# Tagged Questions

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### Approximation to $\sqrt{cos(\theta)}$?

I have this formula, (it is just the law of cosines angle formula): $$d = \sqrt{a^2 + b^2 - 2ab \ cos(\theta)}$$ Here is my issue. I am wondering if there is a way to 'extract' the $cos$ term. My ...
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### Pre College Mathematics

During my school days I was a very keen student of mathematics. But circumstances led me to opt for commerce at the college level. Now I wish to continue learning mathematics on a self study basis. ...
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### Find the height of a triangle, given its angles and base, without the Law of Sines. [closed]

How can you find the height of a 45°, 60°, 75° triangle given its base, 600', without the Law of Sines?
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### Solving all possible triangles?

So we're doing oblique triangles -- Law of Sines and all that good stuff =). I have a bunch of problems that ask you to solve for "all possible triangles that satisfy the given conditions". For ...
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### If $7\sin^2A-3\cos^2A=4$, then $\tan A\neq\pm\dfrac{1}{\sqrt{3}}$

If $7\sin^2A-3\cos^2A=4$, then we have to show that $\tan A=\pm\dfrac{1}{\sqrt{3}}$ The textbook approaches this by substituting $\sin^2A=1-\cos^2A$ and that method does(not) work. ...
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### Mensuration Class 8 [closed]

The inner diameter of a metallic tube of density 7g/cm^3 is 2.5 cm. The thickness of the tube is 0.29 cm. Find the weight of the tube, if it is of length 30 cm.
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### Solving $\tan x \sin^2x=2\tan x$

$\tan x \sin^2 x = 2\tan x \implies \tan x \sin^2x - 2\tan x=0 \implies \tan x(\sin^2x - 2)=0$ $\tan x=0$ or $\sin^2 x-2=0 \implies \sin x=\pm \sqrt{2}$ My question is, why can't you divide by ...
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### Samantha has a rectangular garden with sides x and y. She wants to build a border around her garden with tiles. Each tile is 1 square foot.

So I'm having trouble with this problem anyone know how to solve it?
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### Car chase trajectory and time

I Cannot figure out this problem.(it is in 2d) There are 2 cars. 1st car is chasing second car. Car1 has starting position (2,4) and speed of 5(coordinates per second). Car2 has position of ...
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### Finding the radius, distance of the center of circle inscribed in the square

I am trying to solve this question but can't figure out the last part. I was able to get answers for part A and B but i don't know how to approach/solve part C. Any help will be appreciated. The ...
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### How to determine the length of $x$ in this sketch?

Consider the following construction: Assume that you are given the lengths of the sides $a,b,c,d,e$ as well as the size of the angle $\phi$. The task is to determine the length of $x$ in terms of the ...
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### How to do you find missing vertix in right triangle in a graph?

![enter preformatted text here][2]I'm graphing a line segment. The end points are $A$ and $B$. Then I"m using $10 \%$ of the length of line segment $AB$ to form ...
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### How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
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### Angles in a regular polygon. [closed]

The measure of each interior angle of a regular polygon is $24º$ more than $38$ times the measure of each exterior angle. Find the number of sides of the polygon.
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### Right Pyramid question

In a Right pyramid, that is one with all edges equal to each other and a height which goes to the center of the geometric figure which serves as it's base, can we say that if that figure is an ...
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### Medians and Perpendicular bisectors

There was something I never quite understood about medians and perpendicular bisectors in a triangle, or to be more specific, an isosceles triangle; Aren't they the same in this kind of triangle? If ...
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### Trouble in this circle question

Referring to this diagram (self-made): Question says: In the given figure diameter of the circle is $3$ cm. AB & MN are two diameter such that MN is perpendicular to AB. In addition CG is ...
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### What the floor is exactly?

I came across this question: A rectangular floor is fully covered with square tiles of identical size. The tiles on the edge are white and tiles in interior are red. Number of white tiles is the ...
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### Triangle Calculation Question

In a triangle $ABC$, it is known that $AC = m$, $AB = 3m$, $BC = Rm$. Find for which values of $R$ the triangle is: (i) An acute angle triangle. (ii) A right angle triangle. (iii) An obtuse ...
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### Pyramid Question

Let us suppose we have a right pyramid,that is a pyramid with all edges equal to each other and a height which goes to the center of the geometric shape that serves as it's base. We than also know ...
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### Simple arc/saggita/chord relation rearrangement

I'm stuck with something that I feel should be trivial. Consider the diagram on this page: http://mathworld.wolfram.com/CircularSector.html There are some pretty simple relations between the ...
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### Need assistance on geometry problem

Having a really hard time solving this problem. Given: a circle of radius $a$ an ellipse with minor axis $g$ and major axis $f$ the ellipse is oriented so that the major axis is parallel with the ...
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### Find the radius of the tip of a die punch.

The following image shows a problem out of my math book, Trigonometry, by Michael Corral (problem 13, section 1.3 for those who may be interested). My analysis is that the $1.5$ (as far as I can ...
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### Equation of circle tangent to y=x and x-axis with radius 5

Find the equation of a circle in the 3rd quadrant that is tangent to the line y=x and the x-axis, with a radius of 5. One way I thought of doing it was letting the center point of the circle be ...
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### General form of a circle

My math teacher taught me that the general form (equation) of a circle is: $$ax^2+by^2+cx+dy+e=0$$ He also asked us this: If the product of $c$ and $d$ is negative, then what 2 quadrants can the ...
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### Equation of a dotted circle

What is happening in this dotted circle? $x^2+y^2 < 2x$ I don't understand how this forms this dotted circle that I get when I type this into geogebra.
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### Condition for this set of points

This is for a calculator experimental prob. simulation. So, there is circle in a square and the circle is touching all 4 sides of the square. We need to first choose a coordinate system (two ...
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### Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
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### random circle with radius r on cartesian plane, probability of it not cutting x and y axis with intercepts.

I have a tough question here. Choose a circular disk of radius r on the cartesian plane. What's the probability it is not cut by horizontal lines with integer y intercept, or vertical lines with ...
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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%. ...