or 3,3
#help-0
wheat isle
2^3+n
rocky grove
Okay
Now you have the prime factors ready
Now let's use fraction rules
$\frac{a^b}{a^c} = a^{b-c}$
ocean sealBOT
VulcanOne
wheat isle
Now let's use fraction rules
is what i said below correct?
rocky grove
Yep
wheat isle
how to we sub in what we have into that formula
rocky grove
Hmm
wheat isle
how do we sub*
rocky grove
$\frac{ab}{cd} = \frac{a}{c} \times \frac{b}{d}$
ocean sealBOT
VulcanOne
wheat isle
3^6/2^4 x 2^n+3 / 3^n+8
wheat isle
$\frac{ab}{cd} = \frac{a}{c} \times \frac{b}{d}$
do we just simplify from here
wheat isle
It's a multiplication
ohh my bad
rocky grove
I suggest making the 2's on the same fraction and the 3's on the same fractions and keep the 2's and the 3's separate
wheat isle
I suggest making the 2's on the same fraction and the 3's on the same fractions ...
are you talking about making this on the same fraction?
wheat isle
(3^6)/(3^{n+8})
what do we do from here
rocky grove
wheat isle
are we converting this into that
jagged field
help please!!!
rocky grove
help please!!!
!help
lone heartBOT
help please!!!
Please read #❓how-to-get-help
wheat isle
https://cdn.discordapp.com/attachments/490557019623915520/1070237514310361140/10...
I dont think I understand that rule
Im a little confused because we have two fractions
with multiple variables and coefficients in them
wheat isle
https://cdn.discordapp.com/attachments/490557019623915520/1070237514310361140/10...
i think the a variable and the power of b and c is confusing me
wheat isle
okay
rocky grove
$\frac{3^6}{3^{n+8}} = 3^{6-n-8} = 3^{-n-2} = \frac{1}{3^{n+2}}$
ocean sealBOT
VulcanOne
wheat isle
$\frac{3^6}{3^{n+8}} = 3^{6-n-8} = 3^{-n-2} = \frac{1}{3^{n+2}}$
am i correct here?
rocky grove
Yep but it's 2^3+n /2^4
rocky grove
$\frac{2^{n+3}}{2^4}$
ocean sealBOT
VulcanOne
rocky grove
This is what I meant
rocky grove
Yeah it would be 2^{n+3-4}
wheat isle
would this be the final answer then
wheat isle
Yeah it would be 2^{n+3-4}
this correct?
rocky grove
would this be the final answer then
Nope
wheat isle
oh was it supposed to be 3-4
wheat isle
You put 2^{n+3-4} wrong
what was the correct answer
rocky grove
2^{n-1}
wheat isle
ohh
rocky grove
Multiply 1/3^{n+2} and 2^{n-1}
lone heartBOT
@wheat isle Has your question been resolved?
lavish peak
Hello, I am having a difficult time solving this problem on Integration by parts.
lavish peak
grizzled aspen
Try switching your substitutions
wild trail
I think they are fine, dv should be (x + 5)^(-2) instead of (x + 5)^2
grizzled aspen
you can do it with either way, but finding v if dv is (x+5)^-2 is much harder than differentiating u to find du if u is (x+5)^-2
lavish peak
I think they are fine, dv should be (x + 5)^(-2) instead of (x + 5)^2
Ah yes, forgot the negative sign thank you.
wild trail
you can do it with either way, but finding v if dv is (x+5)^-2 is much harder th...
That is also very true, it'd give a complicated answer
grizzled aspen
That is also very true, it'd give a complicated answer
on second glance, i think while what I said WAS true, there is another aspect of it that complicates it, keep with what you have
you just need to make a subsequent substitution to integrate (x+5)^-2 easily
wild trail
Maybe try and see what happens
inland anchor
why is substitution for solving a system of equations so hard? can anyone help
grizzled aspen
why is substitution for solving a system of equations so hard? can anyone help
go to #❓how-to-get-help
inland anchor
thx
grizzled aspen
you need to find a channel that isnt being used
inland anchor
ahh
grizzled aspen
then i can help you, ping me directly once you are in there
lavish peak
on second glance, i think while what I said WAS true, there is another aspect of...
Would a u-sub be able to work?
grizzled aspen
you just need to make a subsequent substitution to integrate (x+5)^-2 easily
for THIS, yes
u = x+5, continue from there
lone heartBOT
@lavish peak Has your question been resolved?
lavish peak
.closed
normal oak
Can someone suggest how I should obtain the equation in part (a)? I've shown that the speed and acceleration have constant magnitude by differentiating |quantity|^2, but I don't know how to set up the equation
normal oak
wind cloak
You have one based teacher just saying
lone heartBOT
@normal oak Has your question been resolved?
normal oak
<@&286206848099549185>
lone heartBOT
@normal oak Has your question been resolved?
lone heartBOT
@normal oak Has your question been resolved?
sand pawn
is that a cross product?
normal oak
Yes
lone heartBOT
@normal oak Has your question been resolved?
sand pawn
I don't understand one thing here
Is the position here a function of x,y,z axes?
or something else?
cerulean ferry
Need help with quadrilateral theorems
lone heartBOT
Need help with quadrilateral theorems
cerulean ferry
parallelogram/kite/rectangle/rhombus
need help with this stuff
<@&286206848099549185>
.close
lone heartBOT
cerulean ferry
all done thx
lone heartBOT
Available help channel!
fallow basin
lone heartBOT
outer swallow
is the question referring to the tangents that both pass through the intersection point?
fallow basin
is the question referring to the tangents that both pass through the intersectio...
Yes
lone heartBOT
@fallow basin Has your question been resolved?
fallow basin
<@&286206848099549185>
outer swallow
<@&286206848099549185>
my approach so far is that, the lengths of the two tangents passing through (2,1) is sqrt(3). from that you can derive an equation for theta, where theta is the angle made by the radius through the point of contact of a tangent. from here, i want to find two values of theta. then we'd be able to find the points on the circle through which the two tangents pass. then we can use two-point form of linear equations to find the equations of the two tangents and there you go
but i am stuck at how to solve the trigonometric equation of theta i got
i got the equation 2cos + sin = sqrt(2) (i recommend you go through the working yourself)
outer swallow
my approach so far is that, the lengths of the two tangents passing through (2,1...
you can derive the equation by using the fact a point on the circle is (sqrt(2) cos x, sqrt(2) sin x)
then you can use distance formula
with (2,1) and (sqrt(2) cos x, sqrt(2) sin x)
and equate it to sqrt(3)
lone heartBOT
@fallow basin Has your question been resolved?
neon smelt
how do i solve i)
lone heartBOT
how do i solve i)
neon smelt
i've already found these two answers
lone heartBOT
@neon smelt Has your question been resolved?
neon smelt
lone heartBOT
spring plover
how do i solve this problem?
You are given the first two terms, which means you can find the common ratio of this series.
neon smelt
You are given the first two terms, which means you can find the common ratio of ...
oh i already solved the common ratio part
im talking about qn i)
<@&286206848099549185>
thorn tapir
Have you found out the sum to infinity?
neon smelt
yeah its in the steps
ocean sealBOT
rikusp2002
thorn tapir
I don't think I understand, I'm sorry. I'll wait for someone else to help.
neon smelt
<@&286206848099549185>
junior tusk
Yes
neon smelt
i think i have to take log of the equation and then solve for n
brave heron
I'm 7th grade T-T
neon smelt
oh
brave heron
what type of math is it??
timid igloo
The smoothie chain makes multiple $0.15 increases to the average prices of their smoothies. The table shows the average profit of the chain compared to the number of price increases. The data models a quadratic function.
Increases (x) Profit (y)
25 204
60 285
105 368
132 384
155 376
172 356
200 318
254 185
290 70
Use the data in the table to answer questions 3-5.
3. Use technology or hand calculations to determine the equation for the quadratic function modeled by the data in the table. Show an image of your final answer. (10 points)
4. Using the equation from question 3, determine the maximum profit. (5 points)
5. Using the equation from question 34, determine how many price increases will cause the smoothie chain to have zero profit. (7 points)
lone heartBOT
The smoothie chain makes multiple $0.15 increases to the average prices of their...
timid igloo
I really only need help on number 3 heh
I tried but I failed, and it took me so so long to do so
Youtube wasnt helping, so I decided to come here
timid igloo
This is how far I've gotten btw heh
raven rover
3 points can define a quadratic, but if you have more, then you may need to pick 3 points. It doesn't seem like it's a perfect quadratic
You could also try a line of best fit
raven rover
If you have 3 points (x, y), you can plug each of them into y = ax^2 + bx + c, get 3 eqns with 3 unknowns, and solve
timid igloo
Uhhh
I don't think you have noticed but... I am a complete dumb dumb and don't know what to do with that
Hahaha
Oh and whoever comes to help, please ping me
lone heartBOT
@timid igloo Has your question been resolved?
lone heartBOT
@timid igloo Has your question been resolved?
timid igloo
<@&286206848099549185>
lone heartBOT
@timid igloo Has your question been resolved?
lethal flicker
How would I integrate this?
lone heartBOT
How would I integrate this?
lethal flicker
ohhh, I forgot about that thanks
@minor needle Before integrating would this be the simplied version? (7/3)sinx
minor needle
ye
lethal flicker
cool thanks
teal plover
Hello
teal plover
Stuck on 79, is there even enough info to solve?
All I could squeeze out was sin(60)/sin(40) == CB/CA
lone heartBOT
@teal plover Has your question been resolved?
cursive badger
remember the horizontal components of tension counteract each other
since the weight is at rest
teal plover
@cursive badger ye, thats what i used to get the relationship "sin(60)/sin(40) == CB/CA"
teal plover
Q79
cursive badger
oh whoops
teal plover
🥹
cursive badger
very very sorry ;-;
you wrote 60º so I was confused
thought it was a missing angle in Q80
well uh lemme try again
ACsin50+BCsin30=3000lb (net zero vertical force)
ACcos50=BCcos30 (net zero horizontal force)
lone heartBOT
cursive badger
.reopen
lone heartBOT
✅
teal plover
xd
cursive badger
what does total tension even mean?
sum of tension in each of the three sides?
I'm only good at trig ):
cursive badger
... are we stupid then?
isn't it purely vertical then?
I feel like that's wrong though
teal plover
i mean like
cursive badger
in the cable supporting the given load
cursive badger
I mean I guess, but that doesn't make much sense to me
I really really don't like tension lol
ACsin50+BCsin30=3000lb (net zero vertical force)
ACcos50=BCcos30 (net zero horizontal force)
so this is what we know
that's enough, no?
teal plover
arigato
cursive badger
yup two equations of two unknowns lol
teal plover
i can substitute
no?
using eq 2 -> 1:
ACsin50 + ACsin50 = 3000
AC = 1500/sin(50)?
1958.1
arigato scythe ❤️
cursive badger
was it correct though?
lone heartBOT
@teal plover Has your question been resolved?
teal plover
@cursive badger yesh
frail viper
how does those 2 simply like that?
wary stream
how does those 2 simply like that?
Don't open multiple channels
frail viper
ok, but how do they simplify like that?
ocean sealBOT
Modus
lone heartBOT
@frail viper Has your question been resolved?
crude gull
"Given these vectors,find the k values where v and w are perpendicular"
"....where (v^w)^2=89
crude gull
.reopen
lone heartBOT
✅
crude gull
Hello I've done the first one and I need help on the second one
"Given these vectors,find the k values where where (v^w)^2=89"
anyone help so i can go to sleep happy 
lone heartBOT
@crude gull Has your question been resolved?
crude gull
.close
noble current
hey, i have this project im working on about linear equations and im stuck on what its saying, i dont understand anything, may i get some help on this?
gloomy hinge
Assign the calculators variables (x and y) ( I am assuming that this is systems of equations)
noble current
oh ok
gloomy hinge
What is the total profit from the calculators sold, and how much do x and y cost? (It's in the problem)
noble current
the total is 1646, so x(for each) could be $16, but what would 50 be?
gloomy hinge
Ignore that for now, set up to e first equation.
noble current
ok
gloomy hinge
If varying amounts of X and Y combined equal 1646, with X and Y costing 110 and 16...
()x+()y=1646
noble current
wait so 110 is y?
gloomy hinge
What is y, (did you say that scientific or graphing calculators was y)?
noble current
graphing
gloomy hinge
So, how much does a graphing calculator coast? $110, right? So, that means that x is the scientific calculator at $16. However, varying amounts of these (hence the x and y) will add to a final of 1646.
This means that you need the number of calculators sold (of each type) and you know the price to equal the final price of 1646.
noble current
i got 41 scientific calculators, and 9 other is that correct?
gloomy hinge
Yes!
wise warren
I need to solve for x and y. Solution needs to satisfy that x * y = 15000
y = (x * 1686) / (180 - x / (y + 1)) - 1
Non linear eq
fallen verge
!status
lone heartBOT
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
Uhm how do i reply? I got to this eq from another problem. But idk how to use or write in wolfram so it looks for an answer that satisfies the condition.
When i plug in the equation it just drops x = 180 y = 1687 which work but doesnt satisfy the x * y = 15k
Was wondering if anyoe had an alternative or knew how i could plug this in a programm to apply a raphson method or smthing
fallen verge
can you show the original problem please
wise warren
hmm well its not rly a problem, just a challenge i did to myself. Cuz i wanted to calculate something involving liquidity pools from a program.
Ill try and explain gimme a min
sounds good ill try
also this is my made up problem lol
Lets assume the following assets are present in a liquidity pool.
5 WETH (x)
3000 TES (y)
k = 15000 "because x * y = k"
So we know that in the real world 1 eth is equal to 1686 dollars.
Now if a user tries selling(adding to y also dy) 1 TES to the smart contract. It will calculate the return like this:
(x - dx) (y + dy) = K
dx = xdy / (y +dy)
dx = 5 * 1 / 3000+1
dx are the returns in WETH for the user that just gave 1 TES(dy)
So 1 TES = 0.0016 WETH
Which in dollars are: 2.7 dollars
Now i tried calculating what the pool ratio would have to be, if i wanted that 1 tes = 180 dollars, so 1 tes = 0.11 WETH.
To which i came up with this formula via:
1 TES = dx * 1686 dollars
Substituting the value of dx from the above equation, we get:
1 TES = x * 1 / (y + 1 TES) * 1686 dollars
Solving for y, we get:
y = (x * 1686) / (180 - x / (y + 1)) - 1
WHERE "x*y" = 15000.
hope this makes sense 
lone heartBOT
@wise warren Has your question been resolved?
stoic folio
The number of radians in any given circle of any radius R is a constant of approximately 6.28, is that correct?
viral pagoda
The number of radians in any given circle of any radius R is a constant of appro...
Ye
2pie radians is a rotation
lone heartBOT
stoic folio
So along the lines of the last question, is the terminology proper to say that if I walk around the perimeter of a full circle, I've walked 6.28 radians? I mean, its kind of abstract because until we know the length of radius we don't really have a true value, just a ratio.
We could say that we walked a distance of 6.28R
So, that radian or radians (plural) is just a unit of measure for the radius itself?
Saying that I walked 6.28 radians would be a true statement but an abstract one until radius is known, measured or stated.
lone heartBOT
Available help channel!
sharp sonnet
Hey any clue how to do this I don't know where or how to start trying to understand this topic before the test
sharp sonnet
viral pagoda
Rationaluse
wary stream
It tells you what to do
rocky grove
Hmm
stoic folio
How come my question isn't pinned?
rocky grove
Calls you to use conjugate
wary stream
Simplify by rationalizing the numerator
stoic folio
Are my 4 assumptions about radians correct?
red hollow
CN someone check this
lone heartBOT
CN someone check this
cursive badger
Unfortunately we are not able to help you with quizzes or exams. Sorry, and good luck!
red hollow
This a practice one but I don’t want to restart the entire thing
I can send proof if you want
cursive badger
that would be lovely
cursive badger
fair enough
your work looks right for e^(-ln(x^2+1)) question and the log question
inverse trig is a pain though, gimme a sec
red hollow
Np haha I have an exam so I wanna make sure I’m doing this correctly
cursive badger
no worries I've done the same many times :)
yeah ok I think it's right
had to puzzle it out backwards from the unit circle D:
cursive badger
all of these are right though as far as I can tell
red hollow
Ty
lone heartBOT
lone heartBOT
Available help channel!
red hollow
Because what multiplies to what gets -5 and adds to 4
lone heartBOT
Because what multiplies to what gets -5 and adds to 4
red hollow
I said -5 and 1
cursive badger
-5 and 1 should be the right roots?
red hollow
Should it?
cursive badger
though -5 might not work explicitely
just 1, yeah
since if you plug in -5 directly you are adding two logs of negative numbers
but if you simplify first both -5 and 1 work
you get log_5(x^2+4x)=1, log_5(25-20)=1, log_5(5)=1
red hollow
So the x would be -5 and 1
cursive badger
again though -5 would not be a solution I see now
since if you plug it in directly it wouldn't work
it'd be like saying (x^2-x)/(x-1)=x+1 for all x, when x=1 gives you 0/0=2 technically
cursive badger
sure just a sec
red hollow
Alrighty
cursive badger
like this maybe
you see how the simplified and unsimplified versions do not have the same solutions?
red hollow
I can see it
cursive badger
x=1 is a solution to both, but x=-5 is unevaluatable in the first equation
which is what your problem is
red hollow
I meant like how would I change my answer
cursive badger
you would exclude x=-5
you have two potential solutions
x=-5 and x=1
but only one of those fits your domain
your domain would be all x>0, since any negative x would cause log_5(x) to be undefined
red hollow
Is my whole work wrong
cursive badger
no it's all right (literally, I mean, all of it is right)
you just missed the last step that narrows the multiple potential answers to one
red hollow
Ok I see
cursive badger
if you take x=-5 and plug it in, you get no solution
because you cannot evaluate log_5(-1)+log_5(-5), it's not possible without simplifying
red hollow
So I just remove x=-5
cursive badger
yup
red hollow
Do I show why I remove it or no?
cursive badger
if you want, you just have to say it's not in the domain
teachers love it if you specify domain when you start a problem
ie you look at the problem, see log_5(x), and say "as log_5(x) is present, x>0)", or just "x>0"
red hollow
because you cannot evaluate log_5(-1)+log_5(-5), it's not possible without simpl...
Is this supposed to be a positive 1
Ahhh I understand fully now
Thanks I thought it looked weird
cursive badger
hooray! sorry about all the confusion
red hollow
Since it’s negative that’s why
cursive badger
yup
red hollow
.close
last hearth
limit sucks
lone heartBOT
limit sucks
last hearth
can someone give me a lesson on limit?
lone heartBOT
@last hearth Has your question been resolved?
light bridge
warm trout
lone heartBOT
restive chasm
They all use the same concept, that being linear equation in two variables. For instance, in the first question, you are given two points. Find the slope using these points. Then, find the equation of line satisfying any one of the points. The form will be: y - y1 = m ( x - x1) where m being the slope.
solemn juniper
is this a test?
warm trout
Yes
tiny garden
A businessman wants to build his house so that the width is 10m greater than the
long. If the exact measurement of the length is unknown. Propose an algebraic expression that
represent the surface of the house
lone heartBOT
A businessman wants to build his house so that the width is 10m greater than the...
@tiny garden Has your question been resolved?
vivid light
what permutation rule do i use?
lone heartBOT
what permutation rule do i use?
onyx maple
,rotate
ocean sealBOT
lone heartBOT
@vivid light Has your question been resolved?
distant lichen
hi
distant lichen
how do i confirm if this an improper integral
i know the 1st one is improper cause one of the bounds are infinite
for the other 2
do i just plug in the bounds
to check if they're discontinous
or is there a different way of checking
if i plug in the upper bound for the 2nd integral
i get 1/sqrt(2)
lower bound i get 1
since both values are defined does that mean it's not an improper integral??
lone heartBOT
@distant lichen Has your question been resolved?
last tendon
You need to verify more than just the end points. Every value between 0 and 1 also needs to be in the domain of the integrand, which is hopefully obvious in this case.
distant lichen
i see
all the values between 0 and 1 seem to be continuous
but if the bounds were -2 and 1
then it would be improper
because there is a discontinuity at -1
last tendon
If the bounds were -2 and 1 you would have too many problems for the question to be meaningful. Without getting too techncial, you are mostly interested in integrands where the number of problem points are managable, and having an entire continuum of points from -1 to -2 is far too many.
lone heartBOT
lone heartBOT
Available help channel!
haughty gulch
hey, simple question. when writing two column proofs and you state that one angle equals another due to, for example, because they are alt interior angles or corresponding angles, what would you write for the reason?
haughty gulch
definition of alternate interior angles?
vale junco
definition of alternate interior angles?
I guess you could write "alter interior angles are equal"
say like <BCD=<ACF ==> alter interior angles are equal
lone heartBOT
@haughty gulch Has your question been resolved?
wheat isle
I would like some help with these questions
lone heartBOT
I would like some help with these questions
crimson totem
Logarithm might help
wheat isle
I haven’t learned logarithms
kindred anchor
Yes
crimson totem
$a^{m+n} = a^m \times a^n$
ocean sealBOT
Shockshwat
crimson totem
might help
crimson totem
I would like some help with these questions
Try getting the same base in A.
Ok i got the answer for A, its easy really
crimson totem
Try getting the same base in A.
wheat isle
Try getting the same base in A.
by same base you are talking about the 3?
ocean sealBOT
Shockshwat
crimson totem
you need find that something
wheat isle
Isn’t the 3^2x+1 supposed to be equal to 1
strange meadow
Yea but you can wrote one in the form 3^k where k is something
subtle narwhal
i need help
so 41/35 is the answer for 4/7 + 3/5, do i have to turn 41/35 into a mixed number?
alpine sable
subtle narwhal
okay
alpine sable
try to represent 1 as 3 to the power of something
for example, if i were to represent 9 as 3 to the power of something it would be 3^2 right
strange meadow
^
desert tusk
So this can equal anything?
identity law
any number to the power of 0 will always be 1
crimson totem
So this can equal anything?
No
wheat isle
for example, if i were to represent 9 as 3 to the power of something it would be...
Yeah
wheat isle
<@722683408190406667>
If a can be any number like
alpine sable
Yeah
so try to do the same thing, representing 1 as 3 to the power of a number
here, you can use the identity people are talking about (any number)^0=1
subtle narwhal
wait this is help-0
wheat isle
Yes this is my channel
alpine sable
wait this is help-0
if you see the channels there are channels that are available and occupied, so use a channel that is unoccupied
subtle narwhal
if you see the channels there are channels that are available and occupied, so u...
i got an occupied channel now
Thanks
alpine sable
we can write the equation $3^{2x+1}=3^0$ right
ocean sealBOT
starlight
wheat isle
Ye
alpine sable
so do you think you can solve for x?
wheat isle
I’ll try hold on
alpine sable
yep
wheat isle
And is part c the same thing but with 8^0
alpine sable
8^0 is also equal to 1
alpine sable
4^(2n+1) isn't equal to 1
wheat isle
Are you talking about the base
alpine sable
yh
the base would have to be 2 for the lhs too
sorry im a bit sleep deprived i meant lhs instead of fraction 
alpine sable
so if you represent 4 as 2^2, what can you write 4^(2n+1) as
wheat isle
Hm
alpine sable
remember $(a^m)^n=a^{m\cdot n}$
ocean sealBOT
starlight
wheat isle
so if you represent 4 as 2^2, what can you write 4^(2n+1) as
2^4n+2?
alpine sable
yep
alpine sable
2^(2n+1)^2
not this unfortunately though
but if you've written both sides as exponents with 2 as the base, can you try and solve for x?
if we know 8=2^3 and 4^(2n+1)=2^(4n+2)
wheat isle
2^(2n+1)^2
Do I use this to solve for x
wheat isle
if we know 8=2^3 and 4^(2n+1)=2^(4n+2)
Or this
alpine sable
wheat isle
sadge
ocean sealBOT
starlight
alpine sable
and using $(a^m)^n=a^{m\cdot n}$
ocean sealBOT
starlight
alpine sable
$(2^2)^{2n+1}$ would equal to $2^{2(2n+1)}$
ocean sealBOT
starlight
alpine sable
so yes, as you've said the second time, 4^(2n+1)=2^(4n+2)
so that would mean $2^{4n+2}=2^3$
ocean sealBOT
starlight
wheat isle
Ohhh
wheat isle
so that would mean $2^{4n+2}=2^3$
Is that the final answer
alpine sable
welp no, bc we haven't solved for n yet
alpine sable
**starlight**
can you solve for n from here?
it's similar to what you did the last question
wheat isle
Alright cool
alpine sable
lmfao it should be right
wheat isle
I would like some help with these questions
Do you mind helping with one last one part d?
alpine sable
yh it's right
wheat isle
yh it's right
sweet
alpine sable
unfortunately im heading to sleep but if you write $\sqrt5, 5^{x-2}, \frac{1}{25}$ all as exponents with the base 5, you can use the property $a^m \cdot a^n = a^{m+n}$
wheat isle
okay thank you!
ocean sealBOT
starlight
lone heartBOT
@wheat isle Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
jade dagger
lone heartBOT
jade dagger
Part d-f
I’m confused with the ‘projection on to’ formula
What is the correct way of applying it?
Also these parts
lone heartBOT
@jade dagger Has your question been resolved?
lone heartBOT
@jade dagger Has your question been resolved?
lone heartBOT
@jade dagger Has your question been resolved?
pseudo ice
What is the correct way of applying it?
Seems right the way you’ve done it I think?
jade dagger
Thankyou! The last part i figured it out, it’s the cross product of AB xAC * 0.5
.close
lone heartBOT
vivid tulip
.reopen
vivid tulip
can u type in a question for me
prob of winning is 2/23 prob of losing is 7/23 how many games were not played
probability
lone heartBOT
Available help channel!
vivid tulip
do u know how to solve
ornate condor
wraith flame
lone heartBOT
wraith flame
Is the answer to this problem 2?
If 3 M and 3 F is seated in a row alternately there is only 2 way
Am I correct?
fringe idol
No I'm getting 144
Case 1: MFMFMF
then 3! possibilities for males and 3! for females
the same logic can be used for FMFMFM
cold lotus
is that a trick question?
fringe idol
in what sense?
wraith flame
is that a trick question?
I don't think so
fringe idol
No I'm getting 144
up here
cold lotus
so how can you solve it, can you teach me
fringe idol
the whole solution is up there
cold lotus
oh ok
wraith flame
No I'm getting 144
why 144 is it not just 36
fringe idol
how?
wraith flame
3!x3!is 36
fringe idol
oh wait then its 1296
fringe idol
36 for each case so 36^2
wraith flame
Why do i need to squre it?
wraith flame
where do you get 72?
true patrol
36 x 2 = 72
stuck canyon
henlo our prof hasn't showed up for a while and left us smthing to do without teaching :T can anyone help me understand this problem?
remote heron
henlo our prof hasn't showed up for a while and left us smthing to do without te...
what makes a limit not exist
torpid shoal
wat
pseudo ice
what makes a limit not exist
[to add a little elaboration on this: there’s a difference between a limit existing, and continuity!]
lone heartBOT
@stuck canyon Has your question been resolved?
warm field
lone heartBOT
lone heartBOT
Available help channel!
normal sorrel
hi
alpine sable
please dont ping helpers right away
tidal breach
OK
lone heartBOT
hollow sparrow
the channel will be closed since the original message has been deleted
wild trail
You can't reopen if the original message gets deleted
tidal breach
what should i do ?
hollow sparrow
what should i do ?
open another channel
lone heartBOT
Available help channel!
gilded flare
gilded flare
Is my answer correct?
lone heartBOT
@gilded flare Has your question been resolved?
ruby egret
Hi
gilded flare
Hi
lone heartBOT
@gilded flare Has your question been resolved?
plain quartz
It does indeed go to 0, yeah
gilded flare
ok! are the steps that i did correct?
plain quartz
They seem fine to me, yeah
gilded flare
ok! thank u
distant cove
Hey
ocean sealBOT
Kingo
pearl sequoia
!status
lone heartBOT
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
pearl sequoia
You assume that it hold for n-1 and are trying to prove from that, that it stands for n too right?
pearl sequoia
(2n)! = 1x2x...x(2n-2)x(2n-1)x2n = (2(n-1))!x(2n-1)x2n
x stands for multiplication
lone heartBOT
@distant cove Has your question been resolved?
ocean portal
can someone check my work here? (*) represents a differential equation, (**) represents an integral equation
ocean portal
Also, why is it that we can use FTC here? I have a general idea of why (from http://lie.math.okstate.edu/~binegar/2233/2233-l04.pdf) but I'd appreciate it if someone provided more detail
lone heartBOT
@ocean portal Has your question been resolved?
timid roost
Question: find the shortest distance from point (2, 1, 2, 1, 2)
to the subspace in the picture.
I'm struggling to find the matrix representation of the given subspace. I think I know how to calculate the projection to the subspace with A(transpose(A)A)^-1 * transpose(A)x.
lone heartBOT
Question: find the shortest distance from point (2, 1, 2, 1, 2)
to the subspace...
@timid roost Has your question been resolved?
timid roost
<@&286206848099549185>
lone heartBOT
@timid roost Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
candid lantern
why does go from (1,1) to (4,2)
lone heartBOT
why does go from (1,1) to (4,2)
candid lantern
since x is by itself
like why is square root of x graphed like that
huh
idk what unsigned square root is
oh alr
but how come it goes from 1,1 to 4,2
is that just a rule
for square root of x
whats the rate of change for that function
yeah ik like it changes but i forgot what that was called so i jsut called it rate of change
oh
alr
ill try the desmos thx
thx for the help
.close
brazen berry
Any advice? (Calculus)
lone heartBOT
Any advice? (Calculus)
limpid turret
!status
lone heartBOT
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
@brazen berry Has your question been resolved?
sullen maple
im pretty sure the equation is (x+1)^2(x-3)
lone heartBOT
im pretty sure the equation is (x+1)^2(x-3)
fleet tiger
serene junco
im pretty sure the equation is (x+1)^2(x-3)
Yes you're right
serene junco
ok that sounds good
pseudo ice
What level is this question from? A Level?
sullen maple
yes
pseudo ice
You've gotten to differentiation yet or not yet?
sullen maple
i differentiated to get 3x^2-2x-5
pseudo ice
Nice nice, and what happens at the maximum/minimum points?
pseudo ice
i solved to get x
What did you get from here?
sullen maple
i solved and got x=5/3 , x=-1
it cant be -1
and for Y coordinate i just put -5 as thats what the y intercept in the equaton was
but i may be wrong
pseudo ice
and for Y coordinate i just put -5 as thats what the y intercept in the equaton ...
Why not work with the x=5/3 somehow instead 
sullen maple
ahh
i should sub in
i subbed 5/3 into x^3-x^2-5x-3 but what i got doesnt seem correct
ocean sealBOT
pseudo ice
,w x^3 - x^2 - 5x - 3
pseudo ice
i subbed 5/3 into x^3-x^2-5x-3 but what i got doesnt seem correct
What did you get when you did? Did you do it with a calculator?
pseudo ice
Haha no worries, as long as you got it! And a pleasure, have a good one! 
sullen maple
.close
earnest plover
Why do we equate the equations of a curve and a line if they have one or more points that intersect each other?
Example question:
The line y=3x+k is tangent to the curve x^2+xy+16=0. Find all the possible values of k.
minor needle
Why do we equate the equations of a curve and a line if they have one or more po...
we can equate them anyway, amount of points depends on how many solutions we'll get
earnest plover
but why do we equate them?
minor needle
here, we can equate them because we can suppose there is only one common point (one solution)
and then, using discriminant, you can solve D = 0
which gives you possible values of k
serene junco
Say you have two functions f(x) and g(x) whose graphs intersect each other at (a,b).
That means f(a) = b and g(a) = b, since (a,b) is on both curves or lines
So f(a) = g(a).
So, points of intersection on the graph correspond to places where f(a) = g(a)
alpine sable
what is the dim im T
worn fox
for KerT you are looking for all matrices that are mapped to the zero polynomial
exploring this will give you conditions on a,b,c,d
oh i cant read
pseudo ice
Assuming this is in response to dim(im(T)), rank-nullity
alpine sable
remove 1 and ull prolly be fine
pseudo ice
Tbf you could remove any one of those ones really
alpine sable
because u chose any and its a linear combination of the others
pseudo ice
see the c one
alpine sable
since its linearlly dependent
since the whole thing spans im T
the removed set also spans im T
pseudo ice
Ideally but it's easy to convert back to polynomial form really!
alpine sable
.close
twilit relic
Hi, can someone help me with what is happeing here
lone heartBOT
Hi, can someone help me with what is happeing here
twilit relic
I'm being thrown off after applying an identity to sinx
This is original q btw
Seems like a typo on the first step limit of integration?
tacit arch
Seems like a typo on the first step limit of integration?
which part is the typo
twilit relic
which part is the typo
First one
tacit arch
that's not a typo
twilit relic
Oh?
tacit arch
you have to read the next line
tacit arch
read the integral limits on the second line
twilit relic
pi/2 becomes pi
twilit relic
I think I need to graph this
Ok so the two are the same because its an identity
And that is what I seem to make of it
Still can't see the connection
tacit arch
the area under the curve from 0 to pi is half the area from 0 to pi/2
shade the areas
lone heartBOT
@twilit relic Has your question been resolved?
worldly summit
buoyant kayak
this is kind of ambiguous
normally you'd be introduced by proving lhs=rhs
but it could also mean proving identities
worldly forum
I need help with Set theory, particularly this question:
lone heartBOT
I need help with Set theory, particularly this question:
alpine sable
A contains A^B
waxen flame
Please delete your question and ask your question in a different room. This room is occupied by someone already. #❓how-to-get-help
raven haven
,tex \factoid original
ocean sealBOT
eternal mesa
hi could someone pls help me with 62
lone heartBOT
hi could someone pls help me with 62
haughty atlas
just do math
eternal mesa
could you explain the steps? thats what I have most trouble with
eternal mesa
like walking through the problem
i get stuck in the middle of it after the first couple steps
eternal mesa
i was doing the right side first so i changed it to ((1/cos2a-1))/1/(cos2a+1)
then i plugged in the double angle formulas and thats when i got stuck
carmine reef
generally if you have fractions nested inside each other there's a way to simplify
eternal mesa
i forgot I also multiplied them together
carmine reef
so see if you can write the numerator as a single fraction, rather than a fraction minus one
and same for the denominator
eternal mesa
i got cos2a+1/cos2a-1
carmine reef
$\frac {\sec 2a - 1}{\sec 2a + 1}$
ocean sealBOT
monikanicity
carmine reef
$ =\frac {\frac {1}{\cos 2a}-1}{\frac {1}{\cos 2a}+1}\
=\frac {\frac {1-\cos 2a}{\cos 2a}}{\frac {1+\cos 2a}{\cos 2a}}$
$ =\frac {\frac {1}{\cos 2a}-1}{\frac {1}{\cos 2a}+1}\
=\frac {\frac {1-\cos 2a}{\cos 2a}}{\frac {1+\cos 2a}{\cos 2a}}$
thanks tex
eternal mesa
then what do you turn them into