# Tagged Questions

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### Inequality regarding areas of trangles

BdMO Nationals 2013: There is a point O inside ∆ABC. After joining A,O; B,O and C,O extend those line and they will intersect BC, AC and AB at points D, E and F respectively. ...
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### Find the Perimeter of a rectangle

The sides of a rectangle are (3x+2)ft and (4x-3)ft . Find the perimeter of the rectangle I tried adding them up came to 14 to the 4th -2 am I right?
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### Deriving, diff b/w angles of minute and hour hands =11m/2-30h

I encountered this formula, $x=\frac{11m}2-30h$, where x is the angle between the minute hand and hour hand of a clock. m being minutes and h being hours. Ex- at 3:20, m=20 and h=3, so, x=20 degree ...
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### The second hand on a clock sweeps out an area of 10pi square inches in 35 seconds. Find the length of the second hand

How do I solve this question? Can someone please help?
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### Can someone help me simplify this trig expression?

$$( \tan x+ \sec x )( \cot x-\cos x )$$ I got stuck after a few steps of converting and adding and what not.
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### Product of gradients of x=0 and y=0

A friend asked me this question: The product of the gradient of any two lines perpendicular to each other is $-1$. Now, the lines $x=0$ and $y=0$ are perpendicular to each other. If you take the ...
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### Can someone help me solve this problem dealing with area of a sector/circles?

If a pizza is $1/3$ of an inch thick and has a diameter of $8$ inches, how many cubic inches of pizza have you eaten if you eat a sector whose edges form a $20^{\circ}$angle? Answer to the nearest ...
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### How to see and proof that the hyperbola as a constant difference of distances holds for $\frac{1}{x}$?

I understand that a hyperbola can be defined as the locus of all points on a plane such that the absolute value of the difference between the distance to the foci is $2a$, which is the distance ...
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### Expressing a length in a triangle with no angles given

Let there be $ABC$ an isosceles triangle $(AB = AC)$. $D$ is a point on $AB$ such that $AD = 2BD$. $E$ a point on $BC$ such that $2EC = BE$ . Express $DE$ in terms of the base, $a$, and the sides, ...
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### What is a good book on basic high school math (algebra, geometry, trig etc.)?

What is a good book on basic high school math (algebra, geometry, trig etc.)? I want a book that presents mathematics in a rigorous manner and with emphasis on creativity rather than memorization. If ...
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### How can I prove this two identities? $\cos^2 x=\frac{1+\cos(2x)}{2}$ and $\sin^2 x=\frac{1-\cos(2x)}{2}$

How can I simply prove the two following equations? $$\cos^2x=\frac{1+\cos(2x)}{2} \,\,\,\,\,\,\,\,\,\,\text{ and }\,\,\,\,\,\,\,\,\,\, \sin^2 x=\frac{1-\cos(2x)}{2}$$ I already proven them using ...
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### Find the equation defining a perpendicular bisector

Hello fellows, I've not had much time to post questions, but I post this one because while in my Maths lesson, I became annoyed by solving the same thing over and over again, when a good ...
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### Quadratic equation and trig

If the quadratic equation $ax^2+bx+c=0$ has equal roots where $a, b$ and $c$ denote the lengths of the sides opposite to vertices A, B and C of a triangle ABC respectively, then find the sum of ...
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### Percentage Change in the depth of liquid

A certain liquid is placed in a rectangular container. After heating, both the length and the width of the container increase by 2%. At the same time, the volume of the liquid inside increases by 10%. ...
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### Which quadrant does -1.326 rad go? [closed]

Which quadrant does -1.326 rad go? Please tell me how to find out by using the unit circle. Thank you.
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### How to tell where quadrant phase angle goes?

tan(phase angle) = (2/3)/(-1/6) = -4 tan^-1(-4) = -1.326 rad "But this angle is located in the fourth quadrant, hence we must take the phase angle to be the second-quadrant angle" -How do I find out ...
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### Minimizing the length of wire between two poles?

There are two poles (lets say poles A and B) $50$ feet apart and the poles are $15$ and $30$ feet tall. There is a wire which runs from the top of pole A to the ground, and then to the top of pole B ...
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### Rate of Change of Cylindrical Roll's Volume as it Unrolls

This is purely a "for-fun" question. I was minding my own business in the washroom this morning when I began to unroll some toilet paper from the roll, and in typical Breaking Bad fashion (sorry if ...
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### Right triangle problem

Find a right triangle such that the hypotenuse minus either side gives a cube. Use a triangle with sides $x^2 - 4$, $4x$, and $x^2 + 4$
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### Finding slope from straight line equation

Line k lies in the xy-plane. The x-intercept of line k is −4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k ? I ...
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### A curve such that all lines on the plane intersect it : cont..

Further to this question (which appears more or less settled); "Is there a curve on plane such that any line on the plane meets it (a non zero ) finite times ?" I ask now the upper bounds of the ...
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### Determine t such that the triangles have same area.

I have three points $A=(2,3), B=(6,4)$ and $C=(6,6).$ Given $\vec{AB}=\vec v$ and $\vec{BC}={0 \choose 2}$. I have also that for every $t\in [0,1]$ there is a point $D$ given as $\vec{AD}=t\vec{v}.$ ...
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### How is algebra and geometry related to calculus?

Probably a too trivial question but here goes: What is the relationship of algebra and geometry with calculus? Are they pre-required knowledge for calculus, is calculus a different type of theory on ...
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### How to prove $\cos 36^{\circ} = (1+ \sqrt 5)/4$?

Given $4 \cos^2 x -2\cos x -1 = 0$. Use this to show that $\cos 36^{\circ} = (1+ \sqrt 5)/4$, $\cos 72^{\circ} = (-1+\sqrt 5)/4$ Your help is greatly appreciated! Thanks
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### Finding a curve that intersects any line on the plane

Question Is there a curve on plane such that any line on the plane meets it (a non zero ) finite times ? What are the bounds on the number of such intersections. My question was itself ...