Question

Prove: That in an equilateral triangle the distances from a point are always the same value

Answer #1

An equilateral triangle has sides 6cm long. What is the
probability that a point chosen at random in the triangle is within
1 cm of a corner?

Let △ ??? be a triangle. Prove that ? = 2? if and only if △ ???
is equilateral.

Prove that equilateral triangles exist in
neutral geometry (that is, describe a construction
that will yield an equilateral triangle). note that all the
interior angles of an equilateral triangle will be congruent, but
you don’t know that the measures of those interior angles is
60◦.Also, not allowed to use circles.

Three identical point charges are located at the corners of an
equilateral triangle that is 0.3m on each side. If each charge is
+20μC, than the magnitude of the net force (in N)
on one of the charges due to the other two is..

5. Consider an equilateral triangle cut from a thin board. The
triangle has mass M and and edge length L. Determine he moment of
inertia of a triangle for rotation about an axis along one of its
edges.

In the corners A and B of an equilateral triangle of three meters on each side there are two charges of 4µC each. The electric potential at point C of the triangle is
19.2 kV
b.
24.2 kV
c.
7.3 kV
d.
12 kV

A pendulum is made from a thin homogeneous metal plate cut into
an equilateral triangle. What is the frequency of small
oscillations if the plate is suspended by one vertex? What is the
frequency for the same plate suspended at a midpoint of one of the
edges? For both cases assume that the oscillation is in the plane
of the plate.

Three equal 2.00-μCμC point charges are placed at the corners of
an equilateral triangle whose sides are 0.400 mm long. What is the
potential energy of the system? (Take as zero the potential energy
of the three charges when they are infinitely far apart.)
U= J

1. Treacherous Triangle Trickery. Consider a charge distribution
consisting of an equilateral triangle with a point charge q fixed
at each of its vertices. Let d be the distance between the center
of the triangle and each vertex, let the triangle’s center be at
the origin, and let one of its vertices lie on the x-axis at the
point x = −d.
1.1. Compute the electric field at the center of the triangle by
explicitly computing the sum of the...

Three charges are at the corners of an equilateral triangle, as
shown in the figure below. Calculate the electric field at a point
midway between the two charges on the x-axis. (Let
q1 = 2.00 μC,
q2 = 2.00
μC, and
q3 = −3.50 μC.)
Image:
Three charged particles lie in the x
y-coordinate plane at the vertices of an equilateral
triangle with side length 0.500 m.
Positive charge q2 is at the origin.
Positive charge q1 is in the first...

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