Section 7: Circles and Ellipses
In the last section, we saw that the equation of a line \[
y = y_A + m(x  x_A)
\] can be obtained by considering a fixed point \(A(x_A,y_A)\) on the line and another g
Section 5: Introduction to Analytic Geometry
5.1: What is analytic geometry?
Analytic geometry is the study of geometry by placing plane geometric figures (points, lines, circles, etc)
on coordinate a
Section 6: Lines
6.1: Slope of a line
The slope of a line is defined as the change in the \(y\)direction (rise) divided by the change in the \(x\)direction. It is a measure of the steepness of a line
Section 3: Angles and Triangles
3.1: Angular measurement
Consider a pair of parallel lines crossed by a straight line.
As we know, right angles are \(90^\circ\). The sum of all angles on a straight li
Section 2: Length, Area and Volume
2.1: Perimeter, Area and Volume
The perimeter of a plane geometric figure is the total distance around the boundary of the figure. The
perimeter of a circle is also
Section 1: Ratios and rates
5.1: Ratio
The quotient \(\dfraccfw_acfw_b\) is called the ratio of \(a\) to \(b\). This ratio is sometimes written as \(a:b\).
Example 1
A paint that has a specific tone o
Sunday, September 27, 2015
22:17
Find the length of a rod that is required to make the following frame.
201509 28 Circles and Analytic Geometry Page 1
201509 28 Circles and Analytic Geometry Page 2
Friday, September 25, 2015
12:30
A ball bearing sits between two metal grooves as shown below. If the distance between the
vertices of the grooves is 5 mm, what must the radius of the ball bearing be?
Wednesday, September 23, 2015
08:24
A truss structure is shown on the right.
Find the length x.
20150923 Trigonometry Page 1

A piston and rod assembly is shown below. Find the maximum angle betwee
Monday, September 21, 2015
10:32
Find the area of this shape.
How about
New Section 1 Page 1
etc
A cylinder is supported by a cable and a smooth incline plane shown on the left with a freebody diagr
Thursday, September 17, 2015
22:33
If an alloy containing 30% silver by mass (called a 30%
alloy) is mixed with a 55% alloy to get 800 kg of 40%
alloy, how much of each of the alloys must be added?
20
Hydraulic Piping
 Schedule 40 is standard.
P. L. = P.L units are in PSI/ft
Fluid Velocity = Q/A
Hydraulic Tubing
 Normally made from annealed steel w/ low carbon content. Materials with good
bending
Load Sensing PRV
Load sensing PRVs senses the magnitude of the pressure through the circuit and
determines which valves should open. If only much lower pressure is required, a load
sensing PRV minimi
Proportional Valves
a valve that produces an output (pressure,flow,direction) that is proportional to an
electronic control input.
proportional valves stop at intermediates positions, controlled by
Charge Pump
 During normal operation, oil losses occur due to slippage.
Slippage may cause cavitation so a charge pump is required.
 Charge pump accounts for slippage by keeping the loop full of oi
Hydrostatic Transmissions
function: transmit energy received from a prime mover (eg. Internal combustion engine)
to a load having its own operating characteristics. Regulate torque and speed.
A typi