3 Pre calc problems.

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guilage

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Nov 27, 2009
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1 - Let y = mx + b be the image when the line x - 3y + 11 = 0 is reflected across the line y = x. Find the value of m + b.
I've been trying to solve this but I the results I get make no sense. I've been trying to use some trigs but the results I find are not convincing.

2 - The integers from 200 down to 9 are written consecutively to form the large integer N = 200199198197....131211109. Find the value of k such that 3^k is the highest power of 3 that is a factor of N.
What is this supposed to mean? I have no clue.

3 - The radii of the three concentric circles shown are in the ratio of 1:2:3. What is the probability that a random shot that hits the target will hit inside the second circle but outside the innermost circle?
Picture of the problem: http://tinypic.com/r/28koriv/6
I've never solved any problem like this before, I need a lead please!

Thanks for the help!
:)
 
guilage said:
1 - Let y = mx + b be the image when the line x - 3y + 11 = 0 is reflected across the line y = x. Find the value of m + b.
I've been trying to solve this but I the results I get make no sense. I've been trying to use some trigs but the results I find are not convincing.

2 - The integers from 200 down to 9 are written consecutively to form the large integer N = 200199198197....131211109. Find the value of k such that 3^k is the highest power of 3 that is a factor of N.
What is this supposed to mean? I have no clue.

3 - The radii of the three concentric circles shown are in the ratio of 1:2:3. What is the probability that a random shot that hits the target will hit inside the second circle but outside the innermost circle?
Picture of the problem: http://tinypic.com/r/28koriv/6
I've never solved any problem like this before, I need a lead please!

Thanks for the help!
:)
Click to expand...

For the first question, if you reflect the graph of x - 3y + 11 = 0 over the line y = x, you can find the equation of the "new graph" by switching x and y:

y - 3x + 11 = 0

Now...put that equation into slope-intercept form (y = mx + b) and you should be able to answer the question.

I can't help you with the second problem.

For the third problem, did you draw a diagram? You've got three circles, whose radii are in the ratio 1:2:3.

You could let x, 2x and 3x be the radii of the circles, since that would give the desired ratio, 1:2:3.

The smallest circle, the "inner" one, has a radius of x. The area of this circle is pi*x[sup:hwebst79]2[/sup:hwebst79]

The next circle has a radius of 2x. The area of this circle is pi * (2x)[sup:hwebst79]2[/sup:hwebst79]

The biggest circle has a radius of 3x. The area of this circle is pi * (3x)[sup:hwebst79]2[/sup:hwebst79]

I will assume, since you don't say, that the biggest circle is the entire possible area in which shot could land.


You want the probability that a shot lands inside the second circle, but NOT inside the inner circle.

So, the desired "landing area" is (area of second circle - area of inner circle), or pi*(2x)[sup:hwebst79]2[/sup:hwebst79] - pi*x[sup:hwebst79]2[/sup:hwebst79]...I'll let you simplify that.

And the probability that the shot lands inside the desired landing area is

[desired landing area] / [area of biggest circle]

Ok...ball is in your park now.
 
Hey. I've stumbled upon a similar problem to your second question with N= consecutive integers from 200 to 9. I too am looking for the greatest k such that 3^k divides N. However, my integers run all the way down to 1. Did you by any chance figure out a method? I'd be very greatful for any hints or comments :?
 
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