Triangle Definition and 1000 Threads

Homework Statement Here is a drawing with all the needed variables: http://i.imgur.com/192GI.jpgHomework Equations The Attempt at a Solution I have been trying to figure out how this approximation is derived for some time now and have no progress to show for it. Any help in figuring out the...

Homework Statement When the sun is 74° above the horizontal a vertical flag pole casts an 8.5m shadow on the horizontal. Find the shadow cast when the sun lowers to 62° above the horizontal. Homework Equations The Attempt at a Solution I drew the following diagram...

I'm having a hard time figuring out what to do here and it feels as though it involves converting the function into polar coordinates but I'm not a hundred percent sure. Essentially, I have a triangle in which two sides are straight and one side is a curved function. Knowing only the length...

Homework Statement Hi I am really stuck on this problem. It reads as such: A uniform triangular lamina is isocceles and has the line y= 4 as its axis of symmetry. One of the vertices of the triangle is the point (2,1). Given that the x-co-ordinate of the centre of mass of the lamina is -3...

Homework Statement The circle x2 + y2 - 4x - 4y + 4 = 0 is inscribed in a triangle, which has two of its sides along the coordinate axes. If the locus of the circumcentre is of the form x + y - xy + k(x2 + y2)1/2= 0. Find k.The Attempt at a Solution The centre of the given circle is (2,2) and...

Homework Statement Prove that ||a|-|b||\leq |a-b| for all a,b in the reals Homework Equations I know we have to use the triangle inequality, which states: |a+b|\leq |a|+|b|. Also, we proved in another problem that |b|\leq a iff -a\leqb\leqa The Attempt at a Solution Using the...

Homework Statement How many different paths will spell the word BINOMIAL in the following arrangement(moving diagonally downwards to the left or right)? ...B ...I I ..N N N O O O O .M M M ...I I ...A ...L L Homework Equations The Attempt at a Solution Starting from B using Pascal's Triangle...

Homework Statement What is the moment of inertia WRT to the x-axis (Ix) of a right triangle with base b and height h where the legs of the triangle coincide with the x and y axis? It would be helpful to know both the single integral and double integral method. Homework Equations Ix=int(y^2 dA)...

Homework Statement Problem: Find the force on one face of a right triangle of sides 4 meters and altitude of 3 meters. The altitude is submerged vertically with the 4 meter side in the surface. The selections by the way are a. 58.86 kNewton b. 53.22 kNewton c. 62.64 kNewton d...

Homework Statement How can I find the center of mass of a right triangle, of height h, length a, and mass m, without using calculus? Homework Equations The Attempt at a Solution I just need a hint on how to start please

Homework Statement Without parameterizing the path, determine what the value of the line integral (integral of F dot dr) is, if C is the closed, oriented path that travels around the triangle with vertices (0,0) (5,2), and (-3,6) and F=yi + xj Homework Equations Curl possiblY? The...

Homework Statement O is any point inside the triangle ABC. AO, BO, CO are joined and produced to meet the opposite sides BC, CA, and AB at D,E and F respectively. Prove that AO/AD+BO/BE+CO/CF=2 Homework Equations The Attempt at a Solution Obviously, O is meant to be the...

Homework Statement Let ABC be a triangle in which angle A = 600. Let BE and CF be the bisectors of the angles B and C, with E on AC and F on AB. Let M be the reflection of A in the line EF. Prove that M lies on BC. http://img135.imageshack.us/img135/606/sumu.png The Attempt at a Solution I...

Homework Statement You're given a hoop with mass m and radius R balanced on top of a knife blade. (The diagram looks like a triangle with a circle balanced on the tip.) Find the period of small oscillations. (Yes, that is all the problem says.) Homework Equations Moment of inertia of a...

Homework Statement a line passes through the point (1,1/8) and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B? Homework Equations i came up with three slopes for this line m1=-b/a...

How would I find the maximum area of a triangle given a fixed perimeter? I assume that it would be an equilateral triangle, but I'm finding it very hard proving it. I started by drawing a triangle of side lengths a, b and P -(a+b) with angles of alpha, beta and gamma. I then used the...

Prove that in any triangle ABC with a sharp angle at the peak C apply inequality:(a^2+b^2)cos(α-β)<=2ab Determine when equality occurs. I tried to solve this problem... I proved that (a^2+b^2+c^2)^2/3 >= (4S(ABC))^2, S(ABC) - area but I don't know prove that (a^2+b^2)cos(α-β)<=2ab :(...

Homework Statement what is the resultant vector of an isosceles triangle? Homework Equations R^2=a^2+b^2-4abcos(theta) The Attempt at a Solution The books answer R=2acos(theta/2) Using the formula above, and knowing that a=b in a isosceles triangle I am getting...

A triangle has sides of length 10 and 14 units respectively, and one of the non-included angles is 30 degrees. Find the possible lengths of the third side. The answers is the product of these lengths.

Is it true in general that: |\int f(x)dx| < \int |f(x)|dx Not sure if "Triangle Inequality" is the right word for that, but that seems to be what's involved.

The problem Can anyone explain me a step given in my book? This is actually the derivation of the distance between orthocentre and circumcentre of a triangle using vectors. ABC is a triangle. S is the circumcentre and H is the orthocentre. \vec{SA} + \vec{SB} + \vec{SC} = \vec{SA} +...

Homework Statement I know traditionally the center of mass of a triangle is 2/3 the way down its height, but i believe it varies here due to the uneven mass distribution. Here i have to find the center of mass distance from Q http://img508.imageshack.us/f/scn0001p.jpg/ Here is an image...

Homework Statement [PLAIN]http://img59.imageshack.us/img59/9484/fp5.gif to find the moment of inertia through point A Homework Equations I = \int{r^2dm}The Attempt at a Solution Used a double integral from point A: \displaystyle\int_{0}^{h}\displaystyle\int_{-L/2}^{L/2}\rho(x^2+y^2)dxdy =...

Homework Statement Two point particles of mass m are attached to two vertices of an equilateral triangle made of three massless rigid rods of length l. The third vertex is pivoted to a fxed point, so that the triangle can swing in a vertical plane under the effect of gravity. The system...

Homework Statement I need to calculate center of mass of this isosceles triangle using integration: the density is constant. Homework Equations Rcm = integral(xdm) / integral(dm) The Attempt at a Solution I know how to begin: dm = density * dx * dy; x = double-integral(x*dx*dy)...

Homework Statement Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.23 m. Two of the spheres have a mass of 2.84 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces...

The "Tetraktysal Kissing Triangle" (TK_n) & Lower Bounds of Kissing Numbers to D=10 The Tetraktysal Kissing Triangle (TK_n) Nickname: "The TetraKiss Triangle" A Fibonacci, Lucas, Tetrahedral Convolution Construction for Lower Bounds of Sphere Packings to Dimension 10 Based Upon the Pythagorean...

Homework Statement Two sides of a triangle of fixed length measure 12m and 15m. The angle between these two sides increases at a rate of 2 degrees per minute. When the angle between these two sides is 60 degrees, at what rate is the third side increasing? Homework Equations That's the...

Homework Statement d(x,y)=(a|x_1-y_1|^2+b|x_1-y_1||x_2-y_2|+c|x_2-y_2|^2)^{1/2} where a>0, b>0, c>0 and 4ac-b^2<0 Show whether d(x,y) exhibits Triangle inequality? Homework Equations (M4) d(x,y) \leq d(x,z)+d(z,y) (for all x,y and z in X) The Attempt at a Solution I...

Homework Statement A small map shows Atlanta to be 730 miles in a direction of 5 degrees north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21 degrees west of north from Atlanta. Assume a flat Eath and use this information to find the displacement from...

Homework Statement In the figure, a 60 cm length of uniform wire, of 60 g mass, is bent into a right triangle. The x- and y-coordinates of the center of mass, in cm, are closest to... I am going to explain the picture in my textbook. The origin is at (0,0). It goes up 10 cm and to the...

A system consists of three particles located at the corners of a right triangle as shown below. Mass 1 is 7.0 kg, mass 2 is 6.4 kg, and mass 3 is 9.9 kg. If the distances a equals 15.8 m and b equals 2.0 m, then what is the center of mass (in m) in the vertical direction? Y center of...

Three objects of different masses are located at the corners of the triangle shown in the picture. If distance a equals 4.21 m, b equals 1.55 m, and c equals 11.93 m, then what is the center of the mass (in m) of the system in the horizontal with respect to the origin? X center of...

See if anyone can help me with this: Among all triangles of perimeter equal to P, find the one with the largest area. (Hint: use the formula A=\sqrt[ ]{p(p-x)(p-y)(p-z)} where P=2p, P is the perimeter). So, I have f|_s , I think that must be solved using Lagrange multipliers, at least I don't...

Hi all! I am still a GR noob and this example has been puzzling me for a while, so I need some help that's hopfully. Let's imagine that there are stars A and B at 10 LY from Earth (at point C) each and 10 LY from each other. A signal is sent every year from Earth (C) indicating the...

Homework Statement Find the center of mass for the following triange: http://www.ehow.com/how_5132033_calculate-hypotenuse.html above is a picture of a triangle, it is a right triangle the side labeled a in the picture is a length of 1 and side b is length of 2, the total weight of...

Homework Statement A metal sign for a car dealership is a thin, uniform right triangle with base length b and height h. The sign has mass m. What is the moment of inertia of the sign for rotation about the side of length h? Homework Equations I = \intr^{2}dm The Attempt...

I was wonder what conditions a and b have to be for each inequality in order to satifsy the equality?

Homework Statement a right triangle. hypotenuse is 10, the opposite is 8, and the adjacent is 6 Sine .6 Cosine .8 Tangent .75 i need to find angle A (aka Alpha in the problem) With out using a graphing or scientific calculator. Homework Equations i was told to use...

Homework Statement A right angle is moved along the diameter of a circle of radius a (see diagram). What is the greatest possible length (A+B) intercepted on it by the circle. Homework Equations so, the pythagorean theorem might be useful diameter = 2a The Attempt at a Solution...

Hello. In the Wiki entry for "Leibniz harmonic triangle" there one can find a formula L(r, c) = 1/(c * binom(r - 1, c - 1)) where L(r, c) is the entry in the harmonic triangle and the binom() is the usual binomial notation (or the entry from Pascal triangle). I tried to prove the...

Homework Statement Radio direction finders are set up at points A and B, 8.68 mi apart on an east-west line. From A it is found that the bearing of a signal from a transmitter is N54.3*E, while from B it is N35.7*W. Find the distance from B, to the nearest hundredth of a mile. A person...

Hello, given a set \Omega, we consider all its subsets A_1,A_2,A_3,\ldots with same cardinality k. Do you have some hint in order to prove the following: \forall A_x,A_y,A_z\subseteq \Omega such that |A_x|=|A_y|=|A_z|=k |A_x-A_z| \leq |A_x-A_y|+ |A_y-A_z| Thanks

ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle

Pretty much knows the triangle inequality. \left| a + b \right| \le \left| a \right| + \left| b \right| I was reading a source which asserted the following extension of the triangle inequality: \left| a + b \right|^p \le 2^p \left(\left| a \right|^p + \left| b \right|^p\right) This is...

Hi, I'm looking for an efficient way of achieving the following, but having trouble thinking it through: Let's say I have a triangle in three dimensions with vertices A, B and C. Let's say I also have a three dimensional coordinate D. I know the x and z component values for D and I am...

[FONT="Arial Black"]hi every body show if Xn→x then lXnl→lxl hint use trangle inequality 2/ show if lXnl→0 then Xn →0 show by example that lXnl fore all n in N MAY CONVERGE and Xn may not converge

Homework Statement The question says to find a proof for Cauchy's Inequality and then the Triangle Inequality. This is an elementary linear algebra class I'm doing, so I can't use inner products or anything. Homework Equations The Attempt at a Solution I got the proofs using algebra, but I'm...

Homework Statement An object moves around a equilateral triangle with a constant speed (magnitude of velocity is constant) of 22.3 m/s. If it moves from the starting to ending point (as shown below) in a time of 12.69 seconds, what is the magnitude of the average acceleration vector in m/s2...

The area of the triangle in the attachment has to be found. It is not stated in the question what kind of a triangle it is nor are there any angles given. I believe that there is information that has been left out of the diagram to solve this question (This is a question in a maths...