Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°).
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,
In Euclidean geometry, a rhombus is a simple quadrilateral whose
four sides all have the same length. If lengths of each of the
sides are a and the distance between the parallel sides (known as
height) is h, then the area of the rhombus is defined as a × h.
Suppose that you already have a class named Rhombus that can hold a
and h. The class has a method to compute the area as well. The
class is as...
The following conditional statement is true.All of the sides of a quadrilateral are congruent if it is a
rhombus.Which of the following statements must also be true?a) If not all of the sides of a quadrilateral are congruent,
then it is not a rhombus.b) If a quadrilateral is not a rhombus, then all of its sides
are not congruent.c) If a quadrilateral is a rhombus, then not all of its sides
are congruent.d) If all of the sides of a...
A square membrane has all four sides (length a) tightly clamped.
Some of its vibrational modes are also dampened by a clamp placed
at the center of the membrane. Find the first four distinct
vibrational frequencies of this "square drum."
PYTHON:
A rhombus is a parallelogram with four equal sides. It resembles
the diamonds suit in
playing cards. Here are the properties of a rhombus:
- opposite sides are parallel
- all four sides have the same length
- opposite angles are equal
- sum of any 2 adjacent angles is 180 degrees (x + y = 180
degrees)
Write a function called rhombus that uses turtle
graphics to draw a rhombus.
The function rhombus takes three parameters:
1. t,...
Electrostatic Force and Equilibrium
Consider a rhombus with side of length L. The rhombus has two
pair
of equal interior angles. Label one of these pair θ and the other
φ. Four
identical, positive point charges, q are placed on the vertices of
the rhombus.
Draw the configuration.
a) Obtain a symbolic expression for the electric field at one of
the vertices
(your choice) and then at an adjacent vertex (Do you now know the
electric
field at all of...
Four charges of magnitude +q are placed at the corners of a
square whose sides have a length d. What is the magnitude of the
total force exerted by the four charges on a charge Q located a
distance b along a line perpendicular to the plane of the square
and equidistant from the four charges? Ans: bqQ/πε 0 (b2 + d2 / 2)
how to get this answer?
Let S be the square centered at the origin with sides of length
2, and C be the unit circle centered at the origin.
(a) If you randomly throw a point on S, what is the probability
that it will lie in C?
Ans: 0.785
(b) Describe how you could use simulation to estimate the
probability in part (a).
(c) How can you use simulation to estimate a?
For part b and c, there maybe a need to generate random...
A square loop of wire with sides of length 34 cm is in a uniform
magnetic field perpendicular to its area.
Part A
If the field's strength is initially 110 mT and it decays to
zero in 0.011 s , what is the magnitude of the average emf induced
in the loop?
Part B
What would be the average emf if the sides of the loop were only
17 cm ?
Express your answer using two significant figures.
The baseball diamond at Grayson Stadium is a square with 90 ft
sides. A batter hits the ball
and runs to the right toward first base with a constant speed of 24
ft/s. At the same time a
runner on 3rd base runs home at a constant speed of 28 ft/s. At
what rate is the distance
between the two runners changing two seconds after they start
running?
A pentagon is formed by adding two sides of the same
length to attach an isoceles triangle to one side of a rectangle.
If the area is fixed at A, what are the dimensions (in terms of A)
that will minimize the pentagon's perimeter?