Triangle Definition and 1000 Threads

Homework Statement two particles with charges 4e and -4e are fixed at the vertices of an equilateral triangle with sides of length a. If k=1/4 pi Ԑ what quantity of work is required to move a particle with a charge q from the other vertex to the center of the line joining the fixed charges...

Homework Statement Given points of a triangle: A(4,1,-2),B(2,0,0),C(-2,3,-5). Line p contains point B, is orthogonal to \overline{AC}, and is coplanar with ABC. Intersection of p and \overline{AC} is the point B_1. Find vector \overrightarrow{B_1B}. Homework Equations -Vector projection - Dot...

Given an Isosceles triangle with the area of 100 with internal angles of $$40^o, 70^o,70^o$$ $A=\frac{1}{2}bh$ so $100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$ $z$ is length of one the equal sides At least started here

Let $a\,b$ and $c$ be the sides of a triangle. Prove that $$\frac{a}{b+c-a}+\frac{b}{a+c-b}+\frac{c}{a+b-c}\ge 3$$.

I believe I could work this problem fine had the instructor not placed statements #3,4, and 6, as well as the reasons # 5 and 7. I can't seem to understand where he's using the transitive property in #5. If these steps weren't here I would assume, I'm only using substitution to prove that "RS"...

Homework Statement Air (assumed incompressible) flows across the rotor shown in the figure such that the magnitude of the absolute velocity increases from 15 m/s to 25 m/s. Measurements indicate that the absolute velocity at the inlet is in the direction shown. Determine the direction of the...

What would the angular velocity for a phasor be for a triangle wave? I think it would vary sinusoidally but I can't find an expression

Hello everyone. I'm learning Trigonometry right now with myself and at current about how to find the trigonometric ratio of the angle (90° + θ) in terms of θ. I'm quite confused in the Figure. How sin(90° + θ) become equal to sin (90° - θ) of triangle P'OM'. I know that triangle P'OM' and POM...

Prove that there exists a triangle which can be cut into 205 congruent triangles.

Homework Statement In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x? Homework Equations I used the cosine rule here The Attempt at a Solution As we have 2 sides and an angle I used the cosine rule - Am I correct? (2) means squared b(2)...

Homework Statement At the vertices of a triangle there are + 5C, -7C, -3C of charge respectively. What is the electric intensity and direction at its orthocentre? Homework Equations Each side of the triangle is 1 mm in length. The Attempt at a Solution [/B] I failed to find the distance of...

Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.

Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.

Calculate the area of a triangle knowing its 3 heights ha = 3 m hb = 4 m hc = 5 m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 10.03 m2 B) 10.04 m2 C) 10.05 m2 D) Imposible

Calculate the area of a triangle knowing its perimeter and 2 heights perimeter = 30 m ha = 8 m hb = 9 mNOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 41.29 m2 B) 42.93 m2 or 36.28 m2 C) 42.95 m2 or 36.29...

Calculate the sides of a triangle knowing its area, perimeter and angle A. Area = 30 m2 Perimeter = 30m Angle A = 30º NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 6.09, 9.36 and 14.55 B) 7.40, 8.63 and...

Homework Statement The triangle formed by the tangents to the parabola y2=4ax, at the ends of the latus rectum and the double ordinate through it's focus is: 1) equilateral 2) acute angles isosceles 3)right angled isosceles 4) dependent on value of a Homework Equations...

Homework Statement http://i.stack.imgur.com/KzCIl.png From the given picture the known quantities are: ##r = 7*3^{1/2} ## ##BC = 13 ## angle opposite to AC is ##120 ## degrees Homework Equations 3. The Attempt at a Solution [/B] I figured i could use a sine rule to get the side ##AC ##...

Homework Statement Given the isosceles triangle whose sides are : c=10 b=13 find the are of a square drawn inside the triangle whose upper edges touch the b sides of the triangle. Homework Equations 3. The Attempt at a Solution [/B] I named the side of the square a. First i made two equations...

Not sure how to solve considering nothing is given as perpendicular or bisected. Is anyone aware on how to solve this problem? ~S.R.K.

Homework Statement The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin. Homework Equations Ar= xy/2 The Attempt at a Solution Derivative of this function is y'=-e^(-x) I took the formula of the...

Homework Statement Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number. Homework Equations For a right triangle (a,b,c) with c is the hypotenuse. $$a^2+b^2=c^2$$ The Attempt at a Solution In order to create a...

Folks, I am puzzled how one obtains equation 3.2.31 based on the schematic as attached! Can you help? Is there an online source I can refer to to learn how to obtain angles and magnitudes of complex schematics? Thanks

Hi, Can somebody please point me into a direction how to solve the attached trig problem? First step, where can I find such values for sin (alpha)?Thanks.

Homework Statement Suppose the isosceles prism of the figure(http://imgur.com/EQiQSoO) has apex angle φ = 53.4° and index of refraction n = 1.41. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of...

I'm not really sure if this is true, which is why I want your opinion. I have been trying to prove it, but it will help me a lot if someone can confirm this. Let ## v_{1}, v_{2} ... v_{n} ## be vectors in a complex inner product space ##V##. Suppose that ## | v_{1} + v_{2} +...+ v_{n}| =...

Find the lengths of the sides of a triangle with 14, 22 and 28 as the lengths of its altitude.

I found this question in my study guide triangle ABC is similar to triangle DEF. Triangle ABC has sides 4,6,8. Wich could be the corresponding sides of a triangle DEF? Indicate all that apply A) 1, 1.5, 2 B)1.5, 2.25, 3 C)6, 9, 12 D) 8, 12, 16 E)10, 15, 20 What I did was add the...

Hi, I'm trying to solve this exercize : I/3 charges Q, positives, are at the corner of an equilateral triangle of centre O, in (x,O,y) . We want to compute the electric field created by the 3 charges on the axis z, passing by O and perpendicular at (x,O,y), thus computing the electric field...

In the triangle a point $$I$$ is a centre of inscribed circle. A line $$AI$$ meets a segment $$BC$$ in a point $$D$$. A bisector of $$AD$$ meets lines $$BI$$ and $$CI$$ respectively in a points $$P$$ and $$Q$$. Prove that heights of triangle $$PQD$$ meet in the point $$I$$. I've tried to show...

Let ${y}_{n}$ be a arbitrary sequence in X metric space and ${y}_{m+1}$ convergent to ${x}^{*}$ in X...İn this case by using triangle inequality can we say that ${y}_{n}\to {x}^{*}$

Homework Statement a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ? Homework Equations x centre of mass...

For the triangle shown in the below image, ##\sin 60° = \frac{opposite}{hypotenuse} = \frac{y}{r}## ##\sin 30° = \frac{opposite}{hypotenuse} = \frac{x}{r}## The questions are: 1. What is the opposite and hypotenuse of sin 90°? 2. I am guessing that the opposite and hypotenuse of sin 90 is r...

Hello, Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of...

Homework Statement What is the area of a triangle on Earth that goes from the North Pole down to the equator, through the prime meridian, across the equator to 30 degrees east longitude, then back up to the equator? The radius of the Earth is about 6378 km. Homework Equations alpha + beta +...

In the triangle ABC the point D lies on the side BC and point E on the side AB. BD = AC, AD = AE and AB ^ 2 = AC * BC. Show that \angle BAD = \angle CEA

I am unable to find it.

So, i need to proof the triangle inequality ( d(x,y)<=d(x,z)+d(z,y) ) for the distance below But I'm stuck at In those fractions i need Xk-Zk and Zk-Yk in the denominators, not Xk-Yk and Xk-Yk. Thanks in advance

I'm doing LU factorization in linear algebra. And in general, do i know that i got the right one, given that there are many ways to get the desired entries into zeros, but results in different upper and special lower triangles?

In the triangle $$ABC$$ a point $$D$$ lies on the edge $$BC$$, $$E$$ - on the edge $$AB$$. Aditionally, $$BD=AC$$, $$AD=AE$$ and $$AB^2=AC\cdot BC$$. Prove that $$\sphericalangle BAD = \sphericalangle CEA$$. I have to do this task on Maths class on Monday and I need any tips or something...

1. Homework Statement Find forces P,F,and THomework Equations Fx = 0 Fy = 0 The Attempt at a Solution So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you [/B]

Homework Statement Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points D and Ε with MA and MB respectively. Prove that (1) the perimeter of ▲DME, and (2)...

The sides $x,\,y,\,z$ of a triangle satisfy the equality $(x^4+y^4+z^4)^2=2(x^3+y^3+z^3)$. Prove that it's a right triangle.

Homework Statement As shown in the diagram below, the shape consists of a square and a circle with centre Q. Given that QM = 3 cm, prove that MN = 6 cm. Known data: -- triangles APB and BQC are congruent -- angle BMC = 90 -- triangles BMQ and BNA are similar and right-angled 2. Homework...

Homework Statement Triangle ABC have side AB = 10 cm, AC=BC = 13cm, so sin (A-C) is... 2. Homework Equations sin (A-C) = sin A cos C - cos A sin C The Attempt at a Solution I see that the triangle can be split into two right-angle triangles. But, sin (A-C) ?? How to get that?[/B]

How is the generalized triangle inequality in b-metric spaces ? I find something...But I wonder your opinion...Thank you for your attention... Especially if you write for n,m>0 m>n $d({x}_{n},{x}_{m})$$\le$..... I will be happy...

Let $X$ be a non-empty set and let $s\ge1$ be a given real number. A function $d:$ X $\times$ X$\to$ ${R}^{+}$ , is called a b-metric provided that, for all x,y,z $\in$ X, 1) d(x,y)=0 iff x=y, 2)d(x,y)=d(y,x), 3)d(x,z)$\le$s[d(x,y)+d(y,z)]. A pair (X,d) is called b-metric space. İt is clear...

Homework Statement In triangle ABC, ∠C=90∘. Let D, E, F be points on sides BC, AC, AB, respectively, so that quadrilateral CDFE is a rectangle. If [BDF]=7 and [AEF]=28, then find [ABC]. Homework Equations Area of a rectangle, and triangle. Also can cut up the rectangle into some triangles...

Hi everyone I need help in these 2 questions. Please advice. Tis :)

How can I get a right triangle from the inputs and outputs of trigonometric functions? For example: sin(x) = y The triangle would have one angle as x and the opposite edge of the triangle would be y/hyp etc. How can I get all of these values from any trigonometric function? Please tell me if I...