OT: Calculus Challenge of the day.

[liquidtiger720]

So, here's today's Assignment for you guys to solve.


There is a very strong radiation source in the center of a large 120 x 120 foot room. A person must run through this room to get to safety. Her escape route takes her the full lenth along one wall of the room. She is not exposed to radiation outside the room. The strength of the radiation is inversely proprtional to the square of her distance from the source. At 5- feet, her body is absorbing radiation at the rate of 200 un**** per second. If she runs at 12 feet per second, what is the tottal radiation dose she recieves during her dash to safety?


You must show the integral used to solve problem.

[Blitzkrieg Bob]

and heat a cup of green tea

[liquidtiger720]

haha...cmon, where are the mechanical/civil engineers on the board?

[DaveVoorhis]

Oy! Yer just trying to get someone to do your homework assignment for you, aren't you? :D

[liquidtiger720]

Not DO it...just HELP. hahaha.

[rob101]

Yes there are mech engineers on the board, but speaking for myself i finished university so that i would never have to do stuff like that again......... but I'll see what i can come up with

[rob101]

okay dokey
R = rate of rad absorption (units/sec)
x = distance from the source (feet)
k = constant

now R = k/(x^2)
so 200 units/s = k/(5^2)
therefore k = 5000

now in order to solve this you need to find the total units of rad she absorbed

so that will be the Integral of R with respect to time

you will need to find an expression for the distance with respect to time.
that is to say x= f(t)
probably some kind of parabola
then you will find the Integral of k/(x^2) with respect to time
ie integral of 5000/(f(t)^2) with respect to time

you bastard, the horrible memories are flowing back...... nooooooo

edit: the expression for x is something like x = sqrt((60-ut)^2+60^2)
where sqrt is the square root and u is the chick's velocity

[Bellicose Right Winger]

10.9 units





So, here's today's Assignment for you guys to solve.


There is a very strong radiation source in the center of a large 120 x 120 foot room. A person must run through this room to get to safety. Her escape route takes her the full lenth along one wall of the room. She is not exposed to radiation outside the room. The strength of the radiation is inversely proprtional to the square of her distance from the source. At 5- feet, her body is absorbing radiation at the rate of 200 un**** per second. If she runs at 12 feet per second, what is the tottal radiation dose she recieves during her dash to safety?


You must show the integral used to solve problem.

[liquidtiger720]

i just noticed a type while going through the proble....5- is suppose ot be 50. But I think I can manage. Thank you everybody for the well needed boost. Rob and Bellicose, you deserve a cookie!. :)


sorry to bring back bad memories rob!

[632 Regal]

integral is "*&*^%%^$(]}@{" - without the ""s
the answer is 6

[rob101]

Nah they're not all bad memories, I have to deal with politics at work which is waaaaaaaaaaaaaaaaay worse.

what are you studying anyway?

[liquidtiger720]

does this sound right?


500,000/24 * S(1/((60-x)^2)+60^2) dx

S = integral with range 0 to 60.



I'm a business finance major. I have no clue why they want me to take 1.5 years of calculus. I'm hardly up to the task. This is calc 2, and I'm already struggling.

[Bellicose Right Winger]

No problem. That makes it 100x the dose so 1091 units.

My numerical integration is rusty, so be sure you tell us the REAL answer.




i just noticed a type while going through the proble....5- is suppose ot be 50. But I think I can manage. Thank you everybody for the well needed boost. Rob and Bellicose, you deserve a cookie!. :)


sorry to bring back bad memories rob!

[Bellicose Right Winger]

0-60? I integrated over the 10 seconds it takes to run the distance.



does this sound right?


500,000/24 * S(1/((60-x)^2)+60^2) dx

S = integral with range 0 to 60.



I'm a business finance major. I have no clue why they want me to take 1.5 years of calculus. I'm hardly up to the task. This is calc 2, and I'm already struggling.

[rob101]

0-60? I integrated over the 10 seconds it takes to run the distance.
yeah you need to integrate over time not distance, so S dt not S dx.

business and calculus? the business people in this country can't even use Excel when they graduate...... hehe

[liquidtiger720]

lol...the above shows why I shouldn't be in this class.

[GoldenEagleFan]

at 12 feet a second it will take the lady 10 seconds to cross the room. At any given instance in time she is a certain distance from the center of the room. This distance can be calculated by Pythagreons theorom. For instance, at time =0 she is the square root of 60^2+60^2 at from the center. at time =5 seconds she is 60 feet from the center. At time=x she is the square root of (60-12*t)^2 (t=time in seconds)+60^2. Take this equation, then use the fact that at 50ft the absorbtion rate is given, use the info that the rate is inversly proportional to the distance and integrate with respect to time from 0-5 and multiply your answer by two.

[bahnstormer]

cant remeber the last time i did hw....
soph year i think =\

[632 Regal]

no I figured it out again, answer is 6.

[liquidtiger720]

im lost now.

[GoldenEagleFan]

Remember back to your grade scholol days and you wondered how could math ever be practical.....

When you're bored in class remember....Lots of calculus used in designing engines and autos.

For example...

Calculus is the foundation for camshaft design. As a camshaft lobe rotates, the valve lifts or returns. This rate of change of distance with respect to time is dx/dt or velocity. Differentiate again and you dv/dt or acceleration. To fast of acceleration and valves separate from followers or impact their seats too hard. The acceleration rates determine the spring pack you need to keep the system stable. Too high of rate of spring and you can get excessive force on the cam lobe leading to premature wear. On and on and on. All based off of calculus!

[rob101]

at 12 feet a second it will take the lady 10 seconds to cross the room. At any given instance in time she is a certain distance from the center of the room. This distance can be calculated by Pythagreons theorom. For instance, at time =0 she is the square root of 60^2+60^2 at from the center. at time =5 seconds she is 60 feet from the center. At time=x she is the square root of (60-12*t)^2 (t=time in seconds)+60^2. Take this equation, then use the fact that at 50ft the absorbtion rate is given, use the info that the rate is inversly proportional to the distance and integrate with respect to time from 0-5 and multiply your answer by two.
okay, step back for a second
its not that hard, I will post something to you over PM. I have to look up bearings for a crane right now!;)

[632 Regal]

all BS that doesnt need to have a certificate in.

Remember back to your grade scholol days and you wondered how could math ever be practical.....

When you're bored in class remember....Lots of calculus used in designing engines and autos.

For example...

Calculus is the foundation for camshaft design. As a camshaft lobe rotates, the valve lifts or returns. This rate of change of distance with respect to time is dx/dt or velocity. Differentiate again and you dv/dt or acceleration. To fast of acceleration and valves separate from followers or impact their seats too hard. The acceleration rates determine the spring pack you need to keep the system stable. Too high of rate of spring and you can get excessive force on the cam lobe leading to premature wear. On and on and on. All based off of calculus!

[liquidtiger720]

all BS that doesnt need to have a certificate in.


I see them wanting me to take calculus as: learn how to critically think around problems that you will have in the future. So, its not exactly just the math bs.

[GoldenEagleFan]

Didn't mean to imply you needed a certificate to design cams.. just giving an example of how calculus could be used and something to think about while siting bored in the class room.

[liquidtiger720]

Didn't mean to imply you needed a certificate to design cams.. just giving an example of how calculus could be used and something to think about while siting bored in the class room.


I don't think i'm ever bored in my calculus class actually...the material is hard for me, so it keeps me entertained.

[Andrem5]

Let us get to the most relevant question: Why are your Throwing Stars on backwards??


okay dokey
R = rate of rad absorption (units/sec)
x = distance from the source (feet)
k = constant

now R = k/(x^2)
so 200 units/s = k/(5^2)
therefore k = 5000

now in order to solve this you need to find the total units of rad she absorbed

so that will be the Integral of R with respect to time

you will need to find an expression for the distance with respect to time.
that is to say x= f(t)
probably some kind of parabola
then you will find the Integral of k/(x^2) with respect to time
ie integral of 5000/(f(t)^2) with respect to time

you bastard, the horrible memories are flowing back...... nooooooo

edit: the expression for x is something like x = sqrt((60-ut)^2+60^2)
where sqrt is the square root and u is the chick's velocity

[rob101]

Let us get to the most relevant question: Why are your Throwing Stars on backwards??
because a typical retardo frigging used car salesman idiot put them on that way....... are they seriously backwards?
typical my friend brought over this car that'd been roadworthied lately, brakes were faaaaaaaarked, i mean i've never seen brakes that have pitted from corrosion and kickback violently when he brakes not to mention it didn't really brake past a certain point, this car was as roadworthy as a streetluge i could know that from being in the passenger's seat. typical used car ********, most people who give roadworthys here are crooks who don't even look at the carsunless you aren't a dealer then they make it really hard to get one..
lesson is...... used car salesmen are scum who should be exterminated, and that is why they are on backwards. no offensive to any used car people from outside australia, this is not directed at you, but if you are a used car dealer from australia go and kill yourself please now, thank you.

[Andrem5]

because a typical retardo frigging used car salesman idiot put them on that way....... are they seriously backwards?

Yeah, it happens. You always have to remind tire monkeys about that.

If you decide to flip them it is recommended that you replace the OE "triple square" aluminum bolts with something that won't corrode. I used stainless hex bolts and applied anti-sieze.

[onewhippedpuppy]

Try this, disclaimer, I hate Calculus. You're dealing with a triangle, 60ft from the center to the wall, 60 ft along the wall to the edge of the room. As the lady moves from 60 ft to 0 ft (center), the hypotenuse of the triangle represents her distance from the source. So, the distance from the source is sqrt (60^2 + x^2). At 5 ft, the strength is 200, so a constant over the distance equals 200. Your time is a constant because her velocity is constant. 60 ft to the middle / 12 ft/sec = 5 sec, or 10 sec across the room. However, the strength varies with x, so you need to integrate the strength with respect to x, then multiply it by the time. Since we're using the triangle it's only half the room, so the result must be multiplied by 2. Maybe this helps, somebody check my work.
http://img223.imageshack.us/img223/9065/math8iw.png

[Rustam]

So, here's today's Assignment for you guys to solve.


There is a very strong radiation source in the center of a large 120 x 120 foot room. A person must run through this room to get to safety. Her escape route takes her the full lenth along one wall of the room. She is not exposed to radiation outside the room. The strength of the radiation is inversely proprtional to the square of her distance from the source. At 5- feet, her body is absorbing radiation at the rate of 200 un**** per second. If she runs at 12 feet per second, what is the tottal radiation dose she recieves during her dash to safety?


You must show the integral used to solve problem.

envision a triangle from above with sides 60,60 and 84.6. she has to run from 84.6 feet away (at the corner of the room) to 60 feet away from the source, then back to 84.6 feet away now at other corner. The problem makes things tricky by mentioning that she runs next to the wall - the mathematics does not have to account for this scenario - since the source is radioactive, the rate of radiation middle the way through is that of a point 60 feet away from the center. No matter what point it is - at 60 feet away the rate of radiation is same. For that matter, she may as well be running toward the center of the room from the corner 84.6-60=24.6 feet, then turn around and run back same distance getting same load. So you will have to multiply by 2 at the end.

you can use dual integration:

84.6 and 60 are boundaries for first integral

24.6 feet towards the center are covered in 5 seconds - this being maximal boundary for second integral with minimal boundary of zero for starting time. 5 seconds because it takes 5 seconds to run 60 feet at 12 feet per second. in the direction of the source the traverses 24.6 feet hwoever in this limit of time.

now:

dA/dt - time rate of acquisition of radiation gives us:

da/dt=k/r^2 where k =500000

this rate is dependent on distance r away so you have to take its derrivative with respect to r getting:

dda/drdt=-2kr^-3dr/dr

carry dr from left to right side:

d(da/dt)=-2kr^-3dr where dr/dr =1

integrate both sides:

Sd(da/dt)= -2kSr^-3dr

getting:

da/dt= -2kSr^-3dr

carry dt from left to right:

da=-2kSr^-3drdt

and finalize dual integral setup:

a=Sda=-2kSSr^-3drdt

"a" now gives total radioactive material that she received running half way through. Multiply by 2 for the scenario of running by the wall from one corner to another corner.

first integral boundaries low - 60 high 84.6
second integral boundaries low 0 high 5
----
I am still looking for good pics of throttle body setup on m20 engine...

[onewhippedpuppy]

He's only in calc 2, so he won't be doing double integrals. I know that I didn't study those until calc 3. What did you come up with for a final answer?

[Rustam]

He's only in calc 2, so he won't be doing double integrals. I know that I didn't study those until calc 3. What did you come up with for a final answer?

well, in that case he may easily split them - do one first and do second after...

I have to actually come up with final answer for him?

[onewhippedpuppy]

I was just curious if you got the same thing I did.

[DaCan23]

BaGekko (4:09:41 PM): There is a very strong radiation source in the center of a large 120 x 120 foot room

SmarterChild (4:09:42 PM): 120 * 120 = 14,400

>>> Tutor.com Free Day Pass - Missed something in class? Connect to an expert tutor online for help. (sponsorship)

BaGekko (4:09:51 PM): A person must run through this room to get to safety. Her escape route takes her the full lenth along one wall of the room.

SmarterChild (4:09:51 PM): Oh.

BaGekko (4:10:04 PM): She is not exposed to radiation outside the room. The strength of the radiation is inversely proprtional to the square of her distance from the source. At 5- feet, her body is absorbing radiation at the rate of 200 un**** per second.

SmarterChild (4:10:05 PM): What?

BaGekko (4:10:12 PM): If she runs at 12 feet per second, what is the tottal radiation dose she recieves during her dash to safety?

SmarterChild (4:10:14 PM): I have no idea.

BaGekko (4:10:24 PM): You must show the integral used to solve problem.

SmarterChild (4:10:24 PM): Show the integral used to solve problem? Why must I show the integral used to solve problem?

[dacoyote]

Lol....

[rob101]

Why must I show the integral used to solve problem?
Because i told you so, don't ask questions just do it! I want results not excuses!:p

[Rustam]

He's only in calc 2, so he won't be doing double integrals. I know that I didn't study those until calc 3. What did you come up with for a final answer?

now for single integral :

third expression from above must be changed:


carry dt from left to right side:

d(da/dr)=-2kr^-3dt where dr/dr =1

integrate both sides:

Sd(da/dr)= -2kSr^-3dt using limits zero and five

getting:

da/dr= -10kr^-3

carry dr from left to right:

da=-10kr^-3dr

and finalize the integration:

a=Sda=-10kSr^-3dr boundaries - low 60 high 84.6

[Rustam]

BaGekko (4:09:41 PM): There is a very strong radiation source in the center of a large 120 x 120 foot room

SmarterChild (4:09:42 PM): 120 * 120 = 14,400

>>> Tutor.com Free Day Pass - Missed something in class? Connect to an expert tutor online for help. (sponsorship)

BaGekko (4:09:51 PM): A person must run through this room to get to safety. Her escape route takes her the full lenth along one wall of the room.

SmarterChild (4:09:51 PM): Oh.

BaGekko (4:10:04 PM): She is not exposed to radiation outside the room. The strength of the radiation is inversely proprtional to the square of her distance from the source. At 5- feet, her body is absorbing radiation at the rate of 200 un**** per second.

SmarterChild (4:10:05 PM): What?

BaGekko (4:10:12 PM): If she runs at 12 feet per second, what is the tottal radiation dose she recieves during her dash to safety?

SmarterChild (4:10:14 PM): I have no idea.

BaGekko (4:10:24 PM): You must show the integral used to solve problem.

SmarterChild (4:10:24 PM): Show the integral used to solve problem? Why must I show the integral used to solve problem?

well, he is just a child...

[dacoyote]

well, he is just a child...

He is also suppost to be smarter.....

[Rustam]

He is also suppost to be smarter.....

well he did give back 120X120

[rob101]

well, he is just a child...
god dammit I want results not excuses:D

[632 Regal]

who wants to walk around in a microwave anyways?

[Rustam]

who wants to walk around in a microwave anyways?

I have good challenge - how come emergency brakes are red in the train and blue in the airplane?

[rob101]

I have good challenge - how come emergency brakes are red in the train and blue in the airplane?
do you mean air brakes or wheel brakes on an aeroplane?

[onewhippedpuppy]

Why can't we just conclude that she will soon form a 3rd nipple and pancreatic cancer and call it good?

[liquidtiger720]

who is PShovestu? haha. Thanks for the help. :D

[Rustam]

do you mean air brakes or wheel brakes on an aeroplane?

I meant what ever the ones marked "emergency brake"...

[Rustam]

Why can't we just conclude that she will soon form a 3rd nipple and pancreatic cancer and call it good?

I guess that is good too so long as the integral for 3rd nipple formation is shown...

[zhandax]

Do like I did; pay your graduate teaching assistant to tutor you. They will feel too guilty to fail you.

[Rustam]

Do like I did; pay your graduate teaching assistant to tutor you. They will feel too guilty to fail you.

I wouldnt feel guilty if I knew the person did not care for exerting effort

[zhandax]

Hey, the guy is getting a business degree; I feel a kinship. I can tell you the calc I took has been totaly unused in the ensuing 25 years (damn, just realized I am that old; I will have to change my sig). I have developed spreadsheets to calculate the ROR on adjustable-rate mortgage seurities, and another to prepare asset-liability reports, and have had no instance to use calculus. And this includes the time I built a 500sf addition to the back of my house with a vaulted ceiling and a bastard hip roof that the inspector had to call his boss to check out.

[Andrem5]

I can tell you the calc I took has been totaly unused in the ensuing 25 years... and have had no instance to use calculus.
It could be argued that driving a car is an excellent example of the use of "calculus." Or throwing/catching a baseball, etc.

[zhandax]

It could be argued that driving a car is an excellent example of the use of "calculus." Or throwing/catching a baseball, etc.
You are completely correct. But if you calculate it to a decimal point, you may need counseling. Why do you think they call it 'sport'?

[zhandax]

Of course, anyone willing to design a thrust arm which will last 50% longer is exempt from these observations. I simply offered advice to a fellow business major.

[Andrem5]

You are completely correct. But if you calculate it to a decimal point, you may need counseling. Why do you think they call it 'sport'?
It appears the brain is using a type of numerical integration to solve these kinematic problems. So subconsciously you may be "computing" to a few decimal points as needed.
That said, I still may need counseling.