Wdym through substitution?
#help-0
hardy gyro
pure bolt
do you know integration by substitution
hardy gyro
do you know integration by substitution
Yes I do
Gimme a sec
Do I integrate all of these to find the function or do I integrate the first half of the integration?
<@&286206848099549185>
hardy gyro
so the answer is 105/2?
That's what I've got but I'm not sure if thts correct
Wait 105/2 isn't the right ans
wait ill be back in 2 hours because i have another quiz to attend, pls help me press the cross to avoid timeout
lone heartBOT
@hardy gyro Has your question been resolved?
past dagger
lone heartBOT
past dagger
i dont understand how to get from step 1 to step 2
alpine sable
90 (e^0.2)(e^t) > 200 (e^0.1)(e^t)
e^t cancel from both sides
e^0.2 / e^0.1 = e^0.1
alpine sable
.......one sec mb
alpine sable
ok isnt this just e^0.2t / e^0.1t ?
past dagger
no clue, thats why im here
past dagger
i see okay
alpine sable
same here with e and 0.2t
alpine sable
yea
past dagger
okay thanks man
alpine sable
np
past dagger
.close
sly comet
lone heartBOT
ocean sealBOT
Ann
visual bolt
How to break this into partial Fraction. I've done it but at initial term, I'm not getting 1/2r as the answer suggests. I am only getting 1/r
visual bolt
Answer:
alpine sable
How to break this into partial Fraction. I've done it but at initial term, I'm n...
1/r(r+1)(r+2) = A/r + B/(r+1) + C/(r+2)
1 = A(r+1)(r+2) + B r(r+2) + C r(r+1)
let r = 0
1 = A (1)(2)
A= 1/2
which gives 1/2r
visual bolt
ohk thanks a lot.
alpine sable
👍
pearl lily
Can someone please have a look how to do part b of this question. I've solved that a = 2/e and b=-1
north adder
Can someone please have a look how to do part b of this question. I've solved th...
have you taken the derivatives?
pearl lily
yes
north adder
okay... and what do you know about the graph behaviours
north adder
okay cool, now what
whats the graph behaviour of 1/x
is it increasing
or decreasing
after e
pearl lily
decreasing for the interval
pearl lily
decreasing too
pearl lily
like this
hardy gyro
.reopen
hardy gyro
Where do I reopen
hardy gyro
Ok
north adder
the value is going to be greater for the fraction
for every x value you keep in
taking the square root of a number will reduce the number correct? unless its a fraction where the numerator is lesser than the denom
north adder
i gotta show this right, can i show x > the denomiator on the left
you could solve it ig
pearl lily
taking the square root of a number will reduce the number correct? unless its a ...
like this i get but how do i show mathematically, its 3 marks i gotta show
north adder
like this i get but how do i show mathematically, its 3 marks i gotta show
you could solve it
north adder
i gotta show this right, can i show x > the denomiator on the left
multiply both sides
north adder
tell me if the equation looks familiar
pearl lily
wooooow
pearl lily
(x-e)^2>0
pearl lily
dang it was so easy all along lol ok thx so much how to close
pearl lily
.close
foggy charm
i need help with part c
lone heartBOT
i need help with part c
limber kindle
i need help with part c
dR/dt = -{20/(1 + 2t)^2}
Time can only be positive, that means the value inside {} will always be positive. Thus the rate will always become negative i.e. less than 0.
Now if you differentiate dR/dt w.r.t x, you will get a positive number no matter what for t>= 0 (in the same way as above)
lone heartBOT
@foggy charm Has your question been resolved?
foggy charm
find dR/dt and d^2R/dt^2
already did that
foggy charm
$R'=-\frac{20}{(1+2t)^2}$
ocean sealBOT
breadiculous
foggy charm
$R''=\frac{80}{(1+2t)^2}$
ocean sealBOT
breadiculous
carmine oar
**breadiculous**
now let's take a look at (1+2t)^2
it must be greater of equal to 0
but in order to achieve 0, t must be -ve, so no 0 case
therefore (1+2t)^2 > 0
and 20/(1+2t)^2 > 0
@foggy charm
foggy charm
yea i was reading
foggy charm
kind of
is it cause of its positive sign
like at any time t, the function will be positive
where as the concavity will be negative
carmine oar
well my english is bad
I guess you're right
you can see that 20/(1+2t)^2 > 0 so that with the -ve sign it is <0
carmine oar
**breadiculous**
same goes for R''
foggy charm
whats -ve
lone heartBOT
carmine oar
np
lone heartBOT
Available help channel!
unique pumice
Hey. Im curerntly studying Calculus II and I was doing a problem of implicit functions. So iam given this 3 dimensional scalar function f(x,y,u) and have to prove whether a function u(x,y) exists implicitly in one point. I have alredy done that. But in the second part asks me to check whether the gradient in this point is orthogonal to the "level set" for an specific value of u.
unique pumice
Ive got the gradient on that point, but i dont know how to get the tangent vector to the "level set", which is the vector which is supposed to be orthogonal with the gradient
Am i supposed to put in the value of u in my function, get that (x,y) dependent curve and parametrize it in respect to t and then derive and substitute my point?
sorry if my languaje is not accurate, correct me at any point, and thanks
my curve is https://www.wolframalpha.com/input?i2d=true&i=Power[x%2C2]%2BPower[y%2C2]%2Bxy-1%3D0 after u=-1 substitution
<@&286206848099549185>
lone heartBOT
@unique pumice Has your question been resolved?
lone heartBOT
@unique pumice Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
heady briar
I need some help. Anyone can solve this problem and give detailed explanation?
viscid cloud
Ok, so no. of row squares * no. of column squares = 40 right?
note: The no. of squares must be whole number
vale wigeon
Anyone can solve this problem
we don't give solutions here
you should think about the phrase "Andrew found the middle row of squares and colored it in" though.
lone heartBOT
@heady briar Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
narrow star
lim x--->2
|x+2| - |4|
x - 2
I cannot figure out how to handle |x+2| - |4|
oak perch
(|x+2|-4)/(x-2)?
You can just take absolute value away
When x is closed enough to 2, |x+2|=x+2
Then it’s constant 1
oak perch
What does you partition line means here? I thought it was /
narrow star
|x+2| - |4| would be like x-2, right? so then |x-2| = |x+2|
gray isle
so then |x-2| = |x+2|
no, wheres that coming from
narrow star
edge calculation arythmatics limes is that stuff
Dont know the english terms
lim x--->2
oak perch
You just need lim |x+2|-4 when x approaches 2? Then you are correct, it’s just x-2
Lim (x-2) I mean
Which is 0
narrow star
> so then |x-2| = |x+2|
no, wheres that coming from
because -2 cannot exist in between ||
so it has to turn to the positive
gray isle
you have a misunderstanding of the absolute value bars
gray isle
$\red{|}\text{stuff} \red{|}$
narrow star
Oh yeah.
ocean sealBOT
ℝamonov
narrow star
Absolute value bars. They turn into the positive equivalent cause - cant exist in there.
gray isle
they do NOT mean turn every - sign between them to a +
gray isle
they do NOT mean turn every - sign between them to a +
narrow star
Then what does it mean at all?
then why bother putting those confusing lines around stuff?
x_x
gray isle
they don't do nothing either
narrow star
I still have no idea whether |x+2| - |4| makes it be |x+2| or |x+6| or x-2...I am fucking confused mate.
Over an hour stuck on that fucking little thing.
gray isle
consider the piecewise definition of the absolute value
$|\text{this}| = \begin{cases} \text{this}\ &\text{if } \text{this} > 0 \\ -\text{this} \ &\text{if\ } \text{this}\leq 0 \end{cases}$
ocean sealBOT
ℝamonov
gray isle
now consider whether x+2 will be positive or negative around x=2
narrow star
Why would anyone want to do that and not just use like separate variables? Like I know there must be a math reason, but if I would code stuff I would rather have two variables than to go through that headache.
Well I need x-2 at the top to strike it out with the bottom.
so the current term is:
lim x--->2
|x+2| - |4|
x-2
And if I would have x-2 at the top the calculation forward would be easy.
gray isle
will x+2 be positive or negative around x=2?
(this is not supposed to be a trick question)
narrow star
Both? Maybe?
I do have to do the same calculation with lim x ---> -2 too,...
So I wonder why would I have it be positive and negative right now too?
narrow star
gray isle
consider numbers close to 2,
like 1.9, 2.1 and even 2 itself
will x+2 be positive or negative for those values
narrow star
Differenciality has to be proven.
gray isle
this is not supposed to be a trick question
narrow star
I do not know...cause x is still ??? and not like a calculated number on my sheet.
It could be anything.
I havent calculated the x from that term yet.
gray isle
you're interested in what's happening around x=2
narrow star
Yep.
gray isle
because that's what the subscript under the lim is indicating
alpine sable
then why bother putting those confusing lines around stuff?
Its kind of a trick
gray isle
and what you currently want to do is simplify your expression such that it can be expressed withou absolute value bars
which makes things a lot easier
now, ignore all the other stuff for now
and focus on the simpler things
when x is around 2, will x+2 be positive or negative
alpine sable
Absolute value is kind of tricky to work with usually, but here it can be removed pretty easily
gray isle
like if
x = 1.9999999, will x+2 be positive or negative?
narrow star
it can only be removed easily if it is x-2 at the top.
gray isle
if x = 1.99999 will x+2 be positive or negative
alpine sable
|4| is just 4, and when you have x close to 2, its basically the same as without it
gray isle
if x = 1.99999999999999999999999999999999 x+2 be positive or negative
what about if x= 2.00000000000000000001, x+2 be positive or negative for that value of x
alpine sable
what about if x= 2.00000000000000000001, x+2 be positive or negative for that va...
I think hes afk
gray isle
do NOT overthink this,
i must repeat that this is NOT supposed to be a trick question
alpine sable
around x=2, x+2, x+2 will be positive
So you can just remove absolute value, since its already positive
Then simplify
narrow star
So I have to do like 2 cases or what?
alpine sable
So I have to do like 2 cases or what?
No need
gray isle
it should be trivial that x+2 is positive around x=2
you would do case work here if the limit was x→-2
narrow star
Well I cant really say that.
After all I am working with this term.
lim x---> x1
f(x) - (fx1)
x - x1
I cant really say what the first x is.
It is still unknown.
x1 is the 2 here.
But the x must remain the default function to my knowledge.
alpine sable
F(x) is |x+2| right?
narrow star
Eh...
I got g(x) = |x+2|
and x0 = 2
x1 = -2
So right now I think I need 4 cases.
2 for x0
2 for x1
For x > 0 and x < 0
alpine sable
|x+2| - |2+2|
x-2
narrow star
Yep.
alpine sable
|x+2| - 4
x - 2
narrow star
So far so good.
alpine sable
Like we said x+2 is gonna be positive at around 2
narrow star
Now I am confused what to do witht he fucking 4.
alpine sable
x+2-4
-------
x-2
Simplify from there
alpine sable
?
gray isle
since $x+2>0$ as $x\to 2$, $|x+2| = x+2$ as $x→2$ \
4 is also clearly a positive number so $|4| = 4$. \
overall:
$$\lim_{x\to 2} \frac{|x+2|-|4|}{x-2} = \lim_{x\to 2} \frac{x+2-4}{x-2}$$
narrow star
Cause I been chatting with many folks about this and then they were all saying cases for like x > 0 and x < 0 and I got mad confused.
And I cant see the difference even if x > 0 or x < 0
alpine sable
You dont need cases, its the limit as x approaches 2 which will always be positive
narrow star
Can I just drop the absolute value bars though?
alpine sable
So its just at the end
$\frac{(x-2)}{x-2}
narrow star
Dont I have to keep them?
ocean sealBOT
ℝamonov
alpine sable
So its just at the end
$\frac{(x-2)}{x-2}$
ocean sealBOT
7aman
alpine sable
Dont I have to keep them?
Not in this case
X-2/x-2 is just 1
Even if you graph it you will see that around 2 its just 1
gray isle
you can write your expressions without the bars with proper consideration and casework if needed
narrow star
So I should write down both cases x>0 and x<0 but they would be THE SAME?
gray isle
for this question no
narrow star
Just to be complete on that matter of how the general approach is.
So when do I need cases?
gray isle
because you are concerned with the limit as x approaches 2 in this question
and nothing else
alpine sable
So when do I need cases?
If the results differ from 1 side of the limit to the other I think, @gray isle correct me if Im wrong
narrow star
I think I am a bit less confused now
I must say though...
I fucking hate absolute value bars by now.
I want to see those sticks burned and turned into a cozy campfire.
Not a math problem robbing me of my serene mental state.
Well - I am thankful for all the kind help.
I wish you great travels.
gray isle
you should review more on the piecewise definition
narrow star
Aye.
alpine sable
I fucking hate absolute value bars by now.
I feel that way with partial fractions
narrow star
.close
astral breach
Hello, these are axiomatic probability's properties(idk if thats a correct term). I need to prove 3rd one. I can see that A+B=AB' + A'B + AB. The axiom of probability says that if AB = {emptyset}, then P(A+B) = P(A) + P(B) and the proof states that the AB is an emptyset. But from where does it conclude that?
fast patio
flat ore
Hello, these are axiomatic probability's properties(idk if thats a correct term)...
I don't understand A+B=AB' + A'B + AB, what even is AB?
set multiplication?
astral breach
I don't understand A+B=AB' + A'B + AB, what even is AB?
event multiplication yes. Them happening together
prime badge
can't you show the proof too?
astral breach
Its in my native language. Basically 3rd line says that (As the addables multiplications are empty sets, then ...). Thats what I don't understand - why can I presume that they are empty sets
Ah I see, I guess I understood that wrong a little bit. P(A+B) = P(AB'+A'B+AB). And AB'A'BAB=emptyset*AB = emptyset and thats why I can use the said axiom.
prime badge
it just follows from the middle 3 expressions, i don't see why you need to justify that
astral breach
Yes I misunderstood the sentence. I thought that A*B has to be emptyset, but no. Rather it states that AB'A'BAB is emptyset, which is obvious. My bad
prime badge
okay
spare mango
lone heartBOT
gray isle
have you drawn a diagram?
gray isle
isn't 44
spare mango
oh shit
gray isle
also you are explicitly told that the bearing was 56°
so the first thing you should do would be to actually mark that properly
spare mango
How would i do that
gray isle
it would also help to draw another compass axis where the plane turns
and mark the angle you want to find
gray isle
no
the axes should be bigger/longer
and the theta should be next to an arc clearly showing which angle you're interested in
gray isle
show your new diagram
gray isle
no
the arc for your theta is extended longer than it should be
also there are strange curves/arcs in your diagram
spare mango
oh ye let me fix the curves rq
gray isle
wtf happened to your ruler that resulted in the orange parts
what's with the green part
and the arc for theta marked in purple should stop at the red line / path of the plane
(instead of what looks like to be all the way to the south axis)
spare mango
wtf happened to your ruler that resulted in the orange parts
what's with the gre...
lol im just rlly sleepy
dont worry abt it anymore thanks for the help
.close
hollow sluice
hello, can anyone help me with this?
lone heartBOT
hello, can anyone help me with this?
hollow sluice
is PSR an isosceles triangle??
viscid cloud
yes
hollow sluice
if so, then PR= 6√2?
viscid cloud
yes
lone heartBOT
lone heartBOT
✅
hollow sluice
how do you solve for 4 and 5?
gray isle
do you know the definition of perimeter?
hollow sluice
do you know the definition of perimeter?
yea, add all sides. i'm just confused abt the other part of hyp
using altitude theorem
gray isle
wdym other part of hyp
alpine sable
yea, add all sides. i'm just confused abt the other part of hyp
PQ + QR + PR
hollow sluice
PQ + QR + PR
yes
alpine sable
PR is 6sqrt(2)
Like you said
I dont have my calc on me but I think you can use RS and angle Q to find SQ
Since QSR is right, QRS has to be 60°
You have all three angles and a side
hollow sluice
what i mean is finding x since what we are finding is PQR, not RSQ
alpine sable
Oh mb
hollow sluice
its okayy
alpine sable
PSR is right
hollow sluice
it's in the altitude theorem
alpine sable
Shouldnt PRS be 45° aswell?
hollow sluice
yes its 45-45-90
alpine sable
it's in the altitude theorem
6/x=6sqrt(3)/6?
last ether
You also know that x = 6
By definition
So you can solve for your perimeter and area
last ether
Isosceles moment
hollow sluice
sheesh
alpine sable
You also know that x = 6
x=2*sqrt(3) no?
last ether
No
You can assume that PQ is a straight line and so if RSQ is a right angle, so is RSP
That gives you a 45-45-90 triangle
The very properties of a right isosceles triangle
Knowing that RS = 6, and that RSP is an isosceles right triangle (with angle RSP being the right angle), then PS = RS = 6
hollow sluice
can i add 6+ 6√3?
last ether
For what
alpine sable
Perimeter
last ether
PQ is 6 + 6sqrt(3) yes
hollow sluice
is this the final answer for 4? i'm rlly starting to doubt this long answer lol
next pulsar
if something is a surface, it can be entirely covered by surface patches. does it matter if those surface patches intersect?
last ether
I mean it depends
If youre trying to optimize material, it matters
Unless this is some voodoo topology shit then idk
next pulsar
let's say i am just trying to find a collection of surface patches to cover... idk... a sphere of radius 1 centered at (0,0,0)
i could cover that with two patches, right?
like to hemispheres intersecting at the seam
two*
lone heartBOT
@next pulsar Has your question been resolved?
lone heartBOT
@next pulsar Has your question been resolved?
main kraken
Show that a^sqrt(log(a, b)) - b^sqrt(log(b, a)) = 0
lone heartBOT
Show that a^sqrt(log(a, b)) - b^sqrt(log(b, a)) = 0
ocean sealBOT
main kraken
idk where to start basically
limber kindle
(log(b)/log(a)/log(a)/log(b))^1/2 = log(b)/log(a)
=> ((log(b)^2/log(a)^2))^1/2 = log(b)/log(a)
=> log(b)/log(a) = log(b)/log(a)
=> log(b)/log(a) - log(b)/log(a) = 0
hence proved
limber kindle
idk where to start basically
here you go
you put b on the right hand side and take log on both sides, then with the property of log(a)^b = blog(a) you solve it accordingly
uncut plank
(log(b)/log(a)/log(a)/log(b))^1/2 = log(b)/log(a)
=> ((log(b)^2/log(a)^2))^1/2 ...
Is it ((log(b)^2)/(log(a)^2))^(1/2)?
limber kindle
Is it ((log(b)^2)/(log(a)^2))^(1/2)?
yeah?
limber kindle
I just want to correct the second line from your proof
oh yeah
my bad
there, fixed it. Thanks a lot
main kraken
.close
wet spindle
lone heartBOT
wet spindle
I got 8 since 4/2 = 2 so the square = 4 and the rectangle is = 2
limber kindle
wtf are the boxes here?
wet spindle
is that a valid answer?
last ether
Bro what are the boxes
wet spindle
wtf are the boxes here?
variables
last ether
Bruh
limber kindle
then it should be 1/2
the answer
whoever made this test sure did not put brain in it
last ether
Lol
wet spindle
the answer
how
last ether
Lemme show you
I'm gonna set the square as "a", the rectangle as "b"
$\frac{a}{b} = 2$
ocean sealBOT
Umbraleviathan
wet spindle
ok
ocean sealBOT
Umbraleviathan
last ether
As such, $4\cdot\frac{a}{b} = 4\cdot(2) = 8$
ocean sealBOT
Umbraleviathan
last ether
Since you replace that fraction
hot frigate
hot frigate
.close
sterile ravine
How to show that t<=(pi/2)*sin(t) when 0<=t<=pi/2
lone heartBOT
How to show that t<=(pi/2)*sin(t) when 0<=t<=pi/2
marsh rapids
concave down
the general interpretation of concavity (not the one for differentiable functions, the general one) states that a concave down function's graph always lies above its cord
lone heartBOT
@sterile ravine Has your question been resolved?
tacit arch
I think the differentiable one works too
marsh rapids
How would it ? The fact that the derivative is decreasing doesn't tell you much about its actual values
pulsar juniper
lone heartBOT
lone heartBOT
@pulsar juniper Has your question been resolved?
pulsar juniper
<@&286206848099549185>
tacit arch
Have you tried anything
pulsar juniper
Have you tried anything
no I do not understand it
lone heartBOT
@pulsar juniper Has your question been resolved?
wanton kiln
no I do not understand it
Read the problem again and see if you can figure out why the table was set up the way it is.
If you still don't understand it, tell us what part of it you don't understand and we might be able to help.
unreal meteor
I get D but it says the correct answers B?
lone heartBOT
I get D but it says the correct answers B?
half stream
Okay so we know the minimum is somewhere from 10-15 and the max is somewhere from 40-45
unreal meteor
yes
half stream
If we add up the values, what do we get?
unreal meteor
which
unreal meteor
260
half stream
I didn't get that
unreal meteor
195
unreal meteor
85
half stream
I got 85
So 85 is the total number of the values. Now, what do you know about the Q1, median, and Q3?
half stream
median is the middle
Yes, but what does the middle mean specifically?
unreal meteor
Q3 is 3/4
unreal meteor
Yes, but what does the middle mean specifically?
Half
unreal meteor
50%
half stream
Like you said, Q1 is 1/4, or 25%
median is 50%, and Q3 is 75%
Remembering the percentages can be helpful, but you can also just use the fractions
So, we have 85 values. What values lie at the q1, the median, and the q3?
unreal meteor
q1 - 21.25 median - 42.5 q3 - 63.75
half stream
Good! Now, look on the histogram. Which bars contain 21.25, 42.5, and 63.75?
lapis ingot
I get D but it says the correct answers B?
my man just got flipped off by a graph
unreal meteor
Good! Now, look on the histogram. Which bars contain 21.25, 42.5, and 63.75?
None?
unreal meteor
my man just got flipped off by a graph
lol
half stream
None?
Well approximately
Sending it again so we can see it easier
Try counting the values in the bars. Which bar contains the value closest to 21.25?
unreal meteor
Middle
unreal meteor
Oh bar 20
half stream
The middle bar contains 27 values, not the 27th value
unreal meteor
So 2
half stream
Now do the same for 42.5 and 63.75
half stream
Why would you round it?
unreal meteor
because decimals aren’t on it
half stream
Well you are right, there is no 63.75 value, but if there was, where would the value lie?
unreal meteor
At 65
half stream
Which bar I mean
half stream
Let me check
63.75 is the 5th bar, because it is in between 58 (10+10+11+27, the first 4 bars) and 70 (10+10+11+27,+12, the first 5 bars)
Basically what you are doing in your mind is making a cumulative relative frequency graph
young finch
thinking about it analytically since you have so many values in the middle the iqr will be very small
So it makes logical sense that it is B
half stream
This is a good way to think about it
young finch
D has a wide spread iqr which would mean the inner values are more spread out across multiple bars
but the tails are also much smaller
box plots are always divided up into 25% of the data for each segment
unreal meteor
But if it’s B then how can it be bar 2 - bar 4 - bar 5 if bar 2 is 20
half stream
Sorry I made a mistake it was 3 bar
Because 23.25 is in between 20 and 31
And therefore the value lies in the bar from 20 to 25
unreal meteor
.close
silent crane
Could someone walk me through this? Idk what I'm doing wrong
silent crane
"A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. Determine the resultant ground velocity of the plane."
I drew it like this
And the magnitude of the resultant vector I thought was 312.3km/h
Here's their solution
The resultant magnitude shuld be 493 but idk why
<@&286206848099549185>
lone heartBOT
@silent crane Has your question been resolved?
silent crane
I wonder if I word it badly, and thats why no one ever helps me lol
TLDR for anyone checking in, its just a vector problem <@&286206848099549185>
alpine sable
why did you use sin(20) and not sin(200)?
the problem is sin(20) = -sin(200), so the signs get messed up
lone heartBOT
@silent crane Has your question been resolved?
silent crane
the problem is sin(20) = -sin(200), so the signs get messed up
oh HECK i didnt realize that
I used sin20 because I thought i could subtract the bearing of 200 by 180 to make it easier to work with
lone heartBOT
@silent crane Has your question been resolved?
narrow geyser
help
narrow geyser
which are stretched or compressed either vertically or horizontally
- y = -2(x+6)^2 – 5
- y = -0.6(x – 4)^2 + 2
- y=3(x+7)^2+9
<@&286206848099549185> 15 mins have passed
<@&286206848099549185> <@&286206848099549185> <@&286206848099549185>
misty dagger
Pinging helpers wouldn't get u helper fast
narrow geyser
Pinging helpers wouldn't get u helper fast
Ik i'm sorry, its been past 15mins and i'm in a rush
misty dagger
I am currently helping someone else I come back here
narrow geyser
ok thank you
misty dagger
Ok to see whether stretched or compressed you are looking at a. Which is -2,-0.6 and 3 for vertically So you can work from there.
narrow geyser
would -2 and -0.6 be compressed and 3 be stretched? (all vertically?)
misty dagger
would -2 and -0.6 be compressed and 3 be stretched? (all vertically?)
Correct 3 is stretched. Remember if a is less than zero it can be either stretched or compressed
You probably likely look at graph
For negative value to see compare
narrow geyser
misty dagger
Now it should be here obviously here
One of them is stretched and compressed
Which one do you think it's compress and which one is stretched?
Comparing the two
narrow geyser
-0.6 is stretched....
misty dagger
Ye
narrow geyser
the other is compressed right?
misty dagger
Ye
narrow geyser
y = -0.2(x+5)^2+6 is this streched?
misty dagger
You have to compared
Again it can be either compress or stretched looking at your x-axis
Best way to know different when it's negative is by drawing it out
misty dagger
Also for horizontally compressed or stretched do u also want to know that, too?
narrow geyser
sure
narrow geyser
oh
misty dagger
Anyways horizontal stretched u can do same idea
Compare b
Right next to x
Since all graph are just x
This means that horizontal for b is just 1 for every single one of them
narrow geyser
ohhh
misty dagger
bx
narrow geyser
so is that how i can differentiate if its either horizontal or vertical?
misty dagger
You can draw out to see if that is the case
narrow geyser
ok
misty dagger
ok
I just realized that it can't be 1 my bad. I meant in this since there isn't bx I consider a as b
lone heartBOT
@narrow geyser Has your question been resolved?
misty dagger
U know what I just don't think there is horizontally stretched or compress because b is 1
gilded pelican
Unsure on how to approach this question
lone heartBOT
Unsure on how to approach this question
@gilded pelican Has your question been resolved?
true pulsar
You want to solve v = c_1v_1 + c_2v_2 + c_3v_3
So set up a system of equations for it
gilded pelican
Mhm
Ie a linear combination of the eigenvectors?
So would this be correct, and then I just solve for the c values?
true pulsar
Yeah looks good
fast oak
lone heartBOT
fast oak
Someone solve this
lone heartBOT
@fast oak Has your question been resolved?
fast oak
1^2
fiery tusk
swift shore
@fast oak it’s the integral from 1 to 2
It’s just that the formatting is inline, so it had to be squished
fast oak
Ohh ok ty
celest gorge
lone heartBOT
celest gorge
i tried the series formula, and 9*10^13=(1.1^x)3(*10^10)
need this kinda fast so
ping me if u can help
naive valley
are we assuming that meanwhile T'Challa is not increasing his wealth at all? Seems very unlikely..
celest gorge
are we assuming that meanwhile T'Challa is not increasing his wealth at all? See...
yes
its hypothetical idk why onramps made it seem more "relatable"
naive valley
what is "$30 billion, $63 billion, $99.3 billion" supposed to suggest? that's not 10% growth, it's more than 100% growth the first year
naive valley
10% growth from 30 billion would get you to 33 billion after one year
not 63 billion
celest gorge
but you need to add your starting value
naive valley
didn't i?
he starts with 30 billion
he earns 10%, or 3 billion
add that to the original you get 33 billion
celest gorge
idk its weird
naive valley
well ignoring their wrong 63 billion and 99.3 billion numbers, and just focusing on the 10% growth:
after k years he has (30 billion) * (1.1)^k
so you want to find the smallest k such that (30 billion) * (1.1)^k >= 90 trillion
celest gorge
yeah i tried setting that equal to tchallas value
naive valley
it's gonna take a lot of years
celest gorge
i got 84
naive valley
it's a bit more than 84
but less than 85
>> 30*(1.1)^84
ans =
89971.882625238
>> 30*(1.1)^85
ans =
98969.0708877618
yeah but i was told to round up
naive valley
ok then 85 not 84
celest gorge
round to the closest number at least
naive valley
you can solve for the exact k (including fraction)
celest gorge
got it wrong lol
naive valley
30*(1.1)^k = 90000
take logs of both sides
log(30) + k*log(1.1) = log(90000)
so
k = (log(90000) - log(30)) / log(1.1)
>> (log(90000) - log(30)) / log(1.1)
ans =
84.003278391538
so only a tiny bit more than 84
naive valley
ah yeah, "round your answer"
celest gorge
both are wrong
naive valley
if you round then it's 84
celest gorge
both of the answers are wrong
celest gorge
thx for trying anyways
naive valley
unless the moronic wording "add a 10% increase in his wealth to his current worth" actually means "take the current wealth, multiply by 1.1, and add that to to the current wealth"
i.e. 110% growth
in which case why would they not say that
naive valley
at least that would explain the 63
but it does not explain the 99.3
such a weird problem
30*2.1 = 63
but 63*2.1 is 132.2, not 99.3
celest gorge
hm
naive valley
maybe try solving it assuming you multiply by 2.1^k
and see if it accepts that answer
naive valley
oh new numbers each time you try?
celest gorge
also, this is true right?
celest gorge
oh new numbers each time you try?
yeah its to prevent cheating
naive valley
also, this is true right?
wait if you can only go 1/3 the remaining distance wouldn't it be 1/3 + 1/3(2/3) + ... ?
celest gorge
yes
naive valley
putting it another way, after the first step the remaining distance is 2/3
after the second step the remaining distance is (2/3)^2
after the k'th step the remaining distance is (2/3)^k
and the limit as k->infinity is (2/3)^k is zero
so in the limit you get there
naive valley
but not after any finite number of steps
so it depends on what the question means by "eventually"
celest gorge
it's ok tho bc it says eventually
naive valley
you technically will never get there
celest gorge
also i got 11 for this
naive valley
you'll just get arbitrarily close
celest gorge
yea
naive valley
also i got 11 for this
same, i got 11
naive valley
lol fuck this question
naive valley
that seems to be the pattern
it's hard to imagine what investing mechanism would result in that though
celest gorge
it's hard to imagine what investing mechanism would result in that though
so how do i make an equation if i want to find the greatest exponent
naive valley
you could write it as
$45000 \cdot (1 + 1.018 + 1.018^2 + \cdots) = 45000 \sum_{n=0}^{k}1.018^n$
ocean sealBOT
OurBelovedBungo
naive valley
where $\sum_{n=0}^{k}1.018^n = \frac{1.018^{n+1} - 1}{1.018 - 1}$
ocean sealBOT
OurBelovedBungo
merry depot
<@&286206848099549185>
didn't you already get help with this?
celest gorge
no the person helping me couldnt figure it out
merry depot
if the 1.1 didn't work then the 2.1 should
The numbers given would be a 110% increase in wealth per year, not a 10% increase
oh... wait
those numbers don't even make sense for that
42 = 20 +1.1(20)
66.2 = 20 + 1.1(42)
lone heartBOT
@celest gorge Has your question been resolved?
simple turtle
if the 1.1 didn't work then the 2.1 should
The numbers given would be a 110% inc...
Is this a test question?
merry depot
not OP. But doubtful This is the 3rd time they've gotten it wrong. So I suspect it's not a test, but homework
simple turtle
not OP. But doubtful This is the 3rd time they've gotten it wrong. So I suspect ...
I really can not tell either.
alpine sable
How do I solve this?
lone heartBOT
How do I solve this?
lime shore
but the answer says that it should be around 4 per week
you sure the answer is correct?
naive valley
(b) doesn't ask for a sketch of anything... and i don't see how (b) relates to a circle with center (7,2) and radius 2, but maybe i'm missing something
(i don't really see how (b) relates to the rest of the problem tbh)
naive valley
ah i see... the condition $|z + 8 - 4i| = 2$ applies to all three parts, so we need to use it in the second part. to do that, we can write $z + 15 - 2i = (z + 8 - 4i) + (7 + 2i)$
and since $|z+8-4i| = 2$, we're looking at the set of points which are distance 2 from $(7+2i)$ (edit to move the tex to the right place)
lone heartBOT
@analog rose Has your question been resolved?
lone heartBOT
@analog rose Has your question been resolved?
lone heartBOT
@analog rose Has your question been resolved?
raw bone
lone heartBOT
raw bone
This is what I’ve got, do I have to calculate this using Pythagorean Theron or must I derive this in some way
lone heartBOT
@raw bone Has your question been resolved?
raw bone
<@&286206848099549185>
alpine sable
<@&286206848099549185>
shouldnt 30km/h and 100 km/h switch places?
blazing saffron
Implicit differentiation if you can use calculus
raw bone
calculuias is alloweed
HYow would the implicit sum look if i may ask i dont see how to get an implicit function
blazing saffron
you can just take a^2+b^2 = c^2 and take derivative with respect to time, d/dt
2a*da/dt + 2b*db/dt = 2c*dc/dt
Where a=.6, b=.8
raw bone
okay
raw bone
so
blazing saffron
I believe 100km/hr would be negative as it is approaching the intersection
blazing saffron
Yeah that should be right
raw bone
i still need help with more questions
But imma do this first then come bacl
Thank you
blazing saffron
Yup
blazing saffron
You just have to plug in c
blazing saffron
have i done it right so far?
I haven't checked all of your derivatives, assuming they are right then yes
blazing saffron
and is c the x = 2
Yes
raw bone
cool thank you
gonna try get to an answer then
will be back wiuth another question soon
blazing saffron
,ask fourth order taylor of 3/(x^3-7) at x=2
ocean sealBOT
blazing saffron
Should be this
blazing saffron
Ignore the last term though
raw bone
gotcha
once you have iut in that form is it done cause i got to that answer :)
is that the final form
or do i have to expand the x-2 brackets
blazing saffron
once you have iut in that form is it done cause i got to that answer :)
Should be fine
raw bone
would g'(x^3)
blazing saffron
Then replace x in g' with x^3 from g^-1(x)
Yeah
Should be 3(x^3)^(2/3)
Which equals 3x^2
blazing saffron
No that's it
raw bone
picture uploading
xD
okay
so i have a question for you, i know the next qu3estion includes partial differentation
any idea where i can find research on that
or explanation
cause i dont understand how to do that at all
if you care to literally walk trhough it with me that be nice, Bu i feel itd be a waste of ur time and youve helped me so much already
so any resources i give it a try and coem back after that
raw bone
jesus calc 3
im only calc 1 
ill go look
hopefully i understabnds
the funny thing is
im using that site to practice current cacll 1
blazing saffron
It's pretty simple, you just differentiate with respect to the appropriate variable and treat the other variable as a constant
raw bone
am i right in sayiong that the question is partial differentation?
blazing saffron
Yes
raw bone
okay
ill be back
ill try my best
thank you skid
absolute legend
u truly are a very cool person
blazing saffron
After you compute the partials, to prove those parts just plug in the appropriate values
Like leave x and make y equal 0
In the first one
blazing saffron
,ask d/dy [xy (x^2-y^2)/(x^2+y^2)]
ocean sealBOT
blazing saffron
That's the first one with respect to y
So when y is 0 you get x^5/((x^2)^2)=x^5/x^4 = x
lone heartBOT
@raw bone Has your question been resolved?
raw bone
<@&286206848099549185>