# Tagged Questions

0answers
18 views

### Coordinate grid [closed]

Is coordinate grid 2D or a screenshot of a 3D sphere? If it is 3D, would the graph of y=|1/x| form a circle on the top? If so would this circle have a diameter and radius equal to infinity?
0answers
77 views

### For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points?

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points? I don't quite the understand the solution which is in ...
1answer
19 views

### Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
1answer
32 views

### Find if a rectangle passes through another in cartesian plane

I want to know how to prove or find out if the red big rectangle passes through one of these small rectangles i have the coordinates of the big rectangle (the top left) and i have it's width and ...
1answer
35 views

### cylindrical and rectangular coordinates

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be ...
1answer
41 views

### 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 ...
2answers
43 views

### Tangent definition

As far as the definition of a tangent goes it is a line that touches a curve only at one point. Now let us consider the sine function .At (pi)/2 it attains its maximum value and so does it at ...
1answer
31 views

### Determining whether a 3-dimensional equations creates a horizontal or non-horizontal plane?

I am learning about graphing 3-dimensional shapes on x,y,z coordinates axis and am understanding everything for the most part. However, the thing that is continuously tripping me up is distinguishing ...
2answers
84 views

### Graph of Sin(x) along the line y=x

Well, I want the equation of $\sin(x)$ which has the line $y=x$ as it's axis. Basically I want the $\frac\pi4$ rotation of the curve y=$\sin(x)$. I already attempted differentiating the curve and ...
0answers
67 views

### Why does a figure look the same in every coordinate system?

After reading Maximilian M. Answer here: Gauss' Theorem - Can't understand a parameterization I'm trying to figure out why does a figure look the same in every coordinate system I choose. For ...
1answer
262 views

### Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
1answer
471 views

### Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
1answer
89 views

### Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$\int^2_0 \int^\sqrt{4-y²}_0 \sqrt{4-x^2-y^2} dxdy$$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
1answer
68 views

### maximising the angle $\theta$

OK, suppose I have two points in cartesian coordinate system, say $P(x_1,y_1)$ and $Q(x_2,y_2)$. I have a line as well, that is, for simplicity $$y=mx$$ Assuming that $$y_1\neq mx_1,y_2\neq mx_2$$ I ...
1answer
1k views

### When to use cylindrical coordinate and when to use spherical coordinate?

so i was told that any kind of 3 space Cartesian coordinate volume question can be solve using rectangular coordinate, cylindrical coordinate and spherical coordinate. Here is the thing, by using one ...
2answers
50 views

### 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
2answers
152 views

### Calculating 2D positions from a curve?

I am with quite a dylema here, as I need this for a game (so I am going to transform the given answers into programming code) to make a polygon around a curved line. from each line segment I have the ...
1answer
437 views

### Is the “Constant Rank Theorem” the same as the “Domain Straightening Theorem”? Which theorem is which?

Wikipedia says that the inverse function theorem is a special case of the "constant rank theorem". I'm pretty sure this is supposed to be the same theorem as the "Rank Theorem" on p. 47 of Boothby ...
2answers
155 views

### Are there derivations of equations of non-degenerate real quadric surfaces

Take the ellipsoid for example $$(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1$$ in the x-y plane you have an ellipse described by $$(x^2/a^2)+(y^2/b^2)=1$$ (suppose z=constant) in the y-z plane you have an ellipse ...
5answers
6k views

### Find out the differential equation of the following families of curves.

Find out the differential equation of the following two families of curves : Straight lines having slope and $x$-intercept equal in magnitude. Straight lines at a fixed distance $p$ from the origin. ...
1answer
3k views

### Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
0answers
51 views

### Altering the shape of a Gaussian curve

I just posted this on Stack Overflow but then I found out about this forum. I hope I'm not breaking any policies by posting the same question here. I am not allowed to post images here yet, so please ...
0answers
51 views

### General Coordinates property proof

In my problem sheet I need to show: Let $\textbf{r} = \textbf{r} \left( t , \{ q_{j} \} \right)$ Then: \frac{\partial \dot{\textbf{r}}}{\partial \dot{\textbf{q}_{j}}}=\dfrac{\partial ...
1answer
339 views

### Finding the sign of $\phi$ in spherical coordinates

I know its a little silly, but I got the wrong sign several times. Just to be clear, $z=r\cos(\phi), -\frac{\pi}{2}\leq\phi\leq\frac{\pi}{2}$ when converting from cartesian to spherical. So, how do I ...