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 general point \
(P(x,y)\). This equation restricts \(P\)
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 axes. For example, we can analyze a triangle like the on
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. The following gives the formula for finding the slope
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 line is \(180^\circ\), e.g, \(a
+ c = 180^\circ\). We als
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 called the circumference.
The following table lists the
Section 1: Ratios and rates
The quotient \(\dfraccfw_acfw_b\) is called the ratio of \(a\) to \(b\). This ratio is sometimes written as \(a:b\).
A paint that has a specific tone of blue color can be made by mixing 3 parts of normal bl
Sunday, September 27, 2015
Find the length of a rod that is required to make the following frame.
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Friday, September 25, 2015
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?
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Wednesday, September 23, 2015
A truss structure is shown on the right.
Find the length x.
2015-09-23 Trigonometry Page 1
A piston and rod assembly is shown below. Find the maximum angle between the cylinder and
the piston rod.
Monday, September 21, 2015
Find the area of this shape.
New Section 1 Page 1
A cylinder is supported by a cable and a smooth incline plane shown on the left with a free-body diagram on the right.
New Section 1 Page 2
A cylinder is sup
Thursday, September 17, 2015
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?
2015-09-18 Ratios and Rates Page 1
An athlete ran for 4 k
- Schedule 40 is standard.
P. L. = P.L units are in PSI/ft
Fluid Velocity = Q/A
- Normally made from annealed steel w/ low carbon content. Materials with good
bending and flaring properties.
- Nominal size is measured by
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 minimizes the power loss due to heat by friction in 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 associated electronics
and a max frequency response of
- 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 oil by supplying a
sufficient flow to make up for slippag
-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 typical hydrostatic transmission closed loop drive consists