math help

T

train

Guest
help - sum of an infinite series

I need help with these... i'm a little rusty...

sum of series: 1/10 + 2/10^2 + 3/10^3 ... N/10^N

and if a circular table is in the corner of a room, touching both walls( that make the corner) and there is a nick on the table 8 inches from 1 wall and 9 inches from the other wall, what is the table's radius...
 
M

Master Shake

Guest
The problem is, you need to know the angle of the corner.
 
E

EricBess

Guest
I believe that there are still 2 answers, based on whether the nick is on the inside or the outside edge of the table. In other words, is it within the section bounded by the two walls and the table's edge or on the outer edge of the table?
 
E

EricBess

Guest
If the nitch on the table is bounded by the wall, then the table has a radius of 29 inches (which is the likely answer).

If the nitch is on the outer edge of the table, then the table has a radius of 5 inches.

Is this just a brain-teaser, or did you need to know how I came up with this?
 
T

train

Guest
how you came up with it would be nice... It's an actual math problem...

I got lost using tangents and everything...:rolleyes:
 
E

EricBess

Guest
Woah, slow down...This is NOT an advanced trig problem.
Give me a minute, but I'll post in Off-topic.
 
T

train

Guest
It's been 8 years sinc eI've had a problem of this type...

"Compete in a state competition one day... don't know anything the next...":rolleyes:

It's geomertry I'm sure...

:cool:
 
E

EricBess

Guest
Okay, Draw the corner of the room with the table in it.

Now, draw a line going from the center of the table to the nitch (assume bounded - it actually is the same either way, but this is easier to visualize)

Now, draw a line from the center of the table perpendicular to each wall, forming a radius to the wall.

Finally, draw a line from the nitch perpendicular to each radius that you just drew to the walls.

You have now formed two identical (for our purposes) right triangles with the points of the triangles being the nitch, the center of the circle, and the point along the radius of the circle.

Pythagorum Thearom says a squared plus b squared = c squared.

c is your radius, r. a is the radius, minus the distance of the nitch from one wall and b is the radius minus the distance from the other wall.

In short:

(r-8)*(r-8) + (r-9)*(r-9) = r*r

Solve for r.

I assume you know the quadratic formula and can go from there. I actually forgot it and had to figure it out again :p
 
T

train

Guest
thanks EB...

just a note - your info says you're still in vancouver...;)
 
S

Svenmonkey

Guest
Originally posted by train
help - sum of an infinite series

I need help with these... i'm a little rusty...

sum of series: 1/10 + 2/10^2 + 3/10^3 ... N/10^N
Click to expand...
Looks like, from a program I just made, it's .12345678901234567890... repeating forever.

Edit: this is the algorithm, which should work (Math.pow raises the first argument to the second argument):

double sum = 0;
for(double i = 1; i < 1000000; i++)
{
sum += i/(Math.pow(10,i));
}
 
M

Mikeymike

Guest
Is the nick a spatial 8" and 9" away from the walls (a straight line distances), or is it simply 8" & 9" away from the walls following the edge-track of the table (curved edge distances)?

If its a measure of the curved distance your answer is 10.823

The nick parameters essentially define that there is 17 inches of curved edge between the two walls, which is your quadrant circumference. Multiply that by 4, you get 68 inches for the circumference of the table.

C = Pie * 2R

68 = 3.1416 * 2R

68
--- ====== R
3.1416 * 2

68
--- === 10.823 = R
6.2832
 
You must log in or register to reply here.
Top