One test isn't going to ruin everything.
#help-17
karmic imp
slim lily
that's what i told shah, but apparently this whole server is just about maths, maths and maths
obtuse radish
1 test never ruins anything bro; but either way dont discourage him @karmic imp check yt and khan acad bro; doesnt seem like we can help
blissful sentinel
that's what i told shah, but apparently this whole server is just about maths, m...
Please leave this channel
azure zinc
One test isn't going to ruin everything.
its my dream school please i want to ensure i can get in
my math scores in the past hasnt been the best already
karmic imp
Schools look at your gpa, if you have a 4.0 and you fail one test in one subject, you won't get knocked down to a 1.0
obtuse radish
wow bro u just wasting ur time here at this point; just going to sleep or messaging a classmate is better bro
slim lily
wow bro u just wasting ur time here at this point; just going to sleep or messag...
damn bro i'm actually studying and wanted to help this guy because he was nice
azure zinc
...
vocal sleetBOT
damn bro i'm actually studying and wanted to help this guy because he was nice
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
slim lily
but can't understand everything because i don't know all the math terms in english
azure zinc
Pls tell me what you don’t understand I’ll try to translate or even simplify it
Well I don’t want to be wasting my time, I actually want to get a good grade at this test
obtuse radish
am i supposed to somehow care abt ur little story? @slim lily i think u've already helped quite a lot this past 20min
azure zinc
Please it’s already really late for me and I have to wake up early
obtuse radish
if u not gonna trust me its fine but bro this place isnt guaranteed help; msg a friend; wake up early and study
slim lily
am i supposed to somehow care abt ur little story? <@561616150270836756> i think...
oh really, then help him einstein
azure zinc
Mehdi can you help me out
I think these questions are the most important
If I can at least get them right I might be able to achieve a decent grade
This is question 8 graph
By my friend
Hello?
<@&286206848099549185>
Please
blissful sentinel
I can help I guess
blissful sentinel
What is the question though? I don't understand what you've written down
azure zinc
blissful sentinel
Right but I don't understand those questions lol
Can you type them here in complete sentences
blissful sentinel
Is this homework that you're getting from a friend?
vocal sleetBOT
@azure zinc Has your question been resolved?
blissful sentinel
Ping me whenever you reply
foggy shore
how can I prove easily that sqrt(5) + sqrt(7) is irrational. I tried to assume for the sake of the contradiction that it was, in fact, a rational number, so that:
sqrt(5) + sqrt(7) = a/b, where a and b have no common factors. got some weird result in regards to a being equal something with b, but it also contained a on the other side.
vocal sleetBOT
how can I prove easily that sqrt(5) + sqrt(7) is irrational. I tried to assume f...
river wagon
Try squaring
shadow spindle
how can I prove easily that sqrt(5) + sqrt(7) is irrational. I tried to assume f...
Did you prove that sqrt(5) is irrational?
foggy shore
Did you prove that sqrt(5) is irrational?
nope
foggy shore
Consider showing it to understand why this proof has actually sense
alright, thanks, I'll give it a shot
shadow spindle
Suppose sqrt(5) + sqrt(7) is a rational number, what do you get when you multiply it by sqrt(5) - sqrt(7)?
shadow spindle
Exactly, now take sqrt(5) + sqrt(7) to the other side of the equation
shadow spindle
No, we won't use that definition for this proof, since it will be hard to find a contradiction
(√5 + √7)(√5 - √7) = -2
(√5 - √7) = -2/(√5 + √7)
This shows that (√5 - √7) is also a rational (Since division by 2 rationals is a rational, and we supposed that √5 + √7 is a rational)
foggy shore
oh, I see
foggy shore
2sqrt(5)
shadow spindle
Yep, sum of two rationals is also a rational
and if you divide that result by 2, it should also be a rational (since 2∈ℚ)
but we know that √5∉ℚ, which is a contradiction
foggy shore
right, but from the get-go, we also knew that sqrt(7) is also not a part of Q.
and don't we also know that the sum of two irrational numbers is also irrational?
so from that point, it's easy to prove
expect for like sqrt(2) + (-sqrt(2)), or something like that
shadow spindle
and don't we also know that the sum of two irrational numbers is also irrational...
Not always
foggy shore
what if we write sqrt(5) + sqrt(7) as an x, where we assume that x is a rational number
and do the calculations
shadow spindle
Not always
Consider (1 - pi) + pi
foggy shore
Consider (1 - pi) + pi
oh, that's a fair point, not gonna lie
technically, we could get to a form where we have x on one side and an irrational number on the other side, which would prove that it is not true to say that sqrt(5) + sqrt(7) is a rational number
right?
shadow spindle
Yep, but you would have to manage to get that result in the first place
foggy shore
[Proving that sqrt(7) + sqrt(5) is irrational]
Certainly, let's use a different approach to prove that (\sqrt{5} + \sqrt{7}) is irrational without explicitly introducing the ratio (a/b).
Proof:
Assume for the sake of contradiction that (\sqrt{5} + \sqrt{7}) is rational.
Square both sides of the equation (\sqrt{5} + \sqrt{7} = x), where (x) is a rational number:
[(\sqrt{5} + \sqrt{7})^2 = x^2]
Expand the left side of the equation using the FOIL method:
[5 + 2\sqrt{35} + 7 = x^2]
Combine the constants on the left side:
[12 + 2\sqrt{35} = x^2]
Now, we have:
[2\sqrt{35} = x^2 - 12]
Rearrange the equation:
[\sqrt{35} = \frac{x^2 - 12}{2}]
Now this, we do know that is irrational. [\sqrt{35}] is not part of Q, we know that already.
This is what I got from my good old pal, GPT
here is a better picture
calculations seem legit
shadow spindle
Yep, I supposed it would be easier to get a good proof with √5 rather than √35, since it should have been proven before
cunning shale
hi
vocal sleetBOT
@foggy shore Has your question been resolved?
limber tiger
What is the difference between the slope of a tangent line and secant line and how do you identify when to use each?
vocal sleetBOT
What is the difference between the slope of a tangent line and secant line and h...
@limber tiger Has your question been resolved?
vocal sleetBOT
@limber tiger Has your question been resolved?
flat whale
What is the difference between the slope of a tangent line and secant line and h...
Tangent lines are lines
Lines only have one slope
But a curve may have different tangent lines at different points on the curve
And a secant line isn't a tangent line
It's a line that's formed by two points on the curve
Whereas tangent lines are formed only by one point on the curve
vocal sleetBOT
@limber tiger Has your question been resolved?
vast shale
vocal sleetBOT
west raptor
What's the original question?
vast shale
create 5 vectors that will create a state of equilibrium with the given equillbrant (13N N27degreesW)
vocal sleetBOT
@vast shale Has your question been resolved?
west raptor
create 5 vectors that will create a state of equilibrium with the given equillbr...
Does the 13N mean 13 newtons?
vast shale
yeah 13 newtons and then north 27 degrees west
west raptor
Ok so we need 5 vectors that when added up with the 13N N 27° W vector we have 0?
west raptor
and when we make the vectors they can’t be parallel or perpendicular
Ok that makes sense
vast shale
i have a copy of the assignment that i can send in a bit
halcyon plover
Slope of Secant line = f(2) - f(0) / 2 - 0
vocal sleetBOT
Slope of Secant line = f(2) - f(0) / 2 - 0
halcyon plover
(0 , f(0)) (2,f(2))
f(x) = distanced travelled in km , x = 0 at start of the race
how can I find the slope without an equation, I have no idea what the graph should look like
halcyon plover
I guess f(0) = 0 since at the beginning of the race he travelled nothing
I know the average velocity at the first 2 hours mark and the average velocity
so would I just do 45 - 39 / 2?
6/2 = 3
but that doesn't sound right
urban edge
Lets start here: whats f(2)?
halcyon plover
39
urban edge
Not quite
halcyon plover
x = 0 at start of the race? so I'm guessing 2 is 2 hours after
which gives my average velocity to 39 no?
urban edge
Reread the problem
urban edge
Two hours after the start ... a cyclist passes the 78-km mark
halcyon plover
correct
urban edge
So what is f(2)
urban edge
Indeed
halcyon plover
I thought it was the velocity
urban edge
Can you figure out the slope of the secant line from there?
halcyon plover
like I found it, it's 39
halcyon plover
assuming f(0) is the start of the race which should be 0 right?
if f(0) is just 0, it would just be 78 / 2 = 39
... I'm kind of upset at myself for not seeing it earlier
urban edge
It happens, glad you could get it fixed
halcyon plover
Also because it basically asked the same thing twice that I didn't think it could be the same answer
but thanks a lot for the help
.close
vocal sleetBOT
urban edge
Youre welcome
vocal sleetBOT
Available help channel!
dusty void
vocal sleetBOT
cold hedge
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@dusty void Has your question been resolved?
vocal sleetBOT
@dusty void Has your question been resolved?
solemn cape
What
So to know the speed the plane goes you can use $s=\frac dt$ where $d$ is the distance and $t$ the time he took to do the distance.
twin meteorBOT
Joseph.P
dusty void
okay
solemn cape
And s is the speed
finite anvil
vocal sleetBOT
finite anvil
i'm not really sure what to do here
do I distribute the t, then set one vector equal to the other to find that t value? then what?
pale perch
i assume youre aware of the dot product?
you only need to focus on the direction vectors and find the angle between them
thats equivalent to finding the angle between the lines
finite anvil
are the direction vectors the ones with a t next to them?
pale perch
t and s, yes
finite anvil
so I do the dot product of <6,2,8> and <-3,-6,-1>?
like the one with the cos theta in it
pale perch
cos, but yeah
solve for theta
check its the smallest angle though, it can help to draw a diagram for that
pale perch
youll either get the b or the a
note they will sum to 180 so you can subtract one from 180 to get the other
finite anvil
ah
okay let me try part a...
r(t) dot r(s) = -18+-12+8 = -22
-22 = |r(t)| |r(s)| cos(theta)
-22 = sqrt(104)*sqrt(46)*cos(theta)
arccos(-22/(sqrt104*sqrt46)) = 108.55
180-108.55 = 71.75
pale perch
check your last line
finite anvil
hmm, am I not supposed to subtract from 180? It is the larger angle...
finite anvil
oh wait
71.45
heh
so how come I use the direction vector here?
What do the first set of vectors (without the t/s) indicate?
pale perch
the first set of vectors are a position vector for some point that lies on the line
the direction vector is a vector that determines the direction of the line, you can get any point on each line by changing the value of s or t respectively
so for any two lines, the angle between the direction vectors is the angle between the lines when extended infinitely
pale perch
i should probably note you can only find the angle between lines that will actually intersect at some point, but that may be obvious
forest plume
What's another way to write out 42 times 57? At first I tried (40x50) + (2x7) and realized it's wrong. What is an easy way to think it out like this? Thx
vocal sleetBOT
What's another way to write out 42 times 57? At first I tried (40x50) + (2x7) an...
halcyon wing
blazing trail
Not sure what steps to take from here to get the final answer
vocal sleetBOT
Not sure what steps to take from here to get the final answer
vocal sleetBOT
@blazing trail Has your question been resolved?
cunning saddle
help
karmic imp
why out 3/2?
Because 3/2 is a constant
vocal sleetBOT
@cunning saddle Has your question been resolved?
vast shale
would anyone know how to do this porblem (linalg)
vocal sleetBOT
would anyone know how to do this porblem (linalg)
unborn coral
Find the nullspace (kernel or whatever you call it) of the matrix formed by [v1 v2 v3] and then just scale it so that the first entry is 1
halcyon plover
vocal sleetBOT
halcyon plover
I found average velocity in A by substituting 1 and 4 into x^2 + x
which gave me 20 and 2
so the change would be 20 - 2 / 4 - 1 = 18 / 3 = 6
but for B, f(1) = 2 and f(1+h) = h^2 + 2h + 1
so the velocity would be h^2 + 2h + 1 - 2/1+ h - 1 which really just h
h^2 + 2h -1 / h is not factorable
so how can I proceed?
unborn coral
Isn't f(1) = 2 and f(1+h) = h^2 + 3h + 2? It's y = f(x) = x^2 + x
But your answer seems to be based off just f(x) = x^2
halcyon plover
let me check
ah
I see
yes you are right
so it should be h^2+3h/h
which I can factor out an h
unborn coral
yup!
halcyon plover
but that doesn't give me the average velocity right?
at least entering 3 gives me the wrong answer
halcyon plover
but h approaches 0
halcyon plover
ok so I can't just plug that in
and is instantaneous velocity just the derivative?
unborn coral
well yes but also that's exactly when you let h approach 0
halcyon plover
even thought it says x = 1?
unborn coral
the average velocity between t = 1 and t = 1+h is h+3, so instaneous is let h = 0
I guess I mean x, not t, but yes we have from x = 1 to x = 1+h right
so you just set h = 0 for instaneous velocity at x = 1
halcyon plover
which would be 3
ok thank you! I always try to plug in 0 at h when I see limit approaching 0
unborn coral
Haha no limits in averages! only instantaneous
vast shale
Many income tax systems are calculated using a tiered method. Under
a certain tax law, the first $100 000 of earnings are subject to a 35%
tax; earnings greater than $100 000 and up to $500 000 are subject to
a 45% tax. Any earnings greater than $500 000 are taxed at 55%.
Write a piecewise function that models this situation.
vocal sleetBOT
Many income tax systems are calculated using a tiered method. Under
a certain ta...
vocal sleetBOT
Many income tax systems are calculated using a tiered method. Under
a certain ta...
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
vast shale
Find the value of k that makes the following function continuous.
Graph the function.
f (x)= { x^2-k, if x <-1
2x -1, if x >= -1
twin meteorBOT
Statufi
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
no
twin meteorBOT
Statufi
vast shale
thats not what the questons asking lol
twin meteorBOT
Statufi
vocal sleetBOT
@vast shale Has your question been resolved?
turbid glade
Limit
vast shale
nah im not doing limits
turbid glade
Sorry for that, i don't know your math background
That's ok
You just have to find a k that makes the two expression of your function coincides at -1, so replace x by -1 and solve
vast shale
can u explain a lil. more
turbid glade
You want to have k such that $x^2-k=2x-1$ for $x=-1$
twin meteorBOT
Statufi
turbid glade
Because you know how f behaves to the left of -1 and to the right, and you want these two pieces to be connected at -1 so there values must be equal
mental furnace
anyone here has a video that can teach me in about 2-3 days Analytic Trigonometry II (SummDiff, Mult Angle, Power Red, ProdSum, SumProd) and fundational trigonometric identities 😄 we got exam in a week
by teach i mean master that shit 😄
vocal sleetBOT
anyone here has a video that can teach me in about 2-3 days Analytic Trigonometr...
flat whale
Khan academy
mental furnace
anymore?
karmic imp
Youtube
mental furnace
no i mean either a channel name or a website..
flat whale
You're not gonna watch all of Khan videos in 3 days
Help channels are for specific problems. Come back when you start doing them
karmic imp
no i mean either a channel name or a website..
Google them
Like look up that topic in youtube, watch the videos
mental furnace
aye thx
crisp agate
Im in calculus 3 and I just want to know if my answers are correct to my questions?
I tried to graph both of these and i can show my sketches so im unsure 😓
vocal sleetBOT
Im in calculus 3 and I just want to know if my answers are correct to my questio...
crisp agate
pulling up my phone to show sketches
sorry for the bad sketched
this is byfar my worst math
💀
ignore #3, i'm working on that one rn
@high abyss
<@&286206848099549185>
uh
😭
Ig while I wait I'l lzoom the questiosn in
^ I updated to a Family of Circles
<@&286206848099549185>
spiral inlet
^ I updated to a Family of Circles
that's right
crisp agate
@spiral inlet the first question looks like 2 parabolic graphs on the xy plane right??
spiral inlet
parabolas? or hyperbolas?
crisp agate
hyperbolas*
spiral inlet
yeah, it's a set of hyperbolas. the two different directions come from if f(x,y) is positive or negative
crisp agate
so x^2 - y^2 would also be correct
spiral inlet
but x^2-y^2 = z gives hyperbolas with a vertical or horizontal axis of symmetry
no, x^2 - y^2 gives a hyperbola, but one with a horizontal or vertical line of symmetry
not the diagonal ones like we see in that graph
a diagonal hyperbola is like xy = 1
or like, you're probably more familiar with it in the form y = 1/x
crisp agate
yep that is more recognaizable
so that means
f(x,y) = xy
would be the correct answer as it is not horizontal line of symmetry nor vertical
this one is diagonal
crisp agate
@spiral inlet may i check my work with one more question?
i already finished it and can send neat outlined work
spiral inlet
sure
spiral inlet
for the ln, you should have 2-y > 0, not just 2-y not equal to 0
crisp agate
oh 💀
spiral inlet
ln(x) is not defined in the reals for negative x
spiral inlet
y < 2
spiral inlet
yeah
Your graph looks mostly right, you just shouldn't have the bigger area on the top right
just the bit by the origin
spiral inlet
yes, like this
that's where y > x^2 (above the parabola) but y < 2 (below the line)
and yeah x being positive or negative doesn't make a difference
crisp agate
👍
if you dont mind as well soryr to hold oyu
could you explain the 2nd question furtheR?
i just completely wildly guessed with the x^2 + y^2 and the 2x
Repost as to not scroll @spiral inlet
spiral inlet
oh yeah sure
seems like you are pretty familiar with the general equations for conic sections?
you recognized x^2 - y^2 as a hyperbola
crisp agate
iffy but yeah that's the unit we're working on
spiral inlet
are you pretty comfortable with like the equation of a circle, ellipse, etc
crisp agate
yes
spiral inlet
so the equation of the curve given is $z = \frac{2x}{x^2+y^2}$ where $z$ is the height of the function where we're taking the level curve
twin meteorBOT
tatpoj
spiral inlet
$$z = \frac{2x}{x^2+y^2}$$
$$z(x^2+y^2) = 2x$$
$$zx^2 + zy^2 = 2x$$
twin meteorBOT
tatpoj
spiral inlet
if you gather the x terms, and gather the y terms (there's only one in this case), and complete the square on each, you will find an equation for a circle
crisp agate
so it would be
(zx^2 + 2x + 1) + zy^2 = 2x + 1?
spiral inlet
not quite, I haven't actually done it out on paper yet, one sec
are you comfortable with completing the square?
crisp agate
yes
i understand how to do it and the lesson itself, i think here just the z is throwing me off 😵💫
spiral inlet
well we just have to treat z as a constant
since, for any single level curve, it is a constant
crisp agate
ok so treating z as a constant i like ot think of any constant as just "1" in the scenario
x^2 + y^2 = 2x
(x^2 - 2x + _ ) + (y^2 + 0y + 0) = 0
(x^2 - 2x + 1) + (y^2) = 1
(x-1)^2 + (y)^2 = 1
add back in z i believe
(zx-1)^2 + (zy)^2 = 1?
spiral inlet
well, you can interpret z as 1z, but you can't just interpret it as 1
$$zx^2 + zy^2 = 2x$$
$$(zx^2 - 2x) + zy^2 = 0$$
$$z(x^2 - \frac{2}{z}x) + zy^2 = 0$$
twin meteorBOT
tatpoj
spiral inlet
this is how I would start
spiral inlet
yes 👍 awesome
crisp agate
and to make it look like the circle equation fomr of (x-h)^2 + (y-k)^2 = r^2
i need to simplify the first part of the circle equation
spiral inlet
well just finish completing the square, yeah
crisp agate
would you re-distribute the z back in to help with this part?
spiral inlet
$x^2 - \frac{2}{z}x + \frac{1}{z^2} = (x-\frac{1}{z})^2$
crisp agate
zx^2 - 2x + 1/z
(zx - 1/z)^2?
twin meteorBOT
tatpoj
crisp agate
ok
yeah that makes sense
i would double check the answer with foil to mkae sure too
so with level curves, z would be treated as a constant
then try to get it to fit within a certain type of equation shape
whether it's a sphere, ellipse, circle, cone, etc
crisp agate
oh hence the 2d answers
spiral inlet
oof that's never good
crisp agate
Repost as to not scroll <@490649542077841408>
so right away we oculd've elimianted cones and cylinders
spiral inlet
yeah and
even as far back as zx^2 + zy^2 = 2x
you can already kind of see that it's going to be a circle
spiral inlet
since the x^2 and y^2 terms both have the same coefficient: z
they are scaled by the same amount
crisp agate
just didnt know the math to actually get to the formula like in case it was an FRQ and not MCQ like the last one
spiral inlet
oh yeah I gotcha
crisp agate
so a scenario to look out for hyperbola
spiral inlet
completing the square like we did here should always work, but you might have to do it on both the x and y parts
crisp agate
is to get it to be 1/x and 1/y
and parabola would be different coefficients of x and y?
spiral inlet
hm
I think you'll recognize hyperbolas like that if you can make the x's and y's multiply with each other
like y = 1/x
xy=1
no other conic section is going to have a term like xy
crisp agate
okok
and what abt parabolas?
just one of them is x^2
and the other is to a degree of 1
right
spiral inlet
yes
spiral inlet
well, do you have sort of a picture in your head of what a level curve is?
crisp agate
it's like
you have a 3d curve on the plane
the 3d curve's projection onto the xy axis
is the level curve
i think
spiral inlet
well, i wouldn't quite describe it as a projection
like imagine you have this function f(x,y) = whatever
every point has a (x,y) input that determines the output z
crisp agate
mhm
spiral inlet
right, so the height of the surface represents the output z
crisp agate
z = height of surface
spiral inlet
imagine chopping this with a horizontal plane, like at a height of 0.4
do you see that the cross section would be a circle?
crisp agate
yeah
spiral inlet
that is the level curve for z=0.4
we chose a "level" of 0.4
and that circle is specifically defined to have a z of 0.4
so z is constant: 0.4
crisp agate
so the level curve at 0 would be kind of like 2 circles?
crisp agate
hard to tell how high that ripple comes
yeah u get what i meant
so what's the purpose and stuff of finding domain for level curves??
spiral inlet
well essentially it's the set of values that satisfies an equation like f(x,y) = 0.4
if you want your function to output a certain value, the level curve is the set of all inputs (x,y) that give that value
crisp agate
Question/:
so what abt stuff like this
Does finding the domain only tell us like
how the graph would look like on a 3d plane?
spiral inlet
so what abt stuff like this
what you were finding in that problem was essentially the "footprint" of the graph
spiral inlet
yeah, wherever z is defined
hearty dragon
I don’t really know how to start on this either
vocal sleetBOT
I don’t really know how to start on this either
merry python
if a+b is a factor of the equation, then setting a=-b in the polynomial must yield zero
twin meteorBOT
hearty dragon
How do I factorise it tho
merry python
divide it by (a+b)
vocal sleetBOT
@hearty dragon Has your question been resolved?
chrome sail
Help please
chrome sail
Math 124 it’s algebra
cyan shadow
cyan shadow
could you take a screenshot instead of a picture of your screen
chrome sail
No I can’t it’s a practice test
It’s locked
Sorry
I could take a better photo tho
As good as it gets
?
<@&286206848099549185>
vocal sleetBOT
@chrome sail Has your question been resolved?
grizzled halo
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
viral quarry
Why here when i add 60 degrees it counts up to 330 but the correct answer is 300
viral quarry
twin meteorBOT
viral quarry
Here i add 30 and its righr but why is. the 60 wrong
twin meteorBOT
viral quarry
<@&286206848099549185>
neat wave
sorry, I can't read your handwriting. What is the problem to solve
viral quarry
let me log into pc its easier to thpe there one sec
neat wave
np
viral quarry
so basically, in second picture, i have complex number -sqrt(3)-i, and then i get that the angle is -30 and -30, and Re<0 Im>0 so i draw the angle 30 in the third sector anticlokcwise, and i get 180+30 = 210 degrees and thats right
but in first, i have complex number 1/2 - sqrt(3)/2 * i , and i get that sin angle = -60 and cos angle = 60, and as re < 0 , and im > 0 its fourh sector so i draw the angle in fourth sector and i get angle 270+60=330 but thats not what i should get, so i want to know did i draw it wrong or what
neat wave
you mean 270 + 60?
viral quarry
idk should i even draw it there, someone explained to me yesterday and i did understand it but on this one i get trick
okay thank u
maybe i should have drawn the angle different way, so then i get 270+30 , but i think it should be drawn anticlockwise right?
neat wave
ok im getting it now
the values of cos and sin tell u its Q4, that's definitely right. So you can be safe to say that the angle of theta is a form of pi/3 in the 4th quadrant
it's not really a matter of matching a pattern of where to rotate the angles, but you're basically using the given info to deduce where and what angle theta is
viral quarry
So i should just use -Pi/3 and not add anything to that?
neat wave
yeah, there's no pattern to the problems or anything if that's what you were thinking before. You just need to figure out the quadrant and angle based on the given formula. If its in quadrant 2 and sin and cos tell you it's a pi/4 angle, you would deduce that it was 3pi/4. Get it?
Always keep a unit circle handy if you don't have it memorized already too 😉
viral quarry
yeah, there's no pattern to the problems or anything if that's what you were thi...
So thats 45 + Pi/2 = 135 right?
we have Pi/4 in second, and then we add value of the one behind it ( first only ) and we get Pi/4+ Pi/2
I understood that, but i didnt know why i dont add the 270 to 60
so this is this circle, and as Re>0 and Im<0 , i can just say its -60 as it belongs in the right quadrant right?
neat wave
That's what I would think. What does the exact question ask?
viral quarry
I just need to convert to complex trigonometric form
Like r(cos angle + i sin cos angle)
neat wave
yeah that should be fine then. do you know if the answer needs to be in radians or degrees
viral quarry
Also here, would it be right if i just used the value of -30 degrees ( -Pi/6) instead of 210 ( 7Pi/6) ?
neat wave
you should use the actual angle
viral quarry
what would the actual angle mean
neat wave
well you can say it's pi/6 but that doesn't tell you what quadrant it's in really
if you say 7pi/6 you know exactly where that is
viral quarry
So its important to mention the quadrant?
neat wave
no because the angle tells you what quadrant its in
pi/3 is in the first quad
7pi/6 is in the 3rd quad i believe
viral quarry
Y
Yes
Does it stand for like
-Pi/3 is in fourth?
Or i need to write it as 5Pi/3 ( 300 )
neat wave
no you need to write it as the whole 5pi/3 thing
crimson jetty
measure angles in radians anticlockwise from the positive x-axis
neat wave
if that's the case then you need to find what that angle is if you rotate it the opposite direction
like forwards vs backwards
crimson jetty
measure angles in radians anticlockwise from the positive x-axis
yh, im stating this as a convention.
the usual one.
viral quarry
measure angles in radians anticlockwise from the positive x-axis
So that means i should write -60 like this?
neat wave
oh omg im so dumb i totally misinterpreted that
crimson jetty
that -60 is good
viral quarry
and then it makes sense, 270 + 30 = 300
neat wave
yes -60 will work lol
crimson jetty
i havent seen the original question
viral quarry
yes -60 will work lol
ye
viral quarry
did i draw the angle right here ?
neat wave
for that one u either write 210 degrees in the counterclockwise direction or 150 degrees in clockwise direction
viral quarry
so i did 30 and then +90+90 its 210
vocal sleetBOT
Available help channel!
mortal kite
- Find the probability that x < 30.
X ~ N(54, 8)
vocal sleetBOT
51. Find the probability that x < 30.
X ~ N(54, 8)
mortal kite
z score is so confusing
strong rain
Never seen this notation. But is this what it means
μ=54
σ=8
mortal kite
yea
it's like
(x-54)/8
but it's confusing finding Z score because it's like
the same formula
but u come out w a decimal place number
and then you randomly find the Z from that?
idk
. X ~ N(4, 5)
Find the maximum of x in the bottom quartile
this one also confuses me
vocal sleetBOT
@mortal kite Has your question been resolved?
long oriole
quick q, can I use ln properties to move the ^2 so that it becomes 2xlnx?
wide lark
vocal lodge
Hello! Could you help me with this fraction division? The result should be 68.
vocal lodge
But even though I double-check and redo the exercise, it still gives me 17/3 divided by 27/16.
cobalt ocean
i think the problem must be here
(5/10) * (2/9) should be like (10/90) = (1/9)
@vocal lodge
vocal sleetBOT
@vocal lodge Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
cursive fern
can someone please help me understand the solutions of this exercise?
cursive fern
One of my main questions is about the boundsof the first integral which I dont understnad
vocal sleetBOT
@cursive fern Has your question been resolved?
vocal sleetBOT
@cursive fern Has your question been resolved?
vocal sleetBOT
@cursive fern Has your question been resolved?
tranquil trellis
Hi! I'm still a bit confused on this delta stuff for limits. Could someone help me approach this problem?
vocal sleetBOT
Hi! I'm still a bit confused on this delta stuff for limits. Could someone help ...
lapis marten
The distance between (x,y) and (5,1) should be less then delta
(x - 5, y - 1) lies inside a circle centered around the origin with radius delta
tranquil trellis
right
lapis marten
But for all points in this circle the x coordinate is between -delta and delta, right?
I should say disk btw
tranquil trellis
But for all points in this circle the x coordinate is between -delta and delta, ...
yes
so that's basically the problem?
lapis marten
Yeah
I think you can prove this more rigorously with the triangle inequality, haven't figured out the exact details though
tranquil trellis
That's a good idea I'll try that. Thanks!
tranquil trellis
or the pythagorean theorem maybe
how would I go about that?
lapis marten
You need to prove that if a^2 + b^2 < delta^2 then a^2 < delta^2 => |a| < delta
tranquil trellis
Ok
gleaming hare
You have a road that is 1 mile and a car that only has 30 meters before it hits the travelling limit, how much of the could the car cross before hitting the limit? (the limit makes the car stop even at full fuel)
vocal sleetBOT
You have a road that is 1 mile and a car that only has 30 meters before it hits ...
@gleaming hare Has your question been resolved?
prisma imp
vocal sleetBOT
vast shale
helppp
vast shale
barren radish
since it's pr then you know it's what kind of function?
tame raptor
nevermind
vast shale
bro what
tame raptor
what is the name of the function
barren radish
you've already drawn it, right
vocal sleetBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
vast shale
point of origin?
tame raptor
direct proportional function
the equation is y=kx
I don't know if you graph it the right way
barren radish
so when I said function and that you've drawn it I meant that it's a line. the relationship of $ to amount is a line with non-zero slope
vast shale
just tell me what to wright please
barren radish
and it' a + slope meaning it point up and to the right like you've drawn
tame raptor
2 pounds of candies=5 dollar
5=2k
It's kinda weird that the slope aren't the same
my bad
vast shale
just tell me what to wright please
dude
tame raptor
it is
it is
5/2
the function expression will be y=5/2x
how
you just graph it bro
vocal sleetBOT
@vast shale Has your question been resolved?
swift brook
What does this mean? conv is for convex hull, I don't know what is the bar above conv or what cl is (I think its closure)
vocal sleetBOT
What does this mean? `conv` is for convex hull, I don't know what is the bar abo...
sly sierra
yes, the closure of the convex hull
swift brook
so the conv bar is just notation for the closure of convex hull? but what does that mean (closure)?
vocal sleetBOT
@swift brook Has your question been resolved?
swift brook
I don't get how closure is different from convex hull
vocal lodge
(5/10) * (2/9) should be like (10/90) = (1/9)
That's true! Thank you very much, have a good afternoon.
vocal sleetBOT
@swift brook Has your question been resolved?
vocal sleetBOT
@swift brook Has your question been resolved?
cyan lagoon
vocal sleetBOT
soft walrus
that's a Diophantine Equation, do you know how to solve them? :)
regal bane
It's a very basic one. I saw in the other chat you outlined your strategy and it's good
cyan lagoon
.close
oblique raven
T
oblique raven
The top problem with C
ok so I plug in 6 for the original function but then I got a weird decimal number. but I continue that and plugged that answer into the inverse function and it not work. so I try the inverse of 2 first, got that answer and plug in for the original equation and that one makes sense
soft walrus
Little fact about inverses, which is what this exercise was trying to show you $f^{-1}(f(x))=f(f^{-1}(x))=x$
twin meteorBOT
MrFancy
soft walrus
albeit they could've chosen a better function to introduct such a concept
soft walrus
indeed, one of my favorites!
oblique raven
Little fact about inverses, which is what this exercise was trying to show you $...
what were they trying to show me
to constraint a domain / range whatever ?
or that maybe one of the function isn’t a function
twin meteorBOT
MrFancy
soft walrus
take some value and put it into f(x)
oblique raven
ok
oblique raven
ok
twin meteorBOT
MrFancy
soft walrus
plug this into $f^{-1}(x)$
twin meteorBOT
MrFancy
oblique raven
,rotate
twin meteorBOT
oblique raven
dang so u gotta do it like that
brisk moss
it should almost work if you decimal anyway
oblique raven
yes I was just deadly weirded out by the 6.000000000001
brisk moss
like it might give you 6.00000000 something but it should be really close still
elder burrow
for "which of the following could be the graph of y=-2(x)^2" the graph would open downward right?
vocal sleetBOT
for "which of the following could be the graph of y=-2(x)^2" the graph would ope...
somber gorge
I think that the one opening downward would be right
I would ask you professor becuase the website may be wrong
regal stirrup
how can i figure this out, im pretty clueless rn
vocal sleetBOT
how can i figure this out, im pretty clueless rn
somber gorge
was any more details given about ABCD?
nevermind I was going to ask whether it was a parallelogram but the answers don't line up with that
regal stirrup
abcd is a paralelogram
somber gorge
oh it is
regal stirrup
but im so confused i tried everything ik i just dont know how to do it
somber gorge
ok so a parallelograms area is base times height
and we have the base of 30 already so we need to find out its height
regal stirrup
yea thats where im stuck
somber gorge
yeah me to
regal stirrup
and i have no idea
somber gorge
let me think about this lol
regal stirrup
any ideas?
somber gorge
ok i think i may have it
give me a second
ok i got it
so
we have the base but we need the height
so notice that angle NDC equals angle DAB
(i'm assuming that they are equal but I think my assumption was right)
but do you see why finding angle NDC/ angle DAB would be useful?
@regal stirrup do you still need help?
fleet salmon
,rotate 270
vocal sleetBOT
,rotate 270
twin meteorBOT
twin meteorBOT
desert spindle
I’m trying to complete the square but idk where to go from here.
soft walrus
I’m trying to complete the square but idk where to go from here.
the LHS is a perfect sqaure trinomial :)
$(a+b)^2=a^2+2ab+b^2$
twin meteorBOT
MrFancy
soft walrus
I feel like I've helped you like 5 times today 
desert spindle
I feel like I've helped you like 5 times today <:kekw:752021756650455061>
Sounds abt right, srry for troubling u
Teacher wasn’t here today and I got so confused during class
desert spindle
**MrFancy**
I’ll try that
soft walrus
Sounds abt right, srry for troubling u
no worries man just pointing it out, nothing wrong with asking questions :)
its how we learn
desert spindle
do I need to factor it first in order to do the perfect square trinomial equation? bc if I do, idk how to do that
soft walrus
do I need to factor it first in order to do the perfect square trinomial equatio...
well take a look at the x^2
that's going to be our a^2, right?
soft walrus
well is x=a
ooo
I could see where this could be confusing
ok
so bear with will me for a sec
desert spindle
ok lol
soft walrus
so imma do a new binomial expansion (d+e)^2=d^2+2ed+e^2 right?
same thing just different letters you'll see why in a sec
desert spindle
ok
desert spindle
Yep
soft walrus
do that middle term 2ed just becomes 2xe, right?
desert spindle
Yes
soft walrus
now compare that with b/a*x and you'll get e :)
minor marten
I’m trying to complete the square but idk where to go from here.
Hint: look at the square you drew. What is x^2 + b/a*x + b^2/(4a^2) (the area of the square) equal to?
desert spindle
Like this? 
soft walrus
Hint: look at the square you drew. What is x^2 + b/a*x + b^2/(4a^2) (the area of...
oh actually that's also an idea
minor marten
Whats the side length of the square?
soft walrus
close
desert spindle
Hint: look at the square you drew. What is x^2 + b/a*x + b^2/(4a^2) (the area of...
My brains tryna process this
minor marten
Like this? <:sadcat:547124024585486359>
Look at what you drew for #4 again
desert spindle
Wouldn’t it be equal to what’s written on the right side of the equation ?
minor marten
The area of that is what you are trying to factor
desert spindle
yes
minor marten
So take a look at the side lengths of that square
desert spindle
b/2a * x ?
sorry I’ve never done perfect squares b4 until rn, I’m rlly confused and them
minor marten
You need to add not multiply
desert spindle
So just b/2a + x ?
minor marten
Yep
Thats the side length
And area = (side length)^2
We know the area is x^2 + b/a*x + b^2/(4a^2) and we can rewrite that as the side length squared (since we know the side length!)
desert spindle
Would the right hand side of the equation still be -c/a + b^2/4a^2 ?
desert spindle
can you please check if I did this right
vocal sleetBOT
Available help channel!
loud elk
vocal sleetBOT
tacit belfry
<@&286206848099549185>
blissful fable
question 4?
loud elk
yeah and prob 5
blissful fable
product rule on the left
blissful fable
d/dx [xe^y] = d/dx[x] * e^y + d/dx[e^y] * x
blissful fable
that's chain rule
see since y is a function of x
you have to apply the chain rule
so
d/dx [e^y] = e^y * dy/dx
blissful fable
you have to differentiate both sides when doing implicite differentiation
oh you did it later
fine
the derivative of y with respect to x wont be y dy/dx
it's just dy/dx
(on the RHS)
blissful fable
for the LHS, use chain rule, and for the RHS use quotient rule
vocal sleetBOT
@loud elk Has your question been resolved?
vocal sleetBOT
@loud elk Has your question been resolved?
vocal sleetBOT
@loud elk Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
craggy granite
log 8 =0.90
, find the value of log√32
vocal sleetBOT
log 8 =0.90
, find the value of log√32
long jackal
log 8 =0.90
, find the value of log√32
What is the common base between 8 and √32
craggy granite
its 10
craggy granite
craggy granite
yea
long jackal
Try to do the same thing to √32
craggy granite
thts it 2^5
long jackal
thts it 2^5
Well there is a root
craggy granite
so 2^5*1/2
long jackal
So you know that log 2^3 =0.9
Try to figure out what log(2^(5/2)) will look like
@craggy granite to solve this problem you need to know this
craggy granite
<@1104412080280444970> to solve this problem you need to know this
i know this so 2/5 log 2
long jackal
No its 5/2
long jackal
Yup
shell laurel
