Rectangle Definition and 239 Threads

Homework Statement Let K ={(x,y)\inℝ2:|x|≤1,|y|≤1} Prove that K is a connected subset of ℝ2 The Attempt at a Solution Suppose f:[-2,2]→K and define f(x)={(x,y):|y|≤1} Dist(f(x),f(y))=sup(d(a,b):a\inf(x),b\inf(y))=d(x,y)=|x-y|. Using this equality it is easily shown that f(x) is...

Justin on Facebook writes:

I have a group of 8 3-D points which all sit on an arbitrary plane (The points were generated by projecting the corners of a axis aligned cube, box, onto the plane) I wish to group all the points in a rectangle with the smallest surface area - so a tight fit rectangle. What I am doing at...

Hello MHB, I wanted to 'challange' myself with solve a problem with midpoint and rule and the double integral f over the rectangle R. This is a problem from midpoint. "Use the Midpoint Rule m=n=2 to estimate the value of the integrab $$\int\int_r(x-3y^2)dA$$, where $$R= {(x,y)| 0\leq x \leq 2, 1...

Hi Folks,I have come across some text where f(x,y)=c_1+c_2x+c_3y+c_4xy is used to define the corner pointsf_1=f(0,0)=c_1 f_2=f(a,0)=c_1+c_2a f_3=f(a,b)=c_1+c_2a+c_3b+c_4ab f_4=f(0,b)=c_1+c_3bHow are these equations determined? F_1 to F_4 starts at bottom left hand corner and rotates counter...

Folks, I have attached a picture illustrating the labelling of the linear reactangle element which can be represented by the following equation ##u(x,y)=c_1+c_2 x +c_3 y +c_4 xy## (1) ##u_1=u(0,0)=c_1## ##u_2=u(a,0)=c_1+c_2a## ##u_3=u(a,b)=c_1+c_2a+c_3b+c_4ab##...

Homework Statement Let R be the region bounded by x^3/2+y^3/2=a^3/2 (x>0, y>0) and the coordinate axes x=0, y=0. Express it in double integral over a rectangle. Homework Equations The Attempt at a Solution How to solve this people please? I tried a couples time but failed to find v u which...

Homework Statement Let S be the self-intersecting rectangle in ##\mathbb{R}^3## given by the implicit equation ##x^2−y^2z = 0##. Find a parametrization for S.Homework Equations The Attempt at a Solution This is my first encounter with a surface like this. The first thing that came to my mind...

Homework Statement Figure 29-36 shows a rectangular, 15-turn coil of wire, 10 cm by 5.0 cm. It carries a current of 0.90 A and is hinged along one long side. It is mounted in the xy plane, at an angle of 30° to the direction of a uniform magnetic field of 0.50 T. Find the magnitude and...

Homework Statement Find the largest open rectangle in the ty-plane that contains the initial value point and satisfies the following theorem: Let R be the open rectangle defined by a<t<b, α<y<β. Let f(t,y) be a function of two variables defined on R where f(t,y) and the partial derivative...

I found one interesting example... We have a rectangle ABCD with his perimeter o. Where is the set of points when their (for each point) sum of distance lines AB, BC, CD, DA is 2/3o ? I tried it, but geometric problems is quite hard for me and I don't know how do it. So, have you got any...

To anyone who saw my previous thread, yes, this is quite similar to it :-p. Homework Statement Given a rectangle, say a painting, with with mass m, height h, and width w with two point supports to a wall at its two upper corners, what force does each support exert? Homework...

Homework Statement the perimeter of a rectangle is 24 ft. the length is 4 ft longer than the width find the dimensions width x length x+4 however, I should be doing it like this: a first equation should start like: 2x+2y=? and the second should start like x=y+? so what's the...

Homework Statement Find the second moment of inertia of a rectangle. The Attempt at a Solution Anyone know why my answer is 4 times too big?

Homework Statement A rectangle is 2 metres longer than it is wide. On the other hand, if each side of the rectangle is increased by 2 metres, then the area increases by 24 square metres. Find the side-lengths of the rectangle. Homework Equations The Attempt at a Solution So my...

Homework Statement Solve Laplace's equation on the rectangle 0< x< L, 0< y< H with the boundary conditions du/dx(0, y) = 0, du/dx(L, y)=y, du/dy(x, 0)=0, U(x, H)=x. Homework Equations The Attempt at a Solution I would be able to solve it by separation of variables if the last...

Homework Statement In how many different non-overlapping ways can a (2 x 10) rectangle be covered by (1 x 1) and (1 x 3) rectangles. Homework Equations The Attempt at a Solution I've never done any question like this. The only solution I can think of is a brute force method but I doubt...

If I want to make a Square or Rectangle storage tank 5 feet deep and 22 feet long and 1 foot wide. The tank will be under 30 psi and also vacuum. That’s not hard to do what I want is the walls not to deflect more then .001 of an inch. The walls can be plastic, plywood with a steel sheet or...

Is the white region a square or rectangle? See my post below for image

"Rectangle Method" for approximating an integral has been rediscovered! http://care.diabetesjournals.org/content/17/2/152.abstract Is this some kind of joke? Has anyone else seen this article before? This is what I felt like after reading it:

Homework Statement Show that the maximum possible area for a rectangle inscribed in a circle is 2r^2 where r is the radius of the circle.Homework Equations Pre-calc ! NO TRIG ! Doesn't matter if it's easier, it's supposed to be solved with algebra. The Attempt at a Solution I have no clue...

Why does the formula [P±√(P^2-16A)]/4 give the values of either of two different lengths of a rectangle? (P is perimeter and A is area) I derived it by solving two simultaneous equations, A = xy and P=x+y and then applying the quadratic formula to the resulting second-order equation 2y^2 +...

This is not really a homework problem, I'm just doing it as an exercise puzzle. I think I'm on the right track, but at this point I feel a little exhausted and would love a hint. Homework Statement Let C be a unit circle: x^2+y^2=1 . Let "p" be a point on the circumference and "q" be a point...

Greetings, I will describe the problem and my proposed solution which leads me to the load bearing question.. Problem: Pickup camper cabover floor is compromised where it attaches to the driver side sidewall, i.e., separation of floor from sidewall due to some dryrot and a blowout doing...

Homework Statement Cross sections are perpendicular to the x-axis and rectangle has the h=1/2b. The region is bounded by the area y=x^2, x-axis and the line x=3 Homework Equations The Attempt at a Solution A=BH A=B(1/2B) A=3/2B V=3/2(x^2-3) just wondering if this is correct...

I'm looking for a 'covering rectangle with smaller rectangles' algorithm with the unique feature of being able to exclude some possible center points of rectangles. Basically, limiting the possible areas the smaller rectangles can be placed, while still having the algorithm try to solve for...

Hi there. I'm having some trouble with some double integrals here. All of them are to be evaluated on the rectangle_{} 1≤x≤2, 0≤y≤1, and the functions are: 1: \int\int_{A}\frac{1}{x+y}dxdy. On this one I made α(y)=\int^{2}_{1}\frac{1}{x+y}dx=ln(\frac{2+y}{1+y}), and finally I should evaluate...

Homework Statement A force acting on a particle moving in XY plane is given by F= 2y i + x^2 j . particle moves from origin to a final position having coordinates (x,y)=(5,5). calculate the work done by force F along B_____________C | | |...

Hey All, I'm trying to create a 3-D rectangle in Mathematica with the following measurements: Mass M=1.5 kg, and sides of length a=10 cm (parallel to the x-axis), 2a (parallel to the y-axis), and 3a (parallel to the z-axis). Let one corner be at the origin, and let the three adjacent edges...

Let's say you have four points that define a rectangle in the xy plane centered at the origin (with the x,y axes bisecting the sides). How can you transform these points so that the rectangle lies in an arbitrary plane (defined by a point p and a normal vector n) so it is centered about point p...

Suppose I have a rectangle with length x and height y:Can this ever be true? That xy = 2x+2y? My guess would be that area of a shape can never equal the perimeter of that shape. And that would be confirmed by the fact that the equation is always false (except if both variables equal zero...

Find the integral $$ \int_C\frac{dz}{z^2 - 3z + 5} = \int_C\frac{dz}{\left(z - \frac{3}{2}-i\frac{\sqrt{11}}{2}\right)\left(z-\frac{3}{2}+i\frac{\sqrt{11}}{2}\right)} $$ Where the path is a rectangle oriented clockwise from (0,0) to (0,4) to (10,4) to (10,0) to (0,0). So $z_1 =...

How can I draw a rectangle oriented clockwise on the complex plane with vertices on (0,0), (0,4), (10,4), and (10,0)? I am guessing the tikz package needs to be used but I am not skilled in making pictures.

Homework Statement A beam of electrons is fired into a rectangular region of space that contains a uniform magnetic field in the -z direction. The electrons are moving in the +x direction, as shown. The speed of the electrons in the beam is 6.00 × 106 m/s. The mass of an electron is me =...

Continious FT of a rectangle is real valued but DFT of it is not!? Continious Fourier Transform of a rectangle with amplitude of 1 between [-u,u] is a real valued function (u is a positive number). Actually it is a sinc function. However when I use discrete Fourier Transform (fft) I obtain...

Hi Given a simple linear equation and the extents of a rectangle, is there a neat way of finding the length of the line section that is contained within the rectangle? The only general method i can think of would involve a bunch of conditional statements to determine whether the line...

Homework Statement This question is taken from 2011 Malaysian Mathematical Olympiad. Mary is standing in a rectangular garden. Her distance to the four corners of the garden are 6 m, 7 m, 9 m and d m, respectively, where d is an integer. Find d. Homework Equations Triangle...

Homework Statement Let R be the rectangle bounded by x - y = 0, x - y = 2, x + y = 0, and x + y = 3. Evaluate \int\int(x + y)ex2-y2dA R The Attempt at a Solution First I rewrote the boundaries so that I could graph them more easily. I got y = x, y = x - 2, y= -x, and y = -x + 3. I was going...

Homework Statement Homework Statement Suppose that a square hole with sides of length 2 is cut symmetrically through the center of a sphere of radius 2. Show that the volume removed is given by where I'm not sure how to approach this, but I figure you can express the sphere in...

Homework Statement This problem had been previously posted, however i have specific questions about it and don't feel that it was completely answered for it did not explain how you use the extreme value theorem in the problem and specifically, HOW DO YOU GET THE INTERVAL [a,b], The answer has...

Homework Statement I was trying to find the moment of inertia of a rectangle with width a and height b were axis of rotation is through it's center of mass Homework Equations The Attempt at a Solution I = integral r^2 dm rho = dm/dA dm = rho dA If I take an infinitely small...

Homework Statement Consider a large triangle, the tip is located at the origo x=0, it is sloped at an angle θ and -θ relative to the x-axis, relative to the x-axis, its dimensions in x can be considered infinite. A large stripe/strip/band is placed on top of the triangle but perpendicular to...

Homework Statement Determine the electric flux through a 6m by 4m rectangular area. The area is oriented such that a vector normal to its surface points in the [1;6] direction. The electric field is [7;1] N/C. Homework Equations Φ=E·A=EA*cosθ The Attempt at a Solution...

As usual I'm working on a program and I'm having trouble with math/efficiency. Homework Statement I need a way to find out if a circle given as a point and a radius C(x,y,r) fully encloses a rectangle given by the top left corner and the width and height R(x,y,w,h) I only need to know...

What I'm looking for is an algorithm to find the details on the intersection of of a circle and rectangle in two dimensional Euclidean space. The information I need to find is straightforward enough; all I need is to know whether the rectangle and circle are not intersecting, partially...

Homework Statement Find the lengths of the sides of rectangle if perimeter is 7,4 m and area is 3m2. Homework Equations S= 2a+2b and P=ab The Attempt at a Solution So i tried getting a form P --> a=P/b and then subsstituting in perimeter formula a with P/b ---> S=2P/b+2b but i am...

Homework Statement file:///Users/LabGuest/Desktop/CH26.tiff Homework Equations FB= qv cross B The Attempt at a Solution If the the rectangle is parallel to the magnetic field and we know that FB is perpendicular to the B field itself than there should be a net Torque but no net...

in some work I'm doing i have a 2D rectangle that can be rotated and/or translated in any direction in 2D space. for example it might look like this: (x=30,y=-10) +-----------+ (x=30,y=2) +-- +y | | |...

Ciao to everybody, I've encountered frequently, in forums and news groups, questions about a rectangle inscribed in another rectangle, but nowhere a general discussion on ways to solve related problems (i.e., given three of the five quantities involved - 2 sides of outer rectangle, 2 sides...

Hi to everyone. I'm developing a puzzle game which involves some concepts of geometry. Suppose you have a rectangle formed by points A, B, C and D. Now, I add points X1 (lies on line AB), X2 (inside the rectangle) and X3 (lies on line AC). I'd like the output to be the two rectangles...