I need only "a" to finish task
#help-39
bitter night
light jolt
that true, use law of cosine. $a^2 = b^2 + c^2 - 2bc*cos75$, b is known, c is known and cos15 is also known, everything is known in that equation
jolly parrotBOT
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bitter night
Thanks finally
light jolt
$a^2 = b^2 + c^2 - 2bc*cos15$
jolly parrotBOT
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light jolt
thats OK. first time reaching it. once you become familiar of these laws, that is just a piece of cake
bitter night
🥹 finally
light jolt
law of cosine is more powerful, it doesnot need to be a Right Angle Triangle
light jolt
if you know two lines and one angle, then you know every line and angle. using which one is convenient, if right-angled, of course using a^2 = b^2 + c^2 where angle A is 90 degree or pi/2
you are welcome. you can do this!
bitter night
:D
pearl pondBOT
@bitter night Has your question been resolved?
ebon marsh
im stuck on question 2. any idea ?
pearl pondBOT
im stuck on question 2. any idea ?
midnight haven
what did you get for 1a) and 1b)?
ebon marsh
J is convergent and its going down(sorry i dont study maths in english)
remote roost
Think about the min and max of 1/(1+x^2) in [0,1]
ebon marsh
it's 1 and 1/2
remote roost
Yes
late sequoia
pearl pondBOT
late sequoia
midnight haven
Set the "missing factor" As some variable y and use what you know of the property of squares
late sequoia
@stark summit
stark summit
yes i saw it
late sequoia
Here I am
stark summit
oh this looks interessting
late sequoia
Tricky
stark summit
@late sequoia i found it
stark summit
the answer is really easy
stark summit
???
late sequoia
just kidding
Please tell
stark summit
sure this is how i find it
consider the top and bottom quadratics
x²+_x+14
x²-_x-15
there something here that gives it away what factor the quadratic factors it has
and it's 14 and -15
well what do i mean with that
14 can be broken down into 2 factors, 2 and 7
stark summit
so it means it's either -3,5 or 3,-5
shy horizon
just add y as the missing part and all sides are equaled so u have equations
stark summit
you know what factors are of a quadratic right?
it's ax²+bx+c can be formed into (x-x1)(x-x2)
x1 and x2 being roots of the quadratic
shy horizon
yes right listen from him
late sequoia
I wish
late sequoia
So it is 7 and 2?
stark summit
yes
stark summit
that's like saying thaat 7x2 and 2x7 don't have the same answer
stark summit
How do I know is 7 first or 2
it doesn't really matter
shy horizon
How do I know is 7 first or 2
man just do what i told u
late sequoia
So it's 4+14+14
shy horizon
make equations
stark summit
So it's 4+14+14
how did you find this?
late sequoia
(x-7)(x-2)
stark summit
(x-7)(x-2)
exactly
late sequoia
X^2-9x+14
late sequoia
Sorry. I'm tired
stark summit
what time is it right now for you?
late sequoia
20:50
stark summit
you live in central europe?
late sequoia
Yeah
late sequoia
(x-3)(x+5)
stark summit
or it can be (x+3)(x-5)
shy horizon
or it can be (x+3)(x-5)
it might be upside down u cannot know that
so there will be 2 options
shy horizon
or it can be (x+3)(x-5)
it might be (x_3)(x+5)
stark summit
it might be (x_3)(x+5)
it actually is (x-5)(x+3) since the number becomes negative in the equation
shy horizon
it actually is (x-5)(x+3) since the number becomes negative in the equation
how could u know this
late sequoia
Ummm
stark summit
look back to the image the quadratic bellow
there's a - behind _x
meaning b has to be negative
late sequoia
Damn
shy horizon
still didnt get it but whatever
late sequoia
That's some wizardry
stark summit
yes
stark summit
That's some wizardry
alright we know all the factors right?
late sequoia
I gues
stark summit
(x-2)(x-7) and (x-5)(x+3)
stark summit
I gues
and you know what the question said right?
that neighboring sides have similar factors
late sequoia
Hmmm
stark summit
late sequoia
Should I factor those as well
shy horizon
the one on the left will be 9 as the top and the one on the right will be -2 same as the bottom
stark summit
the one on the left will be 9 as the top and the one on the right will be -2 s...
and what makes you think in that way?
late sequoia
No 9
shy horizon
try them
late sequoia
In existing
stark summit
Should I factor those as well
see here's the thing you already know all the factors
that neighboring sides have similar factors
so that means that x²+10x+_ could be factorized to maybe (x-2)(x+3) or (x-7)(x-5)
shy horizon
the one on the left will be 9 as the top and the one on the right will be -2 s...
my answer was right
stark summit
@late sequoia you still there buddy?
pearl pondBOT
@late sequoia Has your question been resolved?
pearl pondBOT
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finite obsidian
conditions for having to reverse the order of integration
pearl pondBOT
conditions for having to reverse the order of integration
finite obsidian
the example freely switches the limits and order of integ
but i thought this shouldnt be the case
like for this question you have to work out the respective new limits by sketching the graphs and looking at the limits
pearl pondBOT
@finite obsidian Has your question been resolved?
finite obsidian
<@&286206848099549185>
pearl pondBOT
@finite obsidian Has your question been resolved?
static bloom
conditions for having to reverse the order of integration
There are two famous conditions usually calle Tonelli and Fubini.
the first says you can switch it if the integrand is only positive
and the second says you can switch it if the absolute value of the integrand integrates to a finite value
If it is written like as a double ingtegral it is implicitely assumed already that order does not matter
finite obsidian
the first says you can switch it if the integrand is only positive
but the integrand for this is positive and u cant freely switch it, no?
static bloom
you can
but you need to be careful with x dependency
you have y < e^x
so the reverse would be
ln(y) < x
finite obsidian
exactly so you havent freely switched the exact limits and youve calculated how to reverse it
static bloom
You just have to integrate the right region
you need to integrate {(x,y)|0<x<1 & 1<y<e^x}
finite obsidian
Ok I somewhat understand now, thanks 👍
static bloom
this is the same set as {(x,y)|0<x<ln(y) & 1<y<e}
the function behind the integrals however remains uncahnged
and you do not need to worry about getting different values when switching order
swift furnace
need help
spiral rock
mossy canopy
hey
mossy canopy
this is the task i have
my work thus far
i do see why z cant be 1
however i dont see why this should fail for |z|>1
or z=-1 for that matter
plush bramble
do the ratio test
mossy canopy
do you mean ratio test for bk
nevermind
doing so with bk, i get that the quotient sequence is always greater than 1 and approaches 1 i think
also it is independent of z
this is what i get if i do it for bk*z^k
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pearl pondBOT
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steel solstice
Hello is the answer here 9.98 inches? Because i got approximately 9.75 inches. The topic here is common tangents and secants. Thank you,
toxic lichen
do you have work to show for this?
steel solstice
like a solution?
toxic lichen
yes, show us how you arrived at 9.75 in
steel solstice
yes here]
light helm
0.7^2 isn't 4.9
steel solstice
ahhh yes youre right
thank you for the correction
I was able to find my answer thank you @light helm and @toxic lichen 🙂
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pearl pondBOT
light helm
error in what you wrote at the very end
toxic lichen
.reopen
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toxic lichen
typo'd 9.98 as 9.978 perhaps
pearl pondBOT
@steel solstice Has your question been resolved?
mellow basin
pearl pondBOT
mellow basin
proof eqaution has at least one solutioon
pearl pondBOT
@mellow basin Has your question been resolved?
balmy ember
Ping a helper @mellow basin
mellow basin
<@&286206848099549185>
cloud zephyr
is it good enough to say
(x-b)(x^2+1)+(x-a)(x^6+1)
is an odd degree polynomial,
and the root is not a or b,
so there must be at least one solution?
pearl pondBOT
@mellow basin Has your question been resolved?
mellow basin
Definetly not
Forgot to say in the intervall a,b a and b excluded sry
That at least one solution exists
cloud zephyr
oh!
mellow basin
And b>a
mellow basin
<@&286206848099549185>
gloomy summit
pearl pondBOT
gloomy summit
Where would I start with this one? Not sure how to approach
sharp quest
Breaking into a sum of intersections
and then rewrite those intersections using the conditional probabilities you know
usually called the 'law of total probability' i think
gloomy summit
managed to do something like that, got an answer of 3/10
but not sure if that's correwct
sharp quest
show your work
gloomy summit
let me rewrite it clearly for you it's v messy
severe quartz
This asking p( predicted / actually occur)?
gloomy summit
gloomy summit
This asking p( predicted / actually occur)?
Other way round but yeah
severe quartz
Other way round but yeah
Why other way around? Doesnt it say "given you are delayed"?
gloomy summit
Oh oh my bad
Yeah even I did it your way round lol
But I’m not sure where to go from my working
If I even did it right
gloomy summit
do you have working would be really helpful
severe quartz
Ok but im not exactly sure if its 2/3 or not, better confirm it from someone
gloomy summit
for sure
gloomy summit
alright now i'm gonna try via tree diagrams
Woah
I need to take my methods back to year 12/13
University methods are way too complicated
Tree diagrams are the 🐐
severe quartz
Tree diagrams are nice as long as theres not too many stages
gloomy summit
True
But yeah it’s 2/3
Probability will be the death of me
🫁
Thanks again🙏🏼
close
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pearl pondBOT
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late lark
How can I compute the dot product of u*v? u=1,3 and v=-5,-5
pearl pondBOT
How can I compute the dot product of u*v? u=1,3 and v=-5,-5
empty cloak
How can I compute the dot product of u*v? u=1,3 and v=-5,-5
Btw, the simplification for the other thing: do you know about sin^2(x) + cos^2(x) = 1?
late lark
yes
empty cloak
So 1- sin^2(x) = cos^2(x)
late lark
yes
empty cloak
That's the way to simplify it
late lark
yeah i tried to simplify it further to cos(alpha) = +-sqrt(1-(sin(1/5)^2))
but I think thats where I did something wrong
late lark
That's the way to simplify it
Any idea where I messed up?
empty cloak
Any idea where I messed up?
Uhhh what do you mean?
late lark
yeah i tried to simplify it further to cos(alpha) = +-sqrt(1-(sin(1/5)^2))
on this line
Cause the answer is incorrect
empty cloak
sqrt(1-sin^2(1/5)) is still simplifiable
empty cloak
So 1- sin^2(x) = cos^2(x)
using this
late lark
yes that should be +-(1-(sin(1/5))) then right?
empty cloak
No
empty cloak
So 1- sin^2(x) = cos^2(x)
.
late lark
1-sin^2(1/5) = cos^2(x)
empty cloak
Mhm
late lark
but I need to get the answer in form of cos(x) so then I squareroot both sides so I have 1-sin(1/5) = cos(x)
late lark
oh
empty cloak
Btw, the simplification for the other thing: do you know about sin^2(x) + cos^2(...
It follows from this
x = 1/5
Does that make sense?
empty cloak
The question was sqrt(1-sin^2(1/5) right?
So now we know that's the same thing as sqrt(cos^2(1/5)) right?
Which is just cos(1/5)
late lark
I dont know, I have to check and it will tell me if Im right
late lark
How can I compute the dot product of u*v? u=1,3 and v=-5,-5
I can have a word with my classmates tomorrow to see if they have found the solution so thats why I moved on to this question:
Compute the dot product of u*v? u=1,3 and v=-5,-5
okay
so that would be 1x-5?
empty cloak
And you will get alpha = 1/5, no doubt about it, unless they're doing a weird thing of taking the negative square root, in which case it's pi - 1/5, but idts because you always take positive sqrt root
empty cloak
so that would be 1x-5?
Sorry, made a typing error. Fixed
Nvm I really screwed up the wording there
Dot product is when you do u1 * v1 + u2 * v2.
Where u1, u2 is the first term and second term of u respectively
late lark
And you will get alpha = 1/5, no doubt about it, unless they're doing a weird th...
pi-1/5 wasnt the answer they were looking for either :/
late lark
Dot product is when you do u1 * v1 + u2 * v2.
solved for -20 thx
empty cloak
Can you send the question again? Maybe they wanted it from radians or degrees or smthn
empty cloak
Oh bruh
late lark
?
empty cloak
sighhhh
I've completely misinterpreted the question, sorry
cos^2(x) = 1-sin^2(x)
We know sin^2(x)
So cos^2(x) = 1-(1/5)^2
So cos(x) = (1-1/25)^0.5
late lark
hmm how did u get 0.5 and 25?
late lark
hmm this one is not correct either (1-1/25)^0.5
empty cloak
hmm this one is not correct either (1-1/25)^0.5
Well, yeah, it's 24^0.5/5
taking 25 as the denominator for 1 and all
late lark
Well, yeah, it's 24^0.5/5
24^(1/2)/5 is not correct either (not allowed to use float values)
empty cloak
24^(1/2)/5 is not correct either (not allowed to use float values)
Ah the angle is between pi/2 and pi
late lark
yes
pearl pondBOT
pearl pondBOT
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Available help channel!
runic vault
runic vault
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midnight haven
kk lemme read the question
runic vault
midnight haven
Do u need help?
runic vault
Yes
mild olive
lets try to write this out as an equation
midnight haven
so that would mean 800-?
mild olive
so that would mean 800-?
no
mild olive
sure
midnight haven
Wait is an equation needed?
runic vault
So then theatre 2 = 150 + x
mild olive
Wait is an equation needed?
yes
mild olive
So then theatre 2 = 150 + x
wonderfull
midnight haven
Ok mb
mild olive
uh no
runic vault
oh
mild olive
we know the three sections combined= 800 right
runic vault
yea
runic vault
But we also know that 270 of those seats are taken by theatre one
runic vault
Yeah oh wait
mild olive
mhm
mild olive
where are you getting this 530
mild olive
no
mild olive
so 800=270+x+y
lets try from here
runic vault
Yep
mild olive
so we need the values of theater 2 and 3 now
runic vault
mhm
runic vault
Its 150 more then theater 3
mild olive
if theater=x then what is that as an expression?
runic vault
x+150?
runic vault
800=270+x+150+x
mild olive
uh yes, I wrote the equation a bit unclear
not a y, its an x
as theater 3s value was assigned to x a bit ago
shouldve made it y+x not x+y to be more in order
runic vault
Would that work?
runic vault
Yep okay
mild olive
runic vault
I got 190
mild olive
$$800= 270+(150+x)+x$$
$$800=270+150+2x$$
$$800= 420+2x$$
$$800-420=2x$$
$$380=2x$$
$$\frac{380}{2}=x$$
$$190=x$$
theater 3 is 190
jolly parrotBOT
Bestower
runic vault
<:catthumbsup:614540188747563008>
Anyways thank youu
mild olive
Woah how did u do that
its a bot running a program called LaTEx
it allows you to write math
just surround every equation with $ signs, if you want it on a sperate line uses $$ on each side
mild olive
Anyways thank youu
no problem ❤️
runic vault
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thorny crag
is csc the inverse of the sin function?
pearl pondBOT
is csc the inverse of the sin function?
plush bramble
is csc the inverse of the sin function?
multiplicative inverse yes
but you should learn the difference between that and inverse as a function
finite crown
^
soft fable
^
finite crown
the inverse of sin would be arcsin or sin^-1
thorny crag
could someone explain how you get the inverse
i think im thinking of it as the reciprocal
soft fable
are you using a calculator for this? @thorny crag
thorny crag
no, i was using desmos
soft fable
I see
I'm gonna assume that you're problem with this question is that you don't understand how they're calculating the final answer. I believe you're mixing up the term 'inverse' in this context. It may be true that csc is the multiplicative inverse of sin, like riemann stated (that is, csc(x) = 1/sin(x)), but to calculate the inverse of cos in this context, you'd need a calculator. cos^-1(x) is the same thing as arccos(x). In simple terms, you're finding the angle from the origin that makes cos(x) = 11/14. By plugging in something like
cos^-1(11/14)
into your calculator, you'll see the answer is 38.2132 (or 0.6670 rad if you haven't converted your calculator to degrees)
thorny crag
ok yeah, thats right. I think i'm getting it now
soft fable
Idk how much you've worked on these type of math problems, but if you recall/encounter the unit circle this may make more sense. You're trying to find the angle that is equal to a certain point. In the unit circle, these things are generally memorized because they're easy to calculate and used a lot in mathematics. For example, sin(pi/2) = 1 would mean that arcsin(1) = pi/2
thorny crag
alright, Thank you!
pearl pondBOT
Available help channel!
vivid pilot
pearl pondBOT
vivid pilot
previous discussion:
tall tangle
who is @midnight haven
rough stream
Toby gave you nothing except a rather general theorem
That every number does split uniquely into prime factors. I can't see immediately how that helps
Might be easier to prove the contrapositive? If M ≠ N, then there's no way to pair up the numbers the way Monish did.
vivid pilot
Might be easier to prove the contrapositive? If M ≠ N, then there's no way to pa...
right. i was thinking that
not sure how to prove it tho
any ideas?
i really need to solve this
if they are different numbers, then they must have different factors
thats as far as i can get
if i could somehow show that the products will be different for different M and Ns
pearl pondBOT
@vivid pilot Has your question been resolved?
brisk lotus
The thing I noticed is, that if M ≠ N, there must be at least one factor, lets call it E, that is part of the set of divisors from one number, but not from the others. If thats the case there must always be one pair (x, E), which when multiplied yields a result different from all the other possible pairs, indicating that these two numbers aren't equal, as two equal numbers would have the same divisors.
Now when all of Monish's products are the same it also disproves the existence of E, meaning the set of divisors of M and N must be equal and as such M and N must be equal
I don't know if thats enough though
pearl pondBOT
@vivid pilot Has your question been resolved?
sharp quest
I was thinking about what happens with 1. Without loss of generallity, assume M > N
you know 1 appears on both lists, and clearly can't be paired with each other.
Just looking at the M case: If M isn't paired with 1, then M and 1 are paired with some other factors x>1 and y>1 and Mx > M > y(1). So they can't all be equal.
That forces one of the 1's to pair with M
then a similar argument shows that pairing the other 1 with anything will be strictly less than M
graceful tendon
is this simplifiable?
pearl pondBOT
is this simplifiable?
old geyser
I might be
Well wait
It's missing an argument
Is it supposed to be cos^2(t) on the numerator?
old marsh
Yea most likely
Anyways
Know that sin^2(t) + cos^2(t) = 1
Thus, solve for -2cos^2(t)
Now u have everything in terms of sin(t), do a substitution k = sin(t) and rewrite everything from there, see if u can solve after that
pearl pondBOT
@graceful tendon Has your question been resolved?
graceful tendon
ok thanks
atomic quartz
ay bruh
plush bramble
Where's your slope?
atomic quartz
wdym
atomic quartz
i actually dont know watched 5 vids and listened in class still dont get it now my brains messed up
plush bramble
Which video did you last watcg
atomic quartz
Sal on khan
plush bramble
Send link
atomic quartz
-3?
plush bramble
A point is the pair
plush bramble
like u mean (6,-3)
This is a point
plush bramble
whats the diff
y and x are variables in every equation of a line, for now
You don't change or substitute numbers for them when you describe an equation of a line
plush bramble
Sign error
atomic quartz
ok
atomic quartz
okay so basically.. its like this
0 - (-3)
--------
1 - 6
???
so I did that right though, yes??
plush bramble
Yes
plush bramble
y-y₁=m(x-x₁)
Yes. Now plug that in here
plush bramble
y is 0 and y1 is 3
No
plush bramble
y and x are variables in every equation of a line, for now
.
plush bramble
y-3=m(x-6)
No
atomic quartz
😦
plush bramble
What's y1?
atomic quartz
5
plush bramble
No
atomic quartz
nvm 0
plush bramble
yes tyhen 6,-3
.
atomic quartz
-3
plush bramble
Yes
atomic quartz
ookay..
plush bramble
okay so basically.. its like this
0 - (-3)
--------
1 - 6
???
What variable represents this calculation
atomic quartz
x
plush bramble
No
atomic quartz
y
plush bramble
...
atomic quartz
bro
plush bramble
Spend some time thinking
atomic quartz
sorry i just having a hard time thinking been thinking for about 3 hours
atomic quartz
What variable represents this calculation
can you lower the vocab down a bit
plush bramble
okay so basically.. its like this
0 - (-3)
--------
1 - 6
???
Where did you get this formula
plush bramble
y-y
---
x-x
Do you have a textbook or notes
atomic quartz
no
plush bramble
What does that formula mean
plush bramble
It's this but you're missing indices
plush bramble
no
https://www.cuemath.com/geometry/finding-slope-from-two-points/
You should read
atomic quartz
It's this but you're missing indices
IT WAS RISE OVER RUN?!
plush bramble
Did you know slope?
plush bramble
That's slope yes
I said it here
plush bramble
(-3/5) is fine
atomic quartz
im loosing my mind
atomic quartz
can u help me with my whole khan thing just 2 questions left if you want it dont matter
pearl pondBOT
@atomic quartz Has your question been resolved?
atomic quartz
okay im done
abstract junco
pearl pondBOT
abstract junco
pls?
austere tinsel
What do you need help with here? What have you done so far?
abstract junco
i cant set up the equation
austere tinsel
So every month the debt is increased by 12%, meaning the debt after 2 months would be 5000*1.12^2
After 6 months 2000 is removed from the debt, then again at 12 months
How much debt is there at 18 months?
Does that help?
abstract junco
no...
austere tinsel
Can you figure out how much debt there would be at 5 months?
abstract junco
5000(1+12%/12)^(12*5/12)?
austere tinsel
Um, almost? Why are you dividing by 12 and multiplying by 12 in the exponent?
abstract junco
A=P(1+r/n)^nt s.t. A is the final amount, n is the number of compounding periods in a year, P is the principal amount, r is the yearly rate and t is the time in years
austere tinsel
Ah I see, I may have misunderstood what the question. I thought it meant 12% was being applied each month
austere tinsel
Yeah so in that case your equation is (probably) correct
abstract junco
but the answer key says another answer ;-;-;-;
austere tinsel
Okay so calculate how much debt there would be at 6 months (before the 2000 deduction)
abstract junco
5307.60075301
austere tinsel
Then apply the 2000 deduction
austere tinsel
Subtract another 2000 and run it through the last 6 months
abstract junco
3727.08731817
austere tinsel
I think you forgot to deduct the 2000 at the 12 month mark
abstract junco
AHHHHHHHHH
austere tinsel
Got the right answer now?
austere tinsel
np np
abstract junco
.close
drowsy bronze
How to know how many times to differentiate it?
pearl pondBOT
How to know how many times to differentiate it?
drowsy bronze
Like it's 3-
But is it dependant on the values given ?
plush bramble
Can you translate
pearl pondBOT
@drowsy bronze Has your question been resolved?
drowsy bronze
Find the interpolation function fx =sin π/2 in three different points
Xo =-1
X1= 0
X2 =1
And find an upper limit for it's error
drowsy bronze
Can you translate
Didd
pearl pondBOT
@drowsy bronze Has your question been resolved?
meager mountain
please solve, i used mathway, symbolab, wolfram alpha, and they all give the same answer
plush bramble
use exponent rules to put everything under the square
meager mountain
wdym
plush bramble
Product and Quotient rule in the table
meager mountain
i dont quite understand it
plush bramble
please solve, i used mathway, symbolab, wolfram alpha, and they all give the sam...
For quotient, a^m and b^m are the two terms in denominator
m=2
pearl pondBOT
@meager mountain Has your question been resolved?
meager mountain
ok im confused as fuck rn
ill jus ask the teacher
fuck this math class
smh
.close
pearl pondBOT
meager mountain
.reopen
pearl pondBOT
✅
meager mountain
<@&286206848099549185>
pearl pondBOT
@meager mountain Has your question been resolved?
pearl pondBOT
@meager mountain Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
sweet wolf
pearl pondBOT
sweet wolf
yes
jolly parrotBOT
Stephen
old marsh
Ok so
jolly parrotBOT
Stephen
sweet wolf
9
jolly parrotBOT
Stephen
sweet wolf
6^x
finite crown
Mhm
old marsh
Ye
jolly parrotBOT
Stephen
sweet wolf
ye
old marsh
U see anything we can simplify?
sweet wolf
no
manic sparrow
**Stephen**
=3^x•2^x•3²•2^y
so 2^(x+y)•3^(x+2)
old marsh
Ye u right, mb, I missed that
Forgot the most basic rule of basic rules
But yea @sweet wolf u see what he did?
pearl pondBOT
jolly parrotBOT
Stephen
pearl pondBOT
Available help channel!
keen tusk
pearl pondBOT
keen tusk
can someone help me with this please
finite crown
Yea lemme get my magnifying glass
keen tusk
lol mkay
finite crown
So basically
We got an equation
28+ 0.6(x)= 55
Solve for x
There’s your answer in years
Have u been learning compounding recently?
If so the 0.6% I might have interpreted wrong
finite crown
All g
opal cape
To solve this
pearl pondBOT
To solve this
opal cape
How do i solve for x
vital estuary
Set AB equal to CD
coarse dawn
Solve for x
opal cape
Idk how to solve for x
Ok so i add them
I have another example
3x + 4 = x + 14
So i
3x + 4 - 4 = x + 14 - 4
Is it like this?
meager mountain
x is 5 no?
opal cape
5?
Can anyone tell me how to solve x in general
Im preparing for a test and the vid im watching is confusing
Like this why did he add +2
To cancel the -2
coarse dawn
Because that's the process to solve for x
pearl pondBOT
@opal cape Has your question been resolved?
opal cape
Because that's the process to solve for x
He added the plus 2? To remove the -2
Ok so
AB = CD
X + 11 = 16
Do i subtract or add
X + 11 - 11 = 16 -11
So x = 5
opal cape
Because that's the process to solve for x
This correct?
coarse dawn
Plug that value back in to check
warm current
what is your question, @opal cape?
opal cape
On how my answer is not correct
warm current
How is this not correct lol
Oh this is your new question
opal cape
Takes a long time to load
Ty
I still think ns is the correct answer ngl
I have a new question
How did this become 1+5
warm current
Two steps happened
3y was subtracted from both steps to remove it from left side
Then 5 was added to both sides to remove the -5 on the right side
lethal gazelle
So
8y + 3 = 6y - 5
3 + 5 = 6y - 8
Y = 8
im just confused here
where did your 8y go
on the second part
lethal gazelle
So
8y + 3 = 6y - 5
3 + 5 = 6y - 8
Y = 8
if you are solving for y that would be incorrect it wouldnt be y = 8
let me open somethign so i can do this problem one second
warm current
opal cape
I made a bad example 😂
lethal gazelle
then you do 8 divided by -2y
so you get -4 as the answer
y = -4
does that make sense?
opal cape
Yes
opal cape
Yes
lethal gazelle
lets see
opal cape
I gotta hold i have to do something
lethal gazelle
ok
opal cape
Thank you for your help
lethal gazelle
ya
opal cape
I can understand math a little better nlw
lethal gazelle
good
opal cape
Hi
midnight haven
do you know transposition
opal cape
No
light helm
apply the same operations to both sides
one common way would be to use the above
to separate your x terms from non-x terms
e.g. taking a much simpler example of
x - 7 = 35
you can add 7 to both sides to get
x = 42
opal cape
e.g. taking a much simpler example of
x - 7 = 35
you can add 7 to both sides to ...
Ill add
7x + 2 = x + 56
Both sides with 7
light helm
although valid, that doesn't really help you here
doing that to your equation results in
7x + 9 =x + 63
and you aren't any closer to finding x
opal cape
one common way would be to use the above
to separate your x terms from non-x ter...
I dont get this tbh
light helm
e.g. taking a much simpler example of
x - 7 = 35
you can add 7 to both sides to get
x = 42
did you understand that?
opal cape
Yes
light helm
note that adding 7 to both sides led to
having a term(s) with x on one side
and a term(s) without x on the other
and in that simple example doing that already gives you the solution
now lets make this slightly more complicated an start with
2x - 7 = 35
instead
the same approach can be used to
to separate your x terms from non-x terms
by
add 7 to both sides to get
to get
2x = 42
would you be able to solve this equation?
light helm
apply the same operations to both sides
what could you do to get from 2x to just x (ideally without introducing new terms so don't use addition/subtraction)
light helm
(ideally without introducing new terms so don't use addition/subtraction)
e.g. sure you could get from 2x to x by subtracting x,
but doing that to both sides leads to
x = 42 - x
you now have x terms on both sides of the equation which you don't want and you are now further away from solving x
consider a real life example
if 2 delicious premium burgers cost a total $42
how would you determine the cost of 1 of those burgers?
opal cape
By halfing
light helm
yeh, same idea can be applied to
2x = 42
opal cape
2x = 22
light helm
why did you just subtract 20 from the right side
light helm
so
yeh, same idea can be applied to
2x = 42
what do you get upon solving
opal cape
X = 42?
light helm
no
the problem is pretty much equivalent to the real life example i gave you
if 2 delicious premium burgers cost a total $42
how would you determine the cost of 1 of those burgers?
2x = 42
is asking the same thing (where x represents the cost of 1 burger)
opal cape
Im not following now
light helm
recall what you intuitively did in the real life example i gave you
you got that almost instantly
if 2 delicious premium burgers cost a total $42
how would you determine the cost of 1 of those burgers?
By halfing
and doing that, how much does 1 burger cost?
don't overthink this
light helm
22 isn't half of 42
opal cape
21
light helm
So i half 2x = 42
halve both sides (or in other words divide both sides by 2, or multiply both sides by half)
results in
x = 21
does that make sense?
opal cape
Ty
light helm
and try applying those idea to your initial question
light helm
why choose to add 7 to both sdies?
opal cape
7x +2 = x +56
light helm
doesn't answer my question
opal cape
why choose to add 7 to both sdies?
So i add 7 to the right part
opal cape
7x +2 = x +56
This was pre typed lol
light helm
no, adding the same value to both sides is valid
but why are you choosing to use the specific value of 7
opal cape
Cause 7x
light helm
with
2x = 42
you didn't decide to add 2 to both sides of the equation because there was 2x did you?
recall what i initially led you towards
first try separating the x and non-x terms
note that currently on the left side you have
7x + 2
what could you do to that so that you'd only have a single x terms
little sundial
So i add 7 to the right part
7 is being multiplied by x, not added, so 7x+7 does not equal x or anything
opal cape
Divide
little sundial
yessir
opal cape
By 2?
little sundial
well you can't divide yet
light helm
that gets you
$$\frac{7x+2}{2}$$
jolly parrotBOT
ℝamonov
light helm
there's a difference between can't and shouldn't
little sundial
there's a difference between can't and shouldn't
ah mb
light helm
which isn't really what you want
dividing by 2 doesn't really help you in isolating x
opal cape
Divide it by 7?
light helm
consider what i guided you on ealier
little sundial
@opal cape you have 7x + 2 = x + 56
your first objective should be to basically isolate x, so get all the terms with an x in them on one side and all the numbers like 2 and 56 on another side before worrying about the 7
light helm
again, that doesn't really help you
recall this example
2x - 7 = 35
2x - 7 + 7 = 35 + 7
To get 2x = 42
adding 7 to 2x-7 leads to you having a single x term on the left side of the equation
since 2x - 7 + 7 = 2x
hence why 7 was the number chosen to be added to both sides
apply the same idea here
opal cape
I subtract it?
little sundial
subtract what from both sides
opal cape
The 2? I think
opal cape
Oh i remember this from the thing i studied earlier
opal cape
what equation do you have after doing that
7x =54?
light helm
no
light helm
the x initially on the right side of the equation doesn't just vanish into oblivion from subtracting 2
opal cape
So x = 54
light helm
no
little sundial
now the 7 is gone
opal cape
I love the word oblivion
little sundial
can you simplify 7x + 2 - 2 = x + 56 - 2?
light helm
stuff doesn't just disappear and jump around like a hot potato from doing simple subtraction like that
little sundial
take one side at a time
what is 7x+2-2 (left)
and what is x+56-2 (right)
opal cape
7x + 2 - 2 = 7x
little sundial
yep!
opal cape
X+56 -2 is x+54
light helm
yes
little sundial
alright so 7x = x + 54
now can you bring the x on the right to the left? so you can isolate X
opal cape
So 7x = 54
light helm
no
opal cape
Then i divide?
light helm
you obliviated that x again
opal cape
Where do i put the
little sundial
what can you subtract from both sides so that you can get rid of the x from the right
7x = x + 54
light helm
apply the same principles i keep reminding you about
opal cape
54?
light helm
a common approach would be to separate you x terms from terms without x
what could you do to
x + 54 so that you'd only have a constant term
little sundial
that would give you 7x-54 = x which doesn't help you all that much
opal cape
So 7x
little sundial
7x what
opal cape
The one i subtract
little sundial
0 = x + 54 - 7x doesn't help you either
opal cape
I dont know what to do now lol
little sundial
ok you have 7x = x + 54
light helm
what could you do to
x + 54 so that you'd only have a constant term
little sundial
what should you do to get 54 "by itself" (that's what ramonov means by only a constant term)
light helm
similar to what you did to
7x + 2 to only have an x term
what addition or subtraction would you perform
opal cape
Subtract the x
little sundial
yessir
light helm
yes
little sundial
what do you get
light helm
and do that to both sides of the equation