Differential equations (1 Viewer)

[Antwan23q]

Houdini is standing inside a tank of water which he has to escape. The stage upon which the tank is, is 1 m above the ground (x-axis). Houdini is chained to a concrete slab which he is standing on inside the tank The tank is 3 metres high(from stage), and the radius at the top is 0.4m. The equation of the tank is given by:
4/( 7x^2) + (3/7). Note: When X=1, Y=1, and when X=0.4, Y=4
1. Find the Volume of the tank using calculus.
2 a)Express the volume(V) of the water(in L) in the tank, as a function of height(H). I.E find V in terms of H, where H is height above the stage.
b) state the domain and range of the equation ( in Q2 (a) )
Q4. He plans to escape when his head is just submerged in water. Houdini is 180 cm tall and it takes him 10 mins to escape from the chains on the concrete slab. Ignore the volume of houdini or the concrete slab for th moment.
If water is being pumped in at 300 L/min, what should the height of the concrete block be in order for him to escape in 10 mins.

 

[FinalFantasy]

"Houdini is chained to a concrete slab which he is standing on inside the tank "
awww... poor Houdini
someone save him!

 

[Antwan23q]

woah everyone
his question is a bitch, and there is a picture to go with it, but i cant really upload it for some gay reason anyways it looks like

y
__|__
) | (
____/ _|__\_____ y=1
|
______|_________x
|

 

[FinalFantasy]

u try upload onto a website?

 

[Antwan23q]

 

[FinalFantasy]

hahaha, is that Houdini chained to the slab

 

[KFunk]

1. y = 4/( 7x²) + (3/7)

(7x²)(y - 3/7) = 4

x² = 4/(7y - 3)

V = ∫ πx² dy from y= 1 to 4

V = π∫ 4/(7y - 3) dy

= π[ 4/7.ln(7y - 3)] from 1 to 4 = 4π/7. ln(25/4) L

2. a) V = 4π/7. ln{[7(H+1)-3]/4} L since when integrating y will equal H + 1 (1m above stage) and the lower bound will always be y=1.

b) the domain of the function (Height) is 0 ≤ H ≤ 3
the range is 0 ≤ V ≤ 4π/7. ln(25/4) L

There are some ugly numbers in there...

EDIT: if my answer 4π/7. ln(25/4) L is actually litres and they're pumping the water out at 300L/min then I probably did something wrong.

EDIT-2: Or perhaps I should learn my units: 1 L = 1000cm^3 , 1m^3 = 100x100x100 = 1 x 10^6 cm^3 i.e. multiply the above L measurements by 10^3.

 

[Antwan23q]

lol i didnt draw it, one of my friends from melbourn asked me to do it, but for some reason he got a volume of 32 m^3 and i got 10m^3 so i thought, better let the pro's do it like final fantasy and k-funk, my hero. btw, is that george clinton? i love funkadelic/parlament

 

[FinalFantasy]

lol i didnt draw it, one of my friends from melbourn asked me to do it, but for some reason he got a volume of 32 m^3 and i got 10m^3 so i thought, better let the pro's do it like final fantasy and k-funk, my hero. btw, is that george clinton? i love funkadelic/parlament

lol kfunk is da pro not me
im juz here to bum around

 

[Antwan23q]

and solve every integration under the sun. dammit man, give someone else a go. lol

 

[KFunk]

lol kfunk is da pro not me
im juz here to bum around

Which is why I managed such a wonderfully incorrect (possibly) answer...

lol i didnt draw it, one of my friends from melbourn asked me to do it, but for some reason he got a volume of 32 m^3 and i got 10m^3 so i thought, better let the pro's do it like final fantasy and k-funk, my hero. btw, is that george clinton? i love funkadelic/parlament

Close, it's bootsy collins: one of the world's funkiest bass players. He did a fair bit of co-writing with Clinton in Parliament but then the offshoot 'Bootsy's rubber band' developed.

 

[FinalFantasy]

i can onli do integration cuz it's like the easiest lol
it's q1 always on HSC exam kekeke
and for ur question it looks like a lot of trouble to do it lol.. where did u get it from?

 

[KFunk]

Sorry, my misinterpretation, they're adding water to the tank, not taking it away. Well, after 10 minutes the volume of water will be 3000 L

3000 L = 4π/7. ln{[7(H+1)-3]/4}x10³ L

3 = 4π/7. ln{[7(H+1)-3]/4}

[7(H+1)-3]/4 = e^A where A = 21/4π

H = (4e^A +3)/7 - 1 = 2.47 m

Houdini is 1.8 m in height so the height of the concrete block = 2.47 - 1.8 = 0.67 m

Too many numbers :-S.

 

[Antwan23q]

ah one of my friends gave it to me to do. i gave it a go, but like i said i had no idea if it was right