Rectangle Definition and 239 Threads

Homework Statement Stewart Calculus 6E, 3.8 #4 4.) The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 10cm, how fast is the area of the rectangle increasing? Homework Equations A = LW The...

hi all, I am suppose to compare the area of curve y=x2 with rectangles beneath that curve to show that, 1/2 + 1/3 + ...+ 1/n < log(n+1) i believe this some sort of harmonic series. Is there a way around this problem? Regards

Homework Statement http://www.electron.rmutphysics.com/physics/charud/scibook/Physics-for-Scientists-and-Engineers-Serway-Beichne%206edr-4/32%20-%20Inductance.pdf Please flip to page 11/30 you will see a coaxial cable. Read to the end where they begin integrating using Guass's Law...

Homework Statement find |B| at the center of a rectangular loop of wire of sides a and b carrying current I Homework Equations B = uI/2piR The Attempt at a Solution - current flowing counterclockwise - original art work :D I did the proof for biot savart law as a...

Homework Statement A rectangular field to contain a given area is fenced off, along a stright river. if no fencing is required along the river, show that the lest amount of fencing will be required when the length of the field is twice its width. Homework Equations N/A The Attempt...

Homework Statement Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm. the two sides of the rectangle lie along the legs. Homework Equations N/a The Attempt at a Solution

Hi, How to insure that a rectangle \mathbf{R}=\{\mathbf{x}\in R^n:\mathbf{l}\leq\mathbf{x}\leq\mathbf{u}\} lies inside a polyhedron \mathbf{P}=\{\mathbf{x}\in R^n: \mathbf{A}\mathbf{x}\leq\mathbf{b}\} Thanks

Homework Statement Let A(x) be the area of the rectangle inscribed under the curve y = e^-2x^2 with vertices at (-x, 0) and (x, 0), x >= 0 a.) find A(1) b.) what is the greatest value of A(x)? justify your answer c.) what is the average value of A(x) on the interval 0 <= x <= 2 The...

Homework Statement A cmedium carbon steel rod has a rectangular cross section and must cope with a tension of 29 430 Newtons . The thickness of the rod is 15 mm calculate the siz of the cross section? Homework Equations A=P/Ok [b]3. The Attempt at a Solution [/b O = UTS = 750...

I'm hoping for some help as it has been 20 years since I last used trigonometry and Google has come up empty. I'm programming simple image editing software and for a crop function I need a formula to calculate the sides of the largest possible rectangle inside a rotated rectangle, given the...

Find the area of the largest rectangle that can be inscribed (with sides parallel to the axes in the ellipse). x^2/a^2 +y^2/b^2 = 1 I came across the above problem and am not sure how to proceed with it. I drew the ellipse with the inscribed rectangle and tried repositioning the ellipse so...

The question says: Show that if Q = [a1,b1]x...x[an,bn] is a rectangle, the Q equals the closure of Int Q. The definition of closure that I have is Cl(A) = int(A) U bd(A). So I'd like to show that Cl(int(Q)) = int(int(Q)) U bd(int(Q)). But this just seems to be obvious to me which just makes...

Homework Statement http://www.webassign.net/mapleplots/d/e/f859372171ea15352ef17952ba81cb.gifv Use the rectangles in each graph to approximate the area of the region bounded by y = sin(x), y = 0, x = 0, and x = π. (Round your answer to three decimal places.) Homework Equations...

Homework Statement There is no specific problem, I'm just confused after reading the chapter. Consider a pyramid 3 m high with a square base that is 3 m on a side. The cross section of the pyramid perpendicular to the altidude x m down from the vertex is a square x m on a side. Now I...

Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)

if the length of a rectangle = x, show that the area of the rectangle is given by A = 8x - x[2]

Homework Statement Determine the moments of the inertia of the Z-section about its centroidal x0 and y0 axes. I didn't draw them in, but the x0 axis is 80[mm] up from the bottom and the y0 axis is 90[mm] from the left most point. So it is in the middle of the piece. The Attempt at a...

Hi all, first post here but I've long browsed these forums for answers in the past. I couldn't find an answer to my question through searching but I appologise in advance if it has been asked before. Homework Statement I want to find an expression which relates second moment of area to...

Homework Statement Consider charges placed at the corners of a rectangle. This rectangle is a horizontal rectangle and is .43 m long and .25 m wide. At the upper right corner there is a charge of 7.0 µC. At the bottom right there is a charge of -14 µC. At the bottom left there is a charge of...

Homework Statement Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the ellipse x^2 + 4y^2 = 4 Homework Equations The Attempt at a Solution I simplified the equation of the ellipse into the ellipse formula: x^2/4 + y^2 = 1...

Homework Statement A rectangle has sides of length 5cm (right and left) and 15cm (top and bottom). Top left corner has charge (q1) = -5uC Top right corner has charge A = ? Bottom left corner has charge B = ? Bottom right corner has charge (q2) = 2uC a) What are the electric...

Homework Statement A rectangle is placed symmetrically inside an ellipse (i.e. with all four corners touching the ellipse) which is defined by: x^{2} + 4y^{2} = 1 Find the length of the longest perimeter possible for such a rectangle. Homework Equations Within the problem...

Homework Statement The number of lines from A to B if you must travel along the lines going up and right is... (there is a rectangle with that has 4 cubes going down vertically and 7 horizontally (4x7) and a is at the bottom left, be is at the top right)

Homework Statement If the perimeter of a rectangle is fixed in length, show that the area of the rectangle is greatest when it is square Homework Equations The Attempt at a Solution if the perimeter is fixed in length, then 2x + 2y = c then no idea to continue from there

Homework Statement The overall question is to construct an asymptotic approximation for a harmonic field on a rectangle with a small disk. However, I'm having difficulty finding the unperturbed field. Perhaps I've been staring at it for too long, but I can't seem to find a solution. The...

Homework Statement Let Q=I\times I (I=[0,1]) be a rectangle in R^2. Find a real function f:Q\to R such that the iterated integrals \int_{x\in I} \int_{y\in I} f(x,y) \; and \int_{y\in I} \int_{x\in I} f(x,y) exists, but f is not integrable over Q. Edit: f is bounded Homework...

I'm trying to figure out the radius of gyration of the frame about O. Homework Statement A rectangular frame is put together with massless rods having identical 1.8 lb weights placed at the corners as shown in the figure. The frame is pivoted about an axis passing through O, the center of...

Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...

Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...

Homework Statement Find the average value of f(x,y)=sin(x+y) over the rectangle 0 ≤ x ≤ pi, 0 ≤ y ≤ pi. Homework Equations I need to know if this is the right answer please. The Attempt at a Solution I got 1/pi as a answer.

Homework Statement The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing? Homework Equations V=LW The Attempt at a Solution dL/dt=8...

Homework Statement Imagine you're given a rectangle, with lengths LX and LY. Now we place a point somewhere inside this rectangle, we don't know where it is. What we DO know, is the angle between lines from the corners to that point. (such that if it was at the center, and the point a square...

Homework Statement A rectangular plate is acted upon by the force and couple shown. This system is to be replaced with a single equivalent force. a) for a(alpha)=40 degrees, specify the magnitude and the line of action of the equivalent force. b)Specify the value of a(alpha) if the line of...

I am hoping to find the coordiantes of all 4 vertices when the rectangle is in any orientaion knowing the length l, the width b, the coordinate of its center mark (xcen,ycen), and the coordinate of vertex A as shown below: This is NOT HOMEWORK so although I think it is possible to do, I am...

Hi I'm writing a newspaper page management application and am having trouble trying to directly calculate a "best fit" column/row breakdown for displaying pages into arbitrary rectangles. The arbitrary rectangle in question is the content area of a window and can be resized at will by the...

A uniform 10 cm x 20 cm box is placed on a ramp that rises at angle theta above the horizontal. Assuming that there is enough friction to prevent this box from sliding, what is the largest that theta can be without tipping it over? do i use torque = r*F*sin*(theta), if so how do i use it?

Homework Statement If I have a rectangle rotated at a known angle with respect to a rectangle of known dimensions that inscribes it, how can I find the dimensions of the inscribed/inner rectangle...

I understand calculus, I just don't understand how it is applied to solve these sorts of problems. Homework Statement What is the smallest perimeter for a rectangle with an area of 16, and what are its dimensions?Homework Equations A=L*W P=2W+2L The Attempt at a Solution I managed to get the...

Homework Statement Find the dimensions of of the rectangle with perimeter 200 meters that has the largest area. Homework Equations The Attempt at a Solution This is in the section on Global Maxima/Minima so I know it has to be something with graphing a formula and finding the...

Homework Statement I'm having issues with a deceptively simple Laplace problem. If anybody could point me in the right direction it would be fantastic. It's just Laplace's equation on the square [0.1]x[0,1] (or any rectangle you like) with a mixed boundary. Homework Equations...

Homework Statement What is thea are of the largest rectangle that can be inscribed in the ellipse 4x^2 +9y^2 = 36 A) 6 rad 2 B) 12 C)24 D) 24 rad 2 E) 36 Homework Equations Must be done using optimization and first derivitive The Attempt at a Solution I know I have to use A=...

I have a rectangle i am rotating in 3d on multiple axis. i am trying to calculate the 2d height of the rectangle and I am quite lost. For example, if i rotate the rectangle on the x-axis so the top of the rectangle comes forward and the bottom moves back. i can calculate the height of this...

Hi all: My question is how to calculate the overlapped area of a triangle and rectangle. It sounds a simple question but is there any way to do it efficiently? And is it possible there is a uniformed equation to solve such a problem? As there are many cases the triangle can overlap with...

Homework Statement A rectangle has a constant area of 200m2 and its length L is increasing at the rate of 4 meters per second. Find the width W at the instant the width is decreasing at the rate of 0.5 meters per second. Homework Equations A=200 dA/dt =0 (since the area is constant)...

Homework Statement I have to solve the integral of (ytan^-1(x) - 3) inside the area of the rectangle with vertices (1,0), (0,1), (2,3), (3,2). How do I set up these limits? Homework Equations This is a tilted rectangle so I can't use just values for the limits? The Attempt at a...

Homework Statement Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. Homework Equations (x-a)^2 + (y-b)^2 = r^2 max area = 2x(2y) = 4xy The Attempt at a Solution (x-a)^2 + (y-b)^2 = r^2 = y=r-(x-a)+b I then plug...

Homework Statement Largest possible area of a rectangle inscribed in the ellipse (x2/a2)+(y2/b2)=1 Homework Equations Area of the rectangle = length*height The Attempt at a Solution I have it set up so that the four corners of the rectangle are at (x,y) (-x,y) (-x,-y) (x,-y) and that...

Homework Statement A rectangle has sides on the x and y axes and a corner on the plane x+3y=12. Find its maximum area. Homework Equations A=xy=(12-3y)y (A=12, according to the solution manual.) The Attempt at a Solution At first I thought the corner it was talking about lay...

1) Homework Statement [/b] The surface density of a rectangle varies as: σ(x,y)=12 kg/m2+2 kg/m4(x2+y2) The origin is located at the lower left corner of the rectangle, at point ``A.'' The rectangle has a height h=1.00 m and a length l=1.20 m. What is the total mass of this object?

The Problem is finding the E-field at a point P that is h distance from the center of a rectangle (along a line normal to its surface) with Length L and width W with a constant charge density sigma. This is for an intro E&M class that is supposed to use up through calculus 2, and we have not...