April 22, 2013
The Golden Rectangle and Art
The Golden Rectangle, is also known as, The Golden Ratio, The Golden Mean, Phi, The
Divine Section, The Golden Proportion, The Golden Number and The Golden Spiral. The go
12.1 First Derivative and
Example 1: Estimate the derivative graphically
To find the
at a certain
slope of the
At x = -3, f(-3) = -3/-2 = 3/2 (down 3, left
12.2 Second Derivative and
If we think the derivative as a rate of
change, then the second derivative is the
rate of change of the rate of change
* The second derivative is the derivative of
Compare f(x) and g(x)
Both are increasing
12.5: Absolute Maxima and
Finding the absolute maximum or minimum
value of a function is one of the most
important uses of the derivative.
Finding the maximum profit, the time it takes
for a drug to reach its maximum concentration
Lesson 12.6: Optimization
Optimization problems are problems that involve finding the absolute maximum value or the
absolute minimum value of a function.
We will be able to calculate:
Area and perimeter
Revenue and profit
The manufacturer of eComputers, an economy-priced computer, recently completed the design for a new
laptop model. eComputers top management would like some assistance in pricing the new laptop. Two
market research firms were contacted and asked to prepare
According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and
electronically file a 1040 tax form. This distribution of times follows the normal distribution and the
standard deviation is 80 minutes. A consumer watchdog age
Over the past decade, the mean number of hacking attacks experienced by members of the Information
Systems Security Association is 510 per year with a standard deviation of 14.28 attacks. The distribution
of number of attacks per year is normally distribu
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged
for service from Hermosa Beach to Los Angeles International Airport is $21 and the standard deviation is
$3.50. We select a sample of 15 fares.
What is th
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of
these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard
deviation of 5.5 hours. As a part of its quality assurance progra
PROBLEM 1.1 KNOWN: Heat rate, q, through one-dimensional wall of area A, thickness L, thermal
conductivity k and inner temperature, T1. FIND: The outer temperature of the wall, T2. SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction,
Module 1: Worked out problems
A freezer compartment consists of a cubical cavity that is 2 m on a side. Assume the bottom
to be perfectly insulated. What is the minimum thickness of Styrofoam insulation
(k=0.030W/m.K) which must be applied to t
KNOWN: Plane wall with prescribed thermal conductivity, thickness, and surface temperatures.
FIND: Heat flux, q x , and temperature gradient, dT/dx, for the three different coordinate systems
ASSUMPTIONS: (1) One-dimensional
KNOWN: Diameter and emissivity of spherical interplanetary probe. Power dissipation
FIND: Probe surface temperature.
ASSUMPTIONS: (1) Steady-state conditions, (2) Negligible radiation incident on the probe.
KNOWN: Width, input power and efficiency of a transmission. Temperature and convection
coefficient associated with air flow over the casing.
FIND: Surface temperature of casing.
ASSUMPTIONS: (1) Steady state, (2) Uniform convection
MAE 311: Machines and Mechanisms I
Assignment #1 Solution
Due Date: 2/17/2014
For the given state of stress, draw and label the stress element.
a) xx = 1000 psi, yy = 0 psi, zz = 0 psi, xy = 500 psi, yz = 0 psi, zx = 0 psi
(3 5 = 15)