of change of f along the xaxis. Now we like to consider the rates of change of a function in two variables
Functions of Several Variables  (12.1)
1. Functions of Several Variables A function of two variables, say x and y, is a relation that assigns exactly one real number to each ordered pair of real numbers x, y . A function of three variables, say x, y and
Tangent and Normal Vector  (11.5)
1. Principal Unit Normal Vector r Let C be the curve traced out by the vectorvalued function !t" "# f!t", g!t", h!t" $. The vector 1 ! ! % !t" r T!t" " % ! !t" r is the unit tangent vector to the curve C. Define ! N!t"
Tangent Vector and Curvature  (11.4)
1. Tangent Vector r Let C be the curve traced out by the vectorvalued function !t" "# f!t", g!t", h!t" $. The vector 1 ! ! % !t" r T!t" " % ! !t" r is the unit tangent vector to the curve C. Observe that ! % !t" r r
Vector Fields  (14.1)
1. Vector Fields ! Definition: A vector field in the plane is a vectorvalued function F!x, y" which maps points in R 2 to a ! vector space V 2 . A vector field in the plane is a vectorvalued function F!x, y, z" which maps points i
Line Integrals  (14.2)
Let C be a curve in R 2 or in R 3 . The curve C is said to be oriented if there is a direction to it. For example, C : !t" "# 2 cos t, 2 sin t $, 0 ! t ! ! . r 2 The curve C is oriented since it goes from the point 2, 0 to 0, 2 cou
Truth in Texas Textbooks
A Summary of Findings of Factual Errors, Omission of Facts,
HalfTruths & Agenda Bias in World History, World Geography & World Cultures
Submitted by the Publishers for TEA Proclamation 2015
Cengage/National Geographic World Cultu
QuestionWhat will
happen to the mass of an egg
when placed in vinegar?
Materials:
#1. An egg
#2. White vinegar
#3. A container big enough to
hold your egg and a cover for
your container
#4. A big spoon
Procedures:
Step #1. Place your egg in the
container
1. Many people in the West think of geisha simply as prostitutes. After reading Memoirs of
a Geisha, do you see the geisha of Gion as prostitutes? What are the similarities, and
what are the differences? What is the difference between being a prostitute a
Alices Adventures in Wonderland
STUDY GUIDE
Test on Thursday (p. 2 & p. 4) / Friday (p. 3)
Review and be familiar with the answers to the following questions:
Ch. 1
1. What is suggested by the fact that the rabbit Alice sees running by speaks and wears cl
Enlightened Absolutism
and the Balance of
Power
Chapter 8, Lesson 3
Enlightened Absolutism
Rulers trying to govern by Enlightenment
principles while keeping their royal powers
o
o
o
Allow natural rights for all people
Support the arts, sciences, and educ
fasdfdfsadfsadfasfwe
NGPF Activity Bank
Budgeting #17
ROLEPLAY: Living Paycheck to Paycheck
Part I: Play the game, Spent.
Go to the Spent website. Click on Continue to Spent on right side of the screen to start game. Be sure to answer the
questions below
Compare and contrast Japanese and Chinese culture
Japan and China are two countries of South East Asia. As the geography suggested, they have
influence each other culturally, in which there are three characteristics that are obvious the most.
Both Japanes
iPrep Personal, Career, and School Choices
Womens History Projects
Ms. West, Period 6
1.) March is Womens History Month. The state of Florida mandates the teaching of
womens contributions to the American society and beyond. What topic(s) would you like
to
Compare and contrast Japanese and Chinese culture
Japan and China are two countries of South East Asia. As the geography suggested, they have
influence each other culturally, in which there are three characteristics that are obvious the most.
Both Japanes
Peer Editing Checklist
Use the following checklist to help you evaluate your partners writing.
Remember to offer 2 constructive suggestions and point out 2 parts you
especially like.
Your Name _Luis_Portillo_ Your Partners Name _Martina Morales_
1. Discus
The Great Debaters
Student Name: _
When I was a child, I spake as a child, I understood as a child, I thought as a child but when I became a man, I put away
all childish things. Freshman classI believe we are the most privileged people in America, because
Paradigm Shif
*Paradigm= Greek word for pattern
*Normal Science= The standard paradigm
*Anomalies= Things that cannot explained by normal science
*Paradigm Shif= a new paradigm is created to account for anomalies.
*The original paradigm was developed by t
Surfaces in Space  (10.6)
1. Cylindrical Surfaces The equation !x ! h" 2 ! !y ! k" 2 " r 2 is a circle with center !h, k" and radius r in the xy !plane. In the xyz !space, the equation !x ! h" 2 ! !y ! k" 2 " r 2 means !x ! h" 2 ! !y ! k" 2 " r 2 !" # z
The Cross Product  (10.4)
1. Determinant of a Matrix A 2 ! 2 matrix and 3 ! 3 matrix of real numbers are of the forms a 11 a 12 a 21 a 22 a 11 a 12 a 13 and a 21 a 22 a 23 a 31 a 32 a 33 ,
respectively. The determinant of a 2 ! 2 matrix of real numbers i
The Dot Product  (10.3)
1. Dot Product u v The dot product of two vectors ! "# u 1 , u 2 , u 3 $ and ! "# v 1 , v 2 , v 3 $ is defined by ! ! ! " u1v1 % u2v2 % u3v3. u v The dot product of two vectors ! "# u 1 , u 2 $ and ! "# v 1 , v 2 $ is defined by u