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.
Create an object called Circle. Declare the following integer
variables for the object Circle, radius, diameter, and pi is
declared as double. Create the following for the Circle object:
● Implicit constructor (default constructor)
● Void method Calculate (double pi, int radius) to calculate the
area of the Circle object. The method must include a system.out
statement that displays the area value. Use the following formula
to calculate area of the circle:
Area = pi * (r * r)
Your...
(a) Let S =
{a, b, ab, aba}. How
many different factorizations are there of
(ab)11 ? It is not enough to give me a
number. You need to prove (i.e., justify or explain very carefully)
that your number is correct.
This is for an automated languages course
: 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...