Section Three HW Answers
1. (10 points)
Given the following information for Marys Taco Shop (TP, AP and MP are measured in
tacos per day):
Please copy each of the following questions into your answer file and then provide your answer
to that question.
There will be a 5 point reduction for not providing the questions along with your answers.
I do this because it allows me to explain better wh
Areas of Surface of Revolution
Rotating an enclosed region (which creates a solid) we only
revolved the bounding curve
It creates just the surface and not the volume
Think of the Basics
If we rotate a horizontal line and unravel
Rent, Hen-est, or Profil-
Chapter 15 concludes the study of the prices of resources
by examining rent, interest, and profits. There is nothing
difficult about this chapter. By now you should understand
that the marginal revenue product of a res
For integrals that have square roots
and U-Substitution fails
In order to integrate complicated functions
that cant be simplified using u substitution
we can use trig identities to simplify.
cos 1 s
1. (5 points)
Sam owns outright (no mortgage payments) two plots of land of equal size
in Southern California. One plot is in Victorville (the High Desert) and the other is
in the coastal community of Newport Beach. Sam was thinking about going into
Torque and Moment of Inertia
Use for questions 2-3 : A beam of length L has 4 forces with identical magnitude acting on it.
1. Which below is true for the force that creates the greatest torque about P.
a) it has the shortest pe
Section Two Homework
Please copy each of the following questions into your answer file and then provide
your answer to that question.
There will be a 5 point reduction for not providing the questions along with your
I do this because it allows me
It is so easy
When fractions have a single monomial term,
we can break it up into multiple, little
fractions, then do what we need to like
reduce, integrate, etc.
x 3 x ln x
Is it possible t
Work and Energy
Potential Energy of a Spring: Us = k x2
Gravitational Potential Energy: Ugravity = m g h
1. What is mechanical energy?
2. How does external work affect mechanical energy?
A pendulum of mass 2 kg has an initial velocity of 3 m/s and the obj
Quiz ch 6 and 7
Momentum and Energy
1. Rank the following from greatest momentum to least:
object X: mass 5 kg traveling at 25 m/s
object Y: mass 10 kg traveling at 2.5 m/s
object Z: mass .1 kg traveling at 100
a) X Y Z
b) Z Y X
c) X Z Y
d) Z X
v vs t
1. Below are velocity vs time graphs. Which object below is traveling is the "+" direction and
2. Below are velocity vs time graphs. Which object below is traveling at a constant velocity in the "+"
x vs t
1. Below are position vs time graphs. Which object below is traveling in the negative direction at a
2. Below are position vs time graphs. Which object below is standing still?
3. Fill in the blank:
The slope of
1. True(a) or False(b) All things being equal, gravity is the strongest force in nature.
2. Suppose you are on a planet that is identical to Earth in every way except, this planet has has a
radius 3 times that of Earth. If you stood on a sc
Use for 1-2. A car travels around a track from V - Z. The speedometer reads 50 mph at V and is at
35 mph at W. The speedometer remains unchanged from W - Y. By the the time the car has
reached Z the speedometer now reads 50 mph.
1. 106 mm (106 = 1,000,000) is how many kilometers?
1000 mm = 1 m
a) 1 meter
1000 m = 1 km
b) 10 meters
c) 100 meters
d) 1000 meters
2. In class we listed reasons why the United States has not switched over to the SI system. Which
A disk of moment of inertia of 3 kg m2 is rotating with an angular velocity of 4 rad/s about the axis
shown. (rad is not a unit but a place holder). A 2nd identical non rotating disk is dropped and lands on
the 1st and they begin
1. A vector is a quantity that has both _ and _.
a) size and scale
b) magnitude (length) and meaning
c) magnitude (length) and direction
c) speed and velocity
2. Find the sum of the following vectors X and Y. (Hint try using the tip to tale
Test 2 Review Sheet
1. If an object travels at constant speed does it have an acceleration? Explain.
2. You are holding a string with a mass on the end and are making the mass traverse a circle above
a) Draw a free bod
Work, KE, PE, and Rotation
Use the following diagram for questions 1 - 2.
1. Which object has the greatest potential energy?
d) all are the same
2. Which object above
Suppose we had two separate sticks, each with a mass attached on the stick as shown below.
1. Answer the following:
a) How does the mass of each compare?
b) How is the mass distribution of each compare?
c) If the same unb
The Beginning of Calculus
In Calculus, we still deal with the same functions that we learned to
manipulate and graph in previous classes.
Polynomial and Rational
Exponential and Logarithmic
Most calculus problems req
The Precise Definition of a Limit
Recall : As we allow to get as
close as we want to 0 , our -value
becomes arbitrarily close to .
In other words, the gap between
() and can be made as small as
we choose if is kept close enough
to 0 .
(0 , )
We will a
Limits at Infinity
When we take a limit as x or x , we are finding the behavior of the
graph on the extreme left and right.
lim 2 .
Example : Find lim
x x + 1
x x + 1
As x , y 3
and as x
Properties of Limits
Calculus concepts follow given laws in much the same way as algebraic
concepts follow the properties of numbers, exponents, radicals, etc.
If we want to find the lim f ( x), and direct substitution works, then the
31 March 2015
Writing Report Of Music And The Mind
According to Aniruddh Patels speech of Music and The Mind, peoples brain has a close
relationship with music. Human beings mind is directly connected with music, and
Average Rates of Change
A rate of change is the measure of how quickly something changes.
We use rates of change to determine how fast the values of a
function increase or decrease as the input changes.
We often think of a rate of change as the speed of
Xiaorui Yang (Rick)
3 May 2015
A Summary of The Genius of Beethoven
Ludwig van Beethoven, one of the most famous and talented pianists and composers, was born
in 1770, Germany. The Beethoven documentary, The Genius of Beethoven, d
April 16th 2015
The Madrigal Music
Back to the sixteenth and seventeenth century, Madrigal music represented a
musical culture of the Renaissance and early Baroque eras. It is a composition of vocal