# Tagged Questions

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### Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
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### Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
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### how to calculate the coordinates center of a squar [closed]

I need to calculate the center of square cells each cell has 4 (x,y) coordinates. Can one help me to Know how can I calculate the coordinates of the center of each cell?
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### Find the maximum length of a line segment enclosed in a given area

$A = \{ (x, y) : x = u + v , y = v , (u^2) + (v^2) \le 1 \}$ . Then what is the maximum length of a line segment enclosed in this area? My friend suggested the answer $\sqrt{5}$, but I think it ...
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### Straight Lines and Curves

If the line $y=x\sqrt3$, intersects the curve $x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0$, in three points $A,B,C$. If $O$ is the origin, then what's the product $OA\cdot OB\cdot OC$?
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### Cartesian Line to Projective Coordinates

I have an equation of a line written in slope intercept form $y = mx + b$ How would I translate it from the 2d space into the projective space? I have been reading ...
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### Convex Sets and extreme supports

Let the set $S$ in $R^n$ consists of the origin $0$ and $n$ lineary independent vectors $T_1, \ldots, T_n$. Show that $C(S)$, the convex hull of of $S$, is the intersection of its extreme supports, ...
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### What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
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### How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
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### Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
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### What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
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### How to find the x-component of a spherical vector?

I am given the point $P(r=0.89, \theta=30^\omicron, \phi=45^\omicron)$ and $\vec E=1/r^2(cos(\phi)\hat a_r +sin(\theta)\hat a_\phi)$. Find the x-component of $\vec E$ at $P$. I found the vector in ...
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### Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
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### Z Spec - How to constrain X Y Coordinates

I'm trying to build a system state schema in Z spec that specifies the following: Points of interest use (X,Y) coordinates to specify their location. a small point of interest exists that only has 1 ...
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### How to work out the unknown vertex of a parallelogram given the other three

I have changed the numbers so you're not giving me the answers. Let A (1, 1), B (5,2), C (2, 4) and D (x, y) be the vertices of a parallelogram ABCD. What are the coordinates of vertex D? -As I am ...
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### equation of a refracted straight line

we have got a line $$x-y=1$$ which after refracting from $x$-axis bends at angle $\pi/6$ from normal what's eqation of that line? what i did was that putting $y=0$ to get points on $x$-axis which ...
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### Changing cylindrical coordinates to cartesians's

I was wondering how to find $e_r$ using $e_x$ and $e_y$ as you can see in the scheme: So what I really want is to prove that: $$\vec{e_r}=\cos\theta\vec{e_x}+\sin\theta\vec{e_y}$$ with a deep ...
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### Integral coordinates Proof

Nine distinct points with all coordinates integral are selected in the space. Prove that the line segment with ends at certain two of these points contains in its interior a point with all coordinates ...
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### Help in question related to locus of pair of tangent to a circle?

This the question in my text-book The tangent to $x^2 + y^2 = a^2$ having inclination $\alpha$ and $\beta$ intersect at $P$. If $cot\alpha$ + $cot\beta = 0$, then the locus of $P$ is : i really ...
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### Converting $(4,-4{\sqrt3}, 6)$ from rectangular to cylindrical coordinates

I'm getting the wrong answer for $\theta$. What am I doing wrong? $$(4,-4{\sqrt3}, 6)$$ $$r =\sqrt{4^4 + (-4\sqrt{3})^2} = 8$$ $$z = 6$$ $$\tan\theta=\frac{-4\sqrt{3}}{4}$$ $$\tan\theta=-\sqrt{3}$$ ...
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### How to determine gradient of vector in cylindrical coordinates?

I am wondering how to actually determine the gradient of a vector in cylindrical coordinates. I have seen a lot of websites that just say what the general form is but I cannot seem to understand how ...
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### Natural dihedral

Can you help me with this: A body of mass $m$ is moving under gravitational force and resistance force proportional to the square of its speed. Write differential equations of motion of a body in ...
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### Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
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### Confusion on the given solution to a homework question.

Question: If the line $x = a+m$, $y = -2$ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) ...
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### Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$\int^2_0 \int^\sqrt{4-yÂ²}_0 \sqrt{4-x^2-y^2} dxdy$$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
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### Expansion of velocity in polar coordinates using kinetic equations

Why does total energy $$E=\dfrac{1}{2}\mu\mathbf{v}^2+U(r)$$ expand to $$E=\dfrac{1}{2}\mu(\dot{r}^{2}+r^2\dot{\phi}^2)+U(r)?$$ It's some form of the kinetic equations in polar coordinates. I know ...
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### How many coordinates are unreachable?

I wanted to know, if a man was to go from $(0,0)$ to $(46,46)$ moving only straight and up with the following constraints:- If he walks right, he will walk atleast $4$ consecutive coordinates. If ...
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### Euclidean space problem

In three-dimensional space, is it true that if you take line $a$ of a plane and line $b$ of the plane perpendicular to the first one, then the angle between line $a$ and $b$ (at which they intersect) ...
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### computing the $y_{cm}$

Suppose I have a half disc and the coordinates axes at the centre of base of the disc. For the given system, I have surface mass density $S$ as $$S=S_0 sin\theta$$($S_0$ being positive constant). I ...
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### Find the tangent to a function

Find the tangent to this $\displaystyle y={1 \over x+3}$ it's crossing the point $(-2,1)$ I have drawn the lines but I can't calculate it
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### Tetrahedron problem (proving)

Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
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### How to determine a Triangle vertices by its coordinates?

I have to solve this problem, yet I'm not sure what is asked. Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
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### Unusual function format and its partial derivatives.

I came across a function of this format: $z = f(u,v)$ where $u = x^2y^2$ and $v = 5x + 1$ Because this function is not in the same format of the ones I've seen before (explicit or implicit), I don't ...