In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle).
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.
Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a rectangle by polygons.
This is how I interpreted the problem,
a) The net torque about point A is zero. This is because the forces F1 and F2 are equal and opposite, and they act at the same distance from point A. Therefore, they produce torques that cancel each other out..
The force F3 doesn’t does not produce any...
I try to divide the area of CDGE into two areas of triangles by drawing line DE.
The ratio of area of triangles ABE and ECD = 4 : 1
The ratio of area of triangles ADG and DGE = AG : GE
The ratio of triangles ADG and AGF = DG : GF
Then I don't know what to do.
we haven't learned howw to do parts d-f yest. could you please give me a hand?
(a)
$$E(X)=E(Y)=\int_0^3\int_0^3\frac{1}{9}dxdy=\frac{3}{2}$$
(b)its typoe suppoesed to be W=Y-2
$$E(Z)=E(X-2)=E(X)-E(2)=-\frac{1}{2}$$
$$E(W)=E(Y-2)=E(Y)-E(2)=-\frac{1}{2}$$
(c) i guess joint pdf from ##E(Z)## and...
I have checked several textbooks about the heat equation in a rectangle and I have found none that deals with my exact problem. I have though to use separation of variables first (to no avail), then Green's function (to no avail), then simplifying the problem for example by defining a new...
I have attached the work to this problem and although it has different parameters than what I have listed in my post the basis to solving the problem is the same.
I am confused on why this rectangle in this problem is considered to b in the j unit vector direction. Is it because its face will...
A regulation NFL playing field of length x and width y has a perimeter of 346_2/3 or 1040/3 yards.
(a) Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle.
(b) Show that the width of the rectangle is y = (520/3)...
Rectangle ABCD is inscribed in the circle shown.
If the length of side $\overline{AB}$ is 5 and the length of side $\overline{BC}$ is 12
what is the area of the shaded region?
$a.\ 40.8\quad b.\ 53.1\quad c\ 72.7\quad d \ 78.5\quad e\ 81.7$
well to start with the common triangle of 12 5...
Figure shows six identical circles inside a rectangle.
The radius of each circle is 24 cm. The radius of the circles is the greatest possible radius so that the circles fit inside the rectangle. The six circles form the pattern shown in Figure so that
• each circle touches at least two other...
Hello,
I am studying geometry with an app on my phone. There was a difficult problem, which had two different explanations for solving. I correctly understood one explanation. I reviewed later without memory of the problem at all. There was an obvious attempt from what was learned previously...
Someone has asked for a fuller explanation of a reply that I gave to this thread on another site eleven years ago.
The question concerns a rectangle (dimensions $l\times w$) whose corners have been replaced by quadrants of a circle of radius $r$. This diagram shows an enlargement of one corner...
I am curious about how to approach the problem mathematically, so I write.
There are 4 dots on the square and I know the location.
The rectangle moves and the positions and angles of the four points change.
I also know the location of the four points that have changed.
I don't know the...
A rectangular enclosure must have an area of at least 600 yd2. If 140 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?
Select one:
A. 35 ≤ w ≤ 60
B. 10 ≤ w ≤ 35
C. 10 ≤ w ≤ 60
D. 0 ≤ w ≤ 10
Hi all,
My teacher assigned us a problem to do a few days ago and have attempted it many times, often leaving and coming back to see if I could figure it out. I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object...
Suppose, a rectangle circumscribes a quadrilateral having length of diagonals p and q, and area A.What is the maximum area of rectangle that circumscribes the given quadrilateral?
Answer:-
How to answer this question using geometry or calculus or by using both techniques.
I am stuck on the following question (Image attached of my work) appears to make sense until i try to take a limit as c--->0 because the result should be 0. Am i missing something, if so can't you point me in the right direction.
Thank you
So, I know it can be proven using calculus, but I need the geometric one.
So, I got that ^c=^d and therefor, the amount of increment in one of a, is equal to the other(^e=^b). (Also 0<a+b<Pi/2)
And AP'=BP'=BD/sin(a) and BP=BD/sin(a+b) and AP=BD/sin(a-b).
AP'+BP'=2AP'=2BD/sin(a) and...
How can the edge of a Möbius strip being projected on a 2 dimensional plane?
Precisely the ending of this video:
I just can get it since his animation goes by it so fast.
Homework Statement
The flour of a rectangular room has dimensions 12 feet 16 feet. How many square tiles each with side of length 1 foot are needed to make a border of single row of tiles on the floor along the edges of the room?
A 28
B 52
C 56
D 58Homework EquationsThe Attempt at a Solution...
Homework Statement
Homework EquationsThe Attempt at a Solution
Part C is confusing me.
I got the height PQ to be 16/3root6
But I'm lost as to how to find the length SP. The mark scheme has the answer as 8, or (SP/2 = 4 therefore SP = 8) but I still can't figure it out, maybe it's 'cause...
Homework Statement
A rectangular structure carries clocks at its four corners. The clocks are synchronized in the structure’s rest frame, in which it has length L =4ft and width W = 3ft. In our laboratory frame the rectangle is moving in the positive x direction at speed v = 0.8c. As the clock...
In the Feynman Lectures on Physics, Feynman explains the curvature of spacetime by drawing a rectangle in spacetime, see
http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18
First waiting 100 sec and then moving 100 feet in height on Earth's surface results in a different situation...
I understand the transformation in general is not homomorphic but what about the transformation minus the splices, that is, contort it all the way up to and not including splicing the edges? Isn't that a homomorphism? Can't we define a bijective function (rotation matrices) to map the two...
Homework Statement
Exercise in integration: Using the Electric Field E of a straight line
segment of charge, find the electric field at height 10 cm above the centre of a
rectangle of sides 10cm and 20 cm carrying charge density 4 μC/m2.
Homework Equations
µ=Q/L
µ = charge density
Q = total...
Hi,
I may have discovered a textbook error but I'm no calc whiz. I need an assist to find out if the question unintentionally described a square instead of a rectangle.
I have attached the textbooks solution as well as my attempt at a solution.
The numbers check out, I just want to make sure...
Homework Statement
The width of a rectangle is increased by one tenth, but the area remains the same. By what fraction has the length of the rectangle been reduced?
The Attempt at a Solution
Length = x
Width = x + 1/10
Set equation:
L * W
x *(10x + x)
10x^2 + x^2
I am stuck... Please help...
Let x denote the width of a rectangle with perimeter 30 feet. Find the area of this rectangle.
Let me see.
P = 2L + 2W
30 = 2L + 2x
(30 - 2x) = 2L
(30 - 2x)/2 = L
A = LW
A = [(30 - 2x)/2]x
Correct?
I guess we can simplify a little more.
A = x(15 - x)
Correct?
Given the width of a rectangle whose area is 25ft^2 is x, find the perimeter of this rectangle.
Let me see.
A = L•W
25 = L•x
25/x = L
P = 2L + 2W
P = 2(25/x) + 2x
P = (50/x) + 2x
Is this right?
If it is right, use the inequality below to show that P ≥ 20.
In the following inequality, a...
I have some data points that I want to plot and suppose I have the function ##f(x) = x##, with the domain having the range ##0\leq x \leq 10##. Assume that the experimental values lies in the range ##4\leq x \leq 7##, how can I put a rectangular region to cover this range behind my plot so as to...
Homework Statement
Find the rate of change of the area of a rectangle whose area is 75cm^2. The length is 3 times the width. The rate of change of the width is 2cm/second.
Homework EquationsThe Attempt at a Solution
A=75 A'=?
L=3x= 15 L'=6
W=x=5 W'=2
A'=L'W+LW'
A'= (6)(5)+ (15)(2)
A'=60cm/sec
Yes, one more reason to be humble, I know. This is the simplest problem I couldn't solve so far.
Assume we have a circle of center O, a ruler of arbitrary size and a pencil.
We use the ruler and the pencil to choose 4 points on the circle - the extremities of two diametral/diagonal segments...
Rita wants to cover a roughly rectangular area with netting. The height is 9 feet (but one side is along a solid fence, so could be 4 feet), two sides are each 6 feet, and the other side is 5_1/2 feet. How much netting does she need? Netting comes as a rectangular or square piece.
My Work:Let A...
Homework Statement
Gelfand - Algebra p.115 problem 264:
Prove that a square has the minimum perimeter of all rectangles having the same area.
Hint. Use the result of the preceding problem.
Homework Equations
Preceding problem: Prove that a square has the maximum area of all rectangles having...
Hello.
I am currently working with a beam with the following cross-section:
It consist of three bended sections with the following parameters, alpha = 90 degrees, Thickness = 4 mm, Radius = 50.59 mm.
The top section consist of a small triangle and a rectangle. the triangle have a width = 4 mm...
Homework Statement
A rectangular windshield is to be assembled by installing a glass plate on a 3 ft by 1 ft frame at 60°C. The glass plate is cut at 68°F in such a way that its length is three times its width. The linear expansivity of glass is 5 x 10-6 /C°. (a) What area of the glass plate at...
I know that the height is not 2 somewhere around 1.9 or 1.85 which is the f()
It is x = 1.0 and x = 1.5
and the strip of the shaded is 0.5 unit wide
Somehow i can get the asnwer
Homework Statement
In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) .
Homework EquationsThe Attempt at a Solution
I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length...
There's a rectangle which the length is x+1 and the breadth is x.
X is -1\pm\sqrt{11}
Show that the area is 11-\sqrt{11}
The workings I have done for far are below.
(-1\pm \sqrt{11})*(-1 \pm \sqrt{11} +1)
(-1\pm \sqrt{11})*( \pm \sqrt{11} )
(-1\pm \sqrt{11})*( \pm \sqrt{11} )
(-1\pm...
1. Homework Statement
calculate the area and perimeter of 2 rectangles(two objetcs and one builder), print the sides, area and perimeter, the function printrectangle must identify which side belongs to base and height...
the teacher suggest this in private: float side1 float side2
and this in...
Hi
I have a question about temperature rise and thermal conductivity.
If I have a small 1 watt heater (3 x 3 x 3mm) in the middle of a rectangular block (100x40x70mm) made of a material that has a thermal conductivity of 0.48W/mk, how do I work out the final temperature that the block settles...
Hello,
How can I use Lagrange Multipliers to get the Extrema of a curve f(x,y) = x2+4y2-2x2y+4 over a rectangular region -1<=x<=1 and -1<=y<=1 ?
Thanks
Homework Statement
I'm having issues with a Laplace problem. actually, I have two different boundary problems which I don't know how to solve analytically.
I couldn't find anything on this situations and if anybody could point me in the right direction it would be fantastic.
It's just Laplace's...
Homework Statement
Given A = [2, 9, 8], B = [6, 4, −2] and C = [7, 15, 7], show that AB and AC are perpendicular, then find D so that ABCD forms a rectangle.
Homework Equations
Dot Product
The Attempt at a Solution
The vector AB = B - A = [4,-5,-10]
The vector AC = C - A = [5,6,-1]
AB⋅AC...