A psycho is stabbing a person with a knife. The victim screams at 30 decibels. The stabbing pressure made by the knife and the victim's stomach is 10 Pa. The victim's height is 160 cm. The stabbed knife is 60 cm above the ground and is sticked at a depth of 5 cm into the victim's stomach. The length of the sharp part of the knife is 20 cm. Let S(t), P(t), H(t), and D(t) be decibels, amount of pressure, height of the stabbed knife above the ground, and the sticked depth of the stabbed knife into the victim's stomach at time t (in seconds). Every centimeter moved up the victim's body by the knife increases the decibel level, pressure, and sticked depth by 5 decibels, 7 Pa, and 3 cm respectively. Given that the psycho will move up the knife by k cm every second. Find:
a) the functions S(t), P(t), H(t), and D(t) in terms of k
b) the value of k so that the knife will have no sharp part left (completely sticks inside the victim's body) as it reaches the victim's forehead (full height)
c) Let X(t) be the psycho's satisfaction level at time t
given by:
X(t) = 8t³×S(t)+4t²×P(t)+t×H(t)+2D(t)
Calculate:
i) the time when the psycho will be the most
satisfied while having fun with the victim
ii) the highest satisfaction level the psycho can
experience
#Help with hard integration problem
gleaming lynx
shell sorrelBOT
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crystal pike
A psycho is stabbing a person with a knife. The victim screams at 30 decibels. T...
what book did you get this question from
I'd love to read it
S(t) = 30+5kt
P(t)=10+7kt
crystal pike
A psycho is stabbing a person with a knife. The victim screams at 30 decibels. T...
how does depth increases by 3cm every centimetre pushed in?
pulsar pumice
bro WHAT?
gleaming lynx
A psycho is stabbing a person with a knife. The victim screams at 30 decibels. T...
this is pretty easy
use Xenon's law of transformation
and youll get the answer
gleaming lynx
what book did you get this question from
it's not from a book
my friend challenged me
he made it up himself
gleaming lynx
S(t) = 30+5kt
P(t)=10+7kt
how?
crystal pike
it's not from a book
my friend challenged me
he made it up himself
and you created a discord account just to ask this question that's why the username
crystal pike
how does depth increases by 3cm every centimetre pushed in?
explain this tho
gleaming lynx
how does depth increases by 3cm every centimetre pushed in?
no it means depth increases by 3 cm every centimetre moved up
gleaming lynx
I think so
crystal pike
S(t) = 30+5kt
P(t)=10+7kt
this is write
every second knife moves up k cm
scream increases by 5k decible
D(t) = 5+ 3kt
H(t)=60+kt
gleaming lynx
and you created a discord account just to ask this question that's why the usern...
I have an account previously but I deleted it, and today my friend challenged me so I created a new account to ask this
crystal pike
that's alright but do you understand my answer for the first question?
crystal pike
for part b
suppose knife reaches the forehead at T
60+kT=160
T=100/k
at the same time D(t)=20
5+3kT+20
T=5/k
so there's no value of k for which this is possible
gleaming lynx
ohh make sense
gleaming lynx
for part b
suppose knife reaches the forehead at T
60+kT=160
T=100/k
at the sam...
so the question is wrong?
crystal pike
$$X(t)=8t^3(30+5kt)+4t^2(10+7kt)+t(60+kt)+2(5+3kt)$$
$$X(t)=40kt^4+(240+28k)t^3+(40+k)t^2+(60+6k)t+10$$
for maximum satisfaction is at T where X'(T)=0 and its answers are too messy
surreal kettleBOT
scilent
crystal pike
so the question is wrong?
no values is also a valid solution I think
,w maxima of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10
surreal kettleBOT
crystal pike
oh wait
I'm an idiot
maximum satisfaction will be when knife is all the way in
so at t= 5/k
,w value of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10 at x=5/k
surreal kettleBOT
crystal pike
@gleaming lynx ask you're friend if these answers are right
and also to see a therapist
gleaming lynx
so at t= 5/k
why at t=5/k?
gleaming lynx
<@456226577798135808> ask you're friend if these answers are right
sure I'll ask him tomorrow
gleaming lynx
and also to see a therapist
LMAO
crystal pike
why at t=5/k?
because at t=5/k D(t)=20 which means knife is all the way in
crystal pike
,w plot of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10
surreal kettleBOT
gleaming lynx
**scilent**
I personally think this is more correct
crystal pike
I think it is
crystal pike
I personally think this is more correct
for positive K maxima is at infinity it only gives answers for negative K
,w minima of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10
surreal kettleBOT
crystal pike
,w minima of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10 in domain (0, 5/k)
surreal kettleBOT
crystal pike
,w maxima of 40kx^4+(240+28k)x^3+(40+k)x^2+(60+6k)x+10 in domain (0, 5/k)
surreal kettleBOT
Requested by scilent314
crystal pike
yeah @gleaming lynx I think I am right
maximum satisfaction will be alwayse at t=5/k
gleaming lynx
I still don't get it
crystal pike
I still don't get it
in normal case (k>0) its maxima is at infinity but the knife can't go infinitely in
I think I am wrong somewhere but I don't see it you'll have to ask your friend
gleaming lynx
ohh
gleaming lynx
I think I am wrong somewhere but I don't see it you'll have to ask your friend
okay then
I have another question
can I ask here or should I make a new post?
gleaming lynx
also you clickbaited me with the title no integration involved here
I thought the first question involves integration
2nd question:
An evil scientist is draining blood from a person's body at a rate of 10 ml/s into a cylindrical tank with a radius of 10 cm and a height of 20 cm. The tank is initially 1/10 full. Find:
a) the rate at which the height of the blood is increasing
b) the general equation of the height of the blood at time t (in seconds) h(t)
c) the general equation of the of volume of the blood at time t (in seconds) V(t)
also from my friend
crystal pike
bro really needs therapy
gleaming lynx
LOL
crystal pike
An evil scientist is draining blood from a person's body at a rate of 10 ml/s in...
v= area * height
rate at which height is increasing:
$$100\pi h=10 cm^3$$
$$h=\frac{1}{10\pi}$$
surreal kettleBOT
scilent
crystal pike
$h(t)=2+\frac{t}{10\pi}$
surreal kettleBOT
scilent
crystal pike
$$V(t)=100\pi h(t)$$
$$V(t)=200\pi + 10t$$
surreal kettleBOT
scilent
crystal pike
why height rate?
10 ml blood is droping every second so area * (height rate) = volume rate
surreal kettleBOT
scilent
crystal pike
x' is derivative of x
gleaming lynx
**scilent**
this part?
gleaming lynx
**scilent**
shouldn't the 2 be 20?
crystal pike
shouldn't the 2 be 20?
tank is 1/10 full so 20(1/10)=2
@gleaming lynx bro you get it?
gleaming lynx
tank is 1/10 full so 20(1/10)=2
ohh you're right
gleaming lynx
<@456226577798135808> bro you get it?
yes
@crystal pike thank you so much bro
appreciate it
rigid oarBOT
@lavish temple has given 1 rep to @crystal pike
gleaming lynx
@crystal pike I've asked my friend and here is the modified version
A psycho is stabbing a person with a knife. The victim screams at 30 decibels. The stabbing pressure made by the knife and the victim's stomach is 10 Pa. The victim's height is 160 cm. The stabbed knife is 60 cm above the ground and is sticked at a depth of 5 cm into the victim's stomach. The length of the sharp part of the knife is 380 cm. Let S(t), P(t), H(t), and D(t) be decibels, amount of pressure, height of the stabbed knife above the ground, and the sticked depth of the stabbed knife into the victim's stomach at time t (in seconds). Every centimeter moved up the victim's body by the knife increases the decibel level, pressure, and sticked depth by 5 decibels, 7 Pa, and 3 cm respectively. Given that the psycho will move up the knife by k cm then drops it by 1 cm every second. Find:
a) the functions S(t), P(t), H(t), and D(t) in terms of k
b) the value of k so that the knife will have no sharp part left (completely sticks inside the victim's body) as it reaches the victim's forehead (full height)
c) Let X(t) be the psycho's satisfaction level at time t
given by:
X(t) = 8t³×S(t)+4t²×P(t)+t×H(t)+2D(t)
Calculate:
i) the time when the psycho will be the most
satisfied while having fun with the victim
ii) the highest satisfaction level the psycho can
experience
hollow bronze
also you clickbaited me with the title no integration involved here
I think you can also do it with integration
for example S(t):
S(0) = 30
dS(t)/dt = 5k
dS(t) = 5k dt
then integrate both sides
S(t) = 5kt+C
plug in t=0
S(0) = 5k(0)+C
30 = C
C = 30
S(t) = 5kt+30
S(t) = 30+5kt
same for the other functions
crystal pike
A psycho is stabbing a person with a knife. The victim screams at 30 decibels. T...
I don't think you can call that a knife anymore
even "sword" seems like too less
gleaming lynx
I don't think you can call that a knife anymore
LOL
gleaming lynx
even "sword" seems like too less
idk I asked him and he just modified it that way