Consider a circle with AB as diameter, and P another point on
the circle. Let M be the foot of the perpendicular from P to AB.
Draw the circles which have AM and MB respectively as diameters,
which meet AP at Q and BP at R. Prove that QR is a tangent to both
circles.
a) Find area between parabola f(x) = x^2/2p and its chord AB
which is perpendicular to y-axis. Here A(a,f(a)), B(-a, f(-a)),
a<0, p>0.
b) Show also that this area is 2/3 of the area of the rectangle
bounded by lines AB, X -axis, x = a,x = b.
The Butterfly Theorem. Suppose M is the midpoint of a chord P Q
of a circle and AB and CD are two other chords that pass through M.
Let AD and BC intersect P Q at X and Y , respectively. Then M is
also the midpoint of XY .
1. Prove the Butterfly Theorem. [10]
Hint: You know a lot about angles in a circle, and about
triangles, and cross ratios, and all sorts of things . . .
Let PQ be a focal chord of the parabola y2 = 4px. Let
M be the midpoint of PQ. A perpendicular is drawn from M to the
x-axis, meeting the x-axis at S. Also from M, a line segment is
drawn that is perpendicular to PQ and that meets the x-axis at T.
Show that the length of ST is one-half the focal width of the
parabola.
: For your selected gears, determine the
following: center distance, pitch circle diameter, outer diameter
(or addendum diameter), dedendum diameter, base circle diameter,
circular pitch, tooth thickness, addendum, dedendum, clearance,
whole depth.
A circular plate having a diameter of 330 mm is held
perpendicular to an axisymmetric horizontal jet of air having a
velocity of 43 m/s and a diameter of 88 mm as shown in the figure
below. A hole at the center of the plate results in a discharge jet
of air having a velocity of 43 m/s and a diameter of 22 mm.
Determine the horizontal component of force required to hold the
plate stationary.
F =
N
the...
Will Rogers spun a lasso in a vertical circle. The diameter of
the loop was 6 ft, and the loop spun 50 times each minutes. If the
lowest point on the rope was 6 inches above the ground, write an
equation to describe the height of this point above the ground
after t seconds.
Please write nicely.
A point on a circle with a diameter of 10m starts at
an upright position P at (0,r) and moves clockwise with an
acceleration .6m/s^2 .
When t=7 :
-Find position
-Find velocity
-Find acceleration
relative velocity