# Tagged Questions

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### Why must closest approach occur when relative velocity is perpendicular to motion?

The first part i) I can solve correctly, but I need some advice and intuition on how to solve the second part ii). Here is the mark-scheme for the question: But for part ii) I do not understand ...
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### Would this thinking about the dot product hold?

Background today I completed the chapter on the dot product of vectors. But in trying to figure out exactly what the dot product is. I came to the conclusion that it can be interpreted as the length ...
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### How to find slope on line that known only point and angle

How to find slope on line that known only point and angle Image will describe more clearly I'm wont to find the orange line slope to find point on it ( b , c , d ) suppose that A and angle are ...
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### At the instant of release of an object from rest. Is the only force that can act its weight? [on hold]

This is the third question from a mechanics exam past paper: I can do parts i) and ii) but for iii) in finding the angular acceleration, i used $C=I\alpha$, where $C$ is the applied couple or ...
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### Why does resolving forces in one direction give a completely different answer to resolving the opposite way?

I can solve parts i), ii) and am able to show that $R=0$ for part iii). In this question $g$ is the acceleration of free fall taken to be $9.8$ Using Newtons 2nd law [$F=ma$] for the last part I ...
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### Geometry, finding the possible values of 'a'

$P (a,4)$, $Q (2,3)$, $R (3,-1)$ and $S (-2,4)$ are four points. If $|PQ| = |RS|$, find the possible values of a I know this is a pretty basic problem but I'm having a lot of trouble with it, here is ...
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### Calculating the angle for a path between two nodes in a graph

I want to (programatically) draw an edge between two nodes in a graph, starting on the outside of the nodes. Below is an illustration of what I'm (poorly) trying to describe: I have the $(x,y)$ ...
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### Simple geometry problem

So I'm asking this question because I'm afraid I would be doing a stupid mistake... the problem associated with this trigonometry problem isn't pulling off. Could you tell me whether my calculation is ...
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### $S$, $I$, $O$ are circumcenter, incenter and orthocenter then $SO\ge IO \sqrt2$

Let $S$, $I$ and $O$ be the circumcenter, incenter and orthocenter of $\triangle ABC$ then prove that $SO\ge IO \sqrt2$, or equivalently $SO^2\ge 2IO^2$. I was able to derive an expression for $SO^2$ ...
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### Acute plane triangle with two sides coinciding with a right triangle

Below are the two questions: 1) If $T$ is a plane triangle with $x, y < z$ such that $x^{2} + y^{2} > z^{2}$ as side lengths, is $T$ necessarily acute? 2) Is an acute plane triangle $T$ such ...
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### Circle Line segment intersection

I have a circle with radius r and center $(c_x, c_y)$. I have a line segment $(x_1, y_1)$ and $(x_2, y_2)$ given $(x_2, y_2)$ is always a point inside the circle. I am trying to find the ...
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### Proof involving an isosceles triangle

I came across this problem in some (maybe) high school book: Let $ABC$ be an isosceles triangle s.t. $AB=AC$. Also, $\alpha>\beta$. It is known/given: ...
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### Splitting a triangle to make two equal halves, find the length of the new line

Could someone please explain to me how I would find this out? I have a triangle and I need to find the length of the line that would split it down the middle so that the areas were even. A = 105 ...
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### Can Angles A and B In A Trapezium Be Solved Using Basic Geometry?

Can angles A and B be solved? Neither the area nor the perimeter was given. Thank you very much if you can help! :)
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### Angle and circle intersection, find the circular segment area

Playing Kerbal Space Program, I found myself wondering about what a satellite would see of a planet depending on its field of view and its altitude. I tried attacking the problem from various angles ...
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### How to find perpendicular point of a vector to another vector 2d

Given the axis x-y and some random points to the vectors AB and CD, how can i find out where will the point D lie when the vector CD(dashed line) is perpendicular to AB. For example if point A has ...
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### Trig equation that fits the plot points (octagonal pyramid)

I'm looking for an equation that satisfies these conditions: Input 90 degrees, result is 90 degrees Input 45 degrees, result is 60 degrees Input 0 degrees, result is 45 degrees For an input value ...
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### How could I calculate the local size of an object given its distance and actual size?

Lets say I take a picture of a sign. I know that sign is 20ft (width), 10ft height. I'm standing 40 feet away. If I were to take a picture, how could I calculate how wide and how high the sign is in ...
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### How to get the third point coordinates in isosceles triangle?

Isosceles triangle $ABC$ $AB = AC = d_1$ $BC = d_2$ $A = (x_1, y_1)$ $B = (x_2, y_2)$ $C = (x_3, y_3)$ $\angle BAC = \phi$ $\angle ABC =\angle ACB = \theta$ I want an equation for $x_3$ and $y_3$ ...
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### Calculation for the chance of finding something a given distance from a starting point by walking straight in a random direction?

The premise is basically a 2D plane with a single point, the starting point. Now a landmark sought by a hiker is a certain distance from that point. If the hiker can only see 1 mile in any ...
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### Different Definitions Of The Sine Function

I was hoping someone could give me a flow chart or high-level map connecting all of the definitions of the sine function, with some of the reasons why we care next to each. I've tried this but I'm not ...
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### The bird pointer problem: finding the angle of rotation

Suppose we have a bird pointer. He is a guy that likes to point at birds in the sky: His legs cannot move, however he can rotate around his torso. Also, his body and his arm always make a right ...
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### Conversion of angle from 360 degree to-90 degree

Here i am trying to convert angle into +90 degree AND -90 DEGREE FORMAT.For desired elevation angle i got answer properly.How to converert angle -90deg to zero, zero to +90 degree format. you can ...
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### Thinking of sohcahtoa with 90 in a triangle.

I know the answers from a unit circle. But when looking at a triangle how do you interpret Angle C sin C = cos C = tan C = I know the cos 90 = 0 and ...
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### Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
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### Solving right triangle given the area and one angle

Given right angle triangle $ACB$ (C is the right angle) has an area of 224 $mm^2$, what is the length of leg b if angle A equals 31.7deg? Here's the scenario: I have one right triangle completely ...
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### Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
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### Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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### A cycloid that goes through the beginning and through a general point

Parametric equations of the general cycloid through the beginning $(0,0)$ are $$x(t)=\frac{2t-\sin2t}{2d}$$ $$y(t)=\frac{1-\cos 2t}{2d}$$ How can we determine $d$ such that the cycloid goes through ...
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### Find the relation the 'maps' 2D points to the corresponding 3D images.

I have this [on hold] question (#857264) re-phrased. Hope that the content is more meaningful now. The following is the picture modified from the original. The question is a rectangular piece of ...
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### Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
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### How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
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### If $(A_1A_2)^2 + (A_1A_3)^2… + (A_1A_n)^2= 14r^2$, then prove that the number of sides is 7.

Let $A_1, A_2,\ldots,A_n$ be the vertices of a regular $n$ sided polygon inscribed in a circle of radius r. If $(A_1A_2)^2 + (A_1A_3)^2+\ldots + (A_1A_n)^2= 14r^2$, then prove that the number of ...
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### what does secant equal 2 mean? [duplicate]

I need your help, I am a little confused. My question is, what does the value of secant mean? I asked this question previously but unfortunately I did not understand the answers so I am trying to ...
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### Vector Magnitude during rotation

Probably something I should now already but this is confusing me no end! Lets say we have a force which is directed at 69 degrees inclination (from the X axis) with a magnitude of 500, shown below: ...
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### Circle area and lim

I was trying to show how to find $\pi$ value from formula $\pi R^2$, but I dont understand where is my mistake. So i am calculating area using $n$ triangles 1 let $R=1$, then one triangle area is ...
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### Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
### Points for which $AX^2-BX^2$ is constant
My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 8: Two points, A and B, are given in the plane. Describe the set of points for which $AX^2-BX^2$ is constant. I would ...
My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, $A$ and $B$, are given in the plane. Describe the set of points $X$ such that $AX^2+BX^2=AB^2.$ The ...