[Guest]

1. You run to the game store on the release day of the next Tomb Raider game. The game cost $59.99 and you had to pay $64.49 after the sales tax was applied. What is the sales tax (in terms of percentage)?

2. Your friend makes a bet with you that he can outsmart you. Your friend tells you that he has a perfectly cylindrical can which is 10 cm tall and 31.4 cm around the circumference. He wants you to find the volume of the can to the nearest square centimeter. What answer do you give to win the bet?

3. A small rectangular cabin has an area of 216 square meters. The ratio of the short side to the long side is 2:3. Find the perimeter.

for a bonus on this question, create a single equation using MS Excel functions - which will calculate the perimeter of our cabin

4. Mike wants to start a garden in his backyard. He has exactly 48 meters of fencing to keep out the deer. He plans to set up the fencing so that it will completely surround his garden. If he wants his garden to be perfectly square, then how big can he make it without getting any extra fencing? Give the answer in terms of the area of the garden.

5. Consider the following statements:

If it is raining, then I am wearing a raincoat.

I am not wearing a raincoat.

Therefore, ___

--------

They get bigger:

6. Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?

7. What does this segment of windows CLI code do?

ver | findstr "5.3"

if errorlevel 1 (

	ver | findstr "5.2"

	if errorlevel 1 (

		ver | findstr "5.1"

		if errorlevel 1 (

		echo Your OS version, below, is not currently supported by this application

		ver

		echo please notify spikejones to receive support

		echo program will now close

		pause

		exit

		) else (

		set os=Windows XP

		goto xp

		)

	) else (

	set os=Windows Server 2003

	goto xp

	)

) else (

set os=Windows Vista

goto vista

)

[Guest]

at any time the distance between A and B is the hypotenuse of the triangle that is formed by

1)The distance A has taken,

2) (30 - The distance B has taken)

Their speed is 1,5 and 1 mile/minute. So the statement is:

(30-1.5x)² + x²=distance.

When the derivation of this is zero, this gives the minimum distance value:

-90+6.5x=0 ---> x=90/6.5 = 13.8 minutes = time, distance is easy...

For instance - this solution seems to be flawed in several ways:

"(30-1.5x)² + x²=distance."

Which distance should this equation show? If it is the distance between the cars (ie. the hypotenuse, you have to take the square-root of the left side of the equation.

"When the derivation of this is zero, this gives the minimum distance value:"

Well, the distance between the 2 cars can never be 0, and that ruins the rest of the calculations.

[Guest]

right - I saw that, and not sure where you were going with that. the correct answer is derived as such:

you must use the pythagorean theorum in the following manner

a^2 + b^2 = c^2

find the distances as relates to a variable time (x)

(60x)^2 + (30-90x)^2 = c^2

3600(x^2) + 8100(x^2)-5400+900 = c^2

11700(x^2) - 5400x +900 = c^2

sqrt(11700(x^2) - 5400x + 900) = c

this equation will hold true regardless of time to give you the length of the hypotenuse given any amount of time.

if you graph it - a parabola is formed. find the y-minimum and that will be the minimum distance

if you use calculus, find the derivative of the equation and set it equal to zero. solve for x - that will give you the time when they are at minimum distance.

Again you seem to assume that the minimum distance between the cars will be 0, which is not the case.

Maybe I'm missing something obvious to everyone else here, but... I don't think so

Edited April 4, 2009 by uhre

[Guest]

Maybe I'm missing something obvious to everyone else here, but... I don't think so

Again you seem to assume that the minimum distance between the cars will be 0, which is not the case.

right... of course distance between the cars will never be zero. please do yourself kindly a favor and graph my equation on the the graphing calculator here:

http://my.hrw.com/math06_07/nsmedia/tools/.../graphCalc.html

derivative:

http://en.wikipedia.org/wiki/Derivative

your answer

Since the cars will be drawing a right triangle where the hypotenuse will be the distance between the cars, the time where the distance between the cars are the shortest will be when the 2 catheti are the same lenghts

Car A moves north at 60 Mph (away from the right angle)

Car B moves west at 90 Mph (towards the right angle = -90 Mph)

A = 60 Mph & B = -90 Mph + 30 Miles

The shortest distance (hypotenuse) was when the catheti were the same lengths, hence

A = B

60 * h = -90 * h + 30

150 * h = 30

h = 1/5

The distance between the cars at this time will be the lenght of the hypotenuse = sqrt(a^2 + b^2) = 16.97 miles

is flawed in the following way, but I understand the logic:

normally, the statement would be true given that the side A shrunk at the same rate at which side B grew. but, given the fact that the cars are moving at different speeds, side A shrinks faster than side B grows. This means that you can't use that logic. given any amount of time, car B moves a unit of 3x distance, while car A moves a unit of 2x distance. This inequality of speeds creates many possibilities where the length of the hypotenuse will be shorter than the distance you posted.

if you take the amount of time you listed, (.2) and plug it into the equation I created - you will notice that the distance (y=16.97) will be output.

[Guest]

right... of course distance between the cars will never be zero. please do yourself kindly a favor and graph my equation on the the graphing calculator here:

http://my.hrw.com/math06_07/nsmedia/tools/.../graphCalc.html

derivative:

http://en.wikipedia.org/wiki/Derivative

your answer

is flawed in the following way, but I understand the logic:

normally, the statement would be true given that the side A shrunk at the same rate at which side B grew. but, given the fact that the cars are moving at different speeds, side A shrinks faster than side B grows. This means that you can't use that logic. given any amount of time, car B moves a unit of 3x distance, while car A moves a unit of 2x distance. This inequality of speeds creates many possibilities where the length of the hypotenuse will be shorter than the distance you posted.

if you take the amount of time you listed, (.2) and plug it into the equation I created - you will notice that the distance (y=16.97) will be output.

Ahh, of course. I see your point. My assumption that the shortest distance between the cars would be when the catheti were the same length is valid only if the cars were travelling at the same speeds (or if car A were the faster car). So I was over-simplifying the problem. Man, I hate when that happens

Thanks for the explanation, spike.

[Guest]

Ahh, of course. I see your point. My assumption that the shortest distance between the cars would be when the catheti were the same length is valid only if the cars were travelling at the same speeds (or if car A were the faster car). So I was over-simplifying the problem. Man, I hate when that happens

Thanks for the explanation, spike.

no problem :tmb:

upon seeing this problem myself originally, my train of thought was originally the same as yours, until I thought about it more. then I was like "WTF"?? I knew there was a way to create an equation to extrapolate what I needed to know, but it eluded me for a bit - till I came back to it later and said "DUH!!"

Edited April 5, 2009 by spikejones

[Guest]

For instance - this solution seems to be flawed in several ways:

"(30-1.5x)² + x²=distance."

Which distance should this equation show? If it is the distance between the cars (ie. the hypotenuse, you have to take the square-root of the left side of the equation.

"When the derivation of this is zero, this gives the minimum distance value:"

Well, the distance between the 2 cars can never be 0, and that ruins the rest of the calculations.

I'm really surprised to face with such a critique in brainden site. An elementary student could notice that in my first equation, distance would be distance² and my second flawed sentence is pretty easy to understand for him or she. I also wonder how my ruined calculation yield a correct value as OP confirmed, a nice coincidence? I apologise for my errors those are result of my rush and scarce english, I should pay more attention.

[Guest]

In alphabetical order....

sales tax 7.5 %

[Guest]

I'm really surprised to face with such a critique in brainden site. An elementary student could notice that in my first equation, distance would be distance² and my second flawed sentence is pretty easy to understand for him or she. I also wonder how my ruined calculation yield a correct value as OP confirmed, a nice coincidence? I apologise for my errors those are result of my rush and scarce english, I should pay more attention.

I guess I could read an insult into this. However, I choose not to. Instead let me clarify - what you should be able to see from subsequent posts - that I was confused by the several different solutions to the problem, yours being one of them - but also the only one that was sufficiently explained to reveal the reasoning behind the result. I was merely trying to figure out, which was the correct one (which, by the way, I expected to by my own - until my flaw was pointed out).

In other words, I was never trying to criticize you, and if it felt that way I apologise.