+0

# Math Challenge (again!) #lim_(x->0)(1/x) (or ∞)

0
73
2
+302

Pleae ignore that all-over-the-place title.

We're back for another $$MATH$$ $$CHALLENGE!$$ (in LaTex) I've been experimenting with some of the other features of the... question-maker? Anyway, you can probably see that in my new post about Euler's formula. Anyway anyway, I should tell you the answer to the last one, eh?

$$wxy=10$$

$$wyz=5$$

$$wxz=45$$

$$xyz=12$$

Find $$w+x+y+z$$

SOLUTION:

Multiply all equations together to get ​$$w^3x^3y^3z^3=2^33^35^3$$

$$wxyz=30$$

Now, divide to get $$w={30\over xyz}$$

Oh, we know $$xyz$$! Substitute to get $$w={5\over2}$$

Repeat to get $$x = 6$$$$y={2\over3}$$, and $$z=3$$. Add, add, add, and we get

$$w+x+y+z=12{1\over6}$$! Many people got this one.

Great! Now for the new problem:

Given point $$P$$ outside a circle, the shortest distance between $$P$$ and the circle's perimeter is 4 units, and the longest distance is 16 units. Find the distance of $$P$$ from its tangent.

I'm excited to see some answers to this...

Mathhemathh  Oct 16, 2017
Sort:

#1
+90986
+2

Given point  P outside a circle, the shortest distance between  P and the circle's perimeter is 4 units, and the longest distance is 16 units. Find the distance of P from its tangent.

Huh       It is 4 units. Oh... you mean the tangent that has the point P on it. ....

I used this property.

$$4*16=d^2\\ 64=d^2\\ distance=8\; units$$

Melody  Oct 16, 2017
edited by Guest  Oct 16, 2017
#2
+302
0

Nice! Not how I did it, but nice. (I didn't know this theorem existed )

Mathhemathh  Oct 17, 2017

### 5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details