All Questions
14
questions
-1
votes
2
answers
80
views
Understanding that $\sqrt{x} + a\sqrt{y} = 2$ is a branch of a parabola
Is there a simple (or simpler) way to understand that the following curve
$$\sqrt{x} + a\sqrt{y} = 2 \tag{1}$$
is a branch of a parabola?
When I say "simpler" I mean simpler with respect to ...
- 3,482
0
votes
1
answer
542
views
How to Find a Point when Given the Equation of the Line it's on, Another Point on the Line and the distance between the Two Points?
(12th Grade Calculus Level)
Let's say I'm given point A(1,2,4) and a line [x,y,z] = [4,3,9] + t[3,1,5]. I have to find point B which is on the line and is a distance of 5 units away from Point A. What ...
- 3
0
votes
2
answers
121
views
Proving a condition of perpendicularity [closed]
Today I've got an insteresting question about geometry. Let's get into it.
Let $ABC$ be a triangle such that $AC$ is its shortest side. A point $P$ is inside it such that $BP = AC.$ Let $R$ be the ...
- 516
2
votes
4
answers
282
views
Number of triangles $\Delta ABC$ with $\angle{ACB} = 30^o$ and $AC=9\sqrt{3}$ and $AB=9$?
I came across the following question just now,
A triangle $\Delta ABC$ is drawn such that $\angle{ACB} = 30^o$ and side length $AC$ = $9*\sqrt{3}$
If side length $AB = 9$, how many possible triangles ...
- 1,190
0
votes
2
answers
105
views
How to solve this analytical geometry problem?-parable inscribed within a square
This problem appeared on the network, and although it looks simple I am not sure of the result.
The polygon $ABCD$ is a square with side $4$ cm and the curve inscribed inside the square is a parabola,...
- 340
1
vote
1
answer
493
views
Complex Quadrilateral Problem
Consider a convex quadrilateral with vertices at $𝑎,~𝑏,~𝑐$ and $𝑑$ and on each side draw a square lying outside the given quadrilateral, as in the picture below. Let $𝑝,~𝑞,~𝑟$ and $𝑠$ be the ...
- 11
1
vote
3
answers
144
views
Find the specific sides of a parallelogram
Two bisectors are drawn from the corners (next to the longest side) of the parallelogram. Both sides of the parallelogram are given. Could you please tell me the steps of calculating the parts on the ...
- 21
0
votes
4
answers
37
views
Can you work out a point from the length of two lines and the position they start at?
I know two points in the plane, $(0,0)$ and $(20,0)$. I also know that a point between and above them(the apex of a triangle formed from these three points) is $15$ from $(0,0)$ and $25$ from $(20,0)$....
1
vote
2
answers
4k
views
In a triangle, does an angle bisector necessarily bisect the opposite side? [closed]
Have a look at the triangle and tell me if $AD=DB$:
- 315
0
votes
0
answers
23
views
What Are the Meaning of the Terms in a 3D Plane Equation
The question is the following:
The equation $3x+5y+7z=15$ can be rewritten as $z = \frac{15}{7} - \frac{3}{7}x-\frac{5}{7}y$. What are the meanings of the three fractions that appear in this ...
- 808
0
votes
0
answers
79
views
Transformations in the plane?
Please Note: I understand how the addition and multiplication of complex numbers work. I'm just little confused by the wording in the book.
I am looking at Visual Complex Analysis by Needham. It ...
- 23.8k
0
votes
3
answers
1k
views
How to solve the word problem below?
Can anyone guide me through this problem? I know how to solve the equation of the circle (the Earth) below but I don't know how to solve the equation of the orbit.
- 55
6
votes
2
answers
510
views
Show that in any triangle, we have $\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$
Show that in any triangle, we have $$\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$$
where $R$ is the circumradius of the triangle.
Here is my work:
...
- 215
0
votes
3
answers
781
views
Determine origin of a circle given ordered pairs.
Given ordered pairs $p_i = (x_i, y_i)$ where $x, y \in I$, find a pair $(x_o, y_o)$ where the distance between $o$ and all $p_i$ is equal.
The problem may also be imagined as trying to find the ...
- 115