2 Attachment(s)

Pre-Calculus "problem solving" problem. (Solved-THANK YOU)

A large room contains twospeakers that are 3 meters apart. The sound intensity of one speaker is twice that of the other, as shown in the figure. (To print an enlarged copy of thegraph, select the MathGraph button.) Suppose the listener is free to move aboutthe room to find those positions that receive equal amounts of sound from bothspeakers. Such a location satisfies two conditions: (1) the sound intensity at the listener’s position is directly proportional to the sound level of a source, and (2) the sound intensity is inversely proportional to the square ofthe distance from the source.

(a) Find the points on the x-axis that receive equal amounts of sound from both speakers.

(b) Find and graph the equationof all locations where one could stand and receive equal amounts of sound from bothspeakers.Attachment 26491

**The Answer to (a) is : x= -3 + 18^(1/2)=1.2426 AND x= -3 - 18^(1/2)= -7.2426**

The Answer to (b) is: (x+3)^{2 }+ y^{2}=18

This is what I have done so far, but I never get the right answer:

Attachment 26492

Any help would be greatly appreciated. I have been working on it for hours, trying different things, but after all that work, I feel as if I had done nothing wrong even though the back of the book says otherwise.

Re: Pre-Calculus "problem solving" problem. Stuck

Let's look at part b) first.

We want to find the locus of points (x,y) that satisfies:

$\displaystyle \frac{kI}{(x-0)^2+(y-0)^2}=\frac{2kI}{(x-3)^2+(y-0)^2}$

$\displaystyle \frac{1}{x^2+y^2}=\frac{2}{(x-3)^2+y^2}$

Now, cross-multiply and put into standard conic form...what do you find?

Re: Pre-Calculus "problem solving" problem. Stuck

Thank you so much!

For some reason, it never occurred to me that I had to complete to square in order to get back to standard conic form.

I had been focusing on checking and rechecking my work constantly to make sure that it was right.

I kept seeing that they had (x+3), and i had (x-3), and it was driving me insane.

Re: Pre-Calculus "problem solving" problem. Stuck

Good work! I was hoping you would find you had to complete the square! :D

Re: Pre-Calculus "problem solving" problem. (Solved-THANK YOU)