#help-13
1 messages · Page 54 of 1
shud u make 4 bigger or smaller?
g(4) = 2
do u realize g is just a function that takes in a number as input, does something to that number, and gives it as input to f, and then outputs whatever f outputs at that number?
do u realize that when u input 4 to g, it must output what f outputs at 1?
how can I figure out the horizontal scaling 4factvor
yes
so what must g do to the number 4, before inputting it into f, to get the same output that f outputs at 1
I have no idea
I don't know
okay if u put 4 into g, and g made the number 4 bigger and then inputs it to f
what kinda number wud f output
6
well a number bigger than 2
if u put 4 into g, and g made the number 4 smaller, and then input it to f, then what kinda number wud f output?
this is because g turns the number 4 into whatever number u need to input into f, to get 2 as output
is that clear?
no I don't understand
oh okay
well thank you for the help
<@&286206848099549185> could someone help me with this problem please
@digital shell Has your question been resolved?
$f(x) = 4\sqrt[3]{x}-2$
ThM
since g(x) should be horizontally scaled is has to look like:
$g(x) = 4\sqrt[3]{ax}-2$
ThM
and we know f(1) = g(4).
yeah
you need to transform 4 -> 1 to get this last equation.
I don't follow
yeah
f(1) = 1, right?
f(1) = 2
$2 = 4\sqrt[3]{ax}-2$
ThM
ThM
we have g(4), so it is:
$4 = 4\sqrt[3]{a4}$
ThM
does that not change the vertical value?
which step do you mean?
when you add 2 to the equation
no. we have g(4) = f(1) = 2 which gives us
$2 = 4\sqrt[3]{4a}-2$
ThM
I don't understand it
which point?
how to solve for a
do you agree with this?
what value has a?
I don't know
so we try to calculate a.
but I don't understand this
again asking. do you agree with this? we have g(4) = f(1) = 2 which gives us
$2 = 4\sqrt[3]{4a}-2$
ThM
we did this, to calculate f(1) = 2.
I didn't see that
this.
I don't see the correlation
which correlation? who is talking about correlations?
I don't see how this could relate to your previouys equation
this
we know f(1) = 2, do we?
yes
we know g(4) = f(1) = 2, do we?
yes
we know g is horizontally scaled, do we?
yes
what does horizontally scaled mean?
that the x value has been scaled by some factor
$g(y) = 4\sqrt[3]{ay}-2$
ThM
with the scale factor a, right?
yes
ok, g(4) = 2, right?
right
just slowly. write 4 instead of y in this equation.
$g(4) = 4\sqrt[3]{4a}-2$
we get $g(4) = 4\sqrt[3]{4a}-2$
$2 = 4\sqrt[3]{4a}-2$
Norahc
add 2 on both sides.
$4 = 4\sqrt[3]{4a}$
Norahc
divide both sides by 4.
$1 = \sqrt[3]{4a}$
Norahc
power both sides by 3.
$1 = {4a}$
Norahc
divide both sides by 4.
you are asked for g. just plugin this a in the previous function equation.
you could have done this in a shorter way. since f(1) = g(4). which factor makes 1 from 4?
exactly.
ok, lets stop this. you have your g:
$g(y) = 4\sqrt[3]{\frac{y}{4}}-2$
ThM
yes thank you
but is there a way to apply this method more generally?
for other problems like this
if you have a f and horizontally scaled g, write the function equation with such an a. and then you need 2 points (as we had here with 1 and 4) and then sovlve for a. This is an general method.
so if I had the points f(2) = g(8). how could I apply it?
if you mean f(2) = g(8): calculate f(2), then use this value for g(8) and write 8 instead of y in your function equation of g.
alright, thank you very much for your help
have a great rest of your day
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i need help on this equation
i know
Would you like a gold medal for your comedy

How about a <@&268886789983436800> ping
Yes
This is like the 5th collatz Shitpost I've seen this month
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please dont misuse help channels for a joke
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can i get a hint for where to start?
anyone?
@kindred hornet Has your question been resolved?
@kindred hornet which direction is troubling you?
well i dont know how to exactly prove this
should i prove that a parrelelogram with 4 equal sides has perpendicular diagonals
even if i do that, where would i go from there
u there?
sorry, was showering
you are proving an if-and-only-if statement
this means that you are to prove two implications
- if a parallelogram is a rhombus, then its diagonals intersect at right angles.
- if a parallelogram's diagonals intersect at right angles, then it is a rhombus.
what you described is (1)
you will still need to have (2) to go
99% of geometric proofs require diagrams.
@kindred hornet Has your question been resolved?
ah ok then
@kindred hornet Has your question been resolved?
@kindred hornet Has your question been resolved?
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can someone help me figure out how to set up this equation?
@umbral adder Has your question been resolved?
i would start by defining a reference point (such as the general store or the roadside eatery) that you're going to call "position 0"
and then write two equations describing the positions of the two people as a function of time
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if f(x) has a domain of |x-7| <= 5, then f(x/3) has a domain of |x/3 - 7| <= 5
what is range tho
well the x/3 won't change the range - that's just scaling the x axis
so focus on the -1/2 and the +8
ok
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how can I simplify
$\frac{x^{3}}{\sqrt[3]{x^2+1}}
how can I simplify
$$\frac{x^{3}}{\sqrt[3]{x^2+1}}$$
Umbraleviathan
I want to take the integral of the function and I think I need to use partial fractions since that's the chapter that the problem is in
$$\int{\frac{x^{3}}{\sqrt[3]{x^2+1}}}$$
$$\int{\frac{x^{3}}{\sqrt[3]{x^2+1}}dx}$$
What
Yeah I guess do a trig sub of some sort
Wolfram
the result looked weird
,w integrate x^3 / (x^2 + 1)^(1/3)
ew
Yeah it looks like a result of a trig sub
Also can you DM me the Fiddy sticker imma steal it
Although symboblab did a u-sub
Doesn't specify what they subbed in
Oh actually
so $$\int{\frac{u^{2}-1}{2\sqrt[3]{u}}du}$$
What
,w integrate 1/(u^(1/3))
,w (u^2) * (u^(-1/3))
so after the u-sub I split what I replied to into 1/2 the integral of u^2 / u^(1/3) and 1/2 the integral of -1 / u^(1/3)
which turns into $$(\frac{3(x^2 + 1)^{11/6}}{16}) + \frac{3(x^2 + 1)^{2/3}}{4} + C$$
What
which isn't the right answer
$$\int{\frac{u^{2}-1}{2\sqrt[3]{u}}du} = (1/2)\int{\frac{u^{2}}{\sqrt[3]{u}}du} + (-1/2)\int{\frac{1}{\sqrt[3]{u}}dx}$$
What
is this true? I must be missing something because I have the two integrals on the right side of the equality correct
this is wrong
should be so $$\int{\frac{u^{2}/sqrt(u-1)-u}{2\sqrt[3]{u}}du}$$
What
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How would I find these measurements with the info I have already written down?
Have you used CAD software before?
But anyway, like all geometrical problems, using geometry
@nova warren Has your question been resolved?
@nova warren Has your question been resolved?
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I need help w #12, plz
Consider ||shared angles||
Right, but there’s only 1 set of congruent angles
I need 2
'Shared angles' means angles shared between the triangles
Well you know what to look for
It's kind of a common sense thing
look at it again
Ok
It angle C congruent to itself by the reflexive property of congruence?
Ah, that makes sense
Could u also rq check what I did for #14? @ancient lodge
sure
Here it is
Are the congruence marks correct, as well as the similarity statement?
,rotate
Looks good to me 👍
Yes, the statement is correct \ \ And you could've also used the shared $\angle N$, though you don't have to since two angles are sufficient to prove similarity
Civil Service Pigeon
There's $3!=6$ ways to order the letters so that's fine
Civil Service Pigeon
👍
Ty @ancient lodge
O
Oh, and, here for example
How do I know that the side that’s 12 units long corresponds with the side that’s 24 units long?
Alternate interior angles
Got it, ty
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In the proof of this theorem
How do we know that anything less than N is bounded
Can elements of a sequence not be infinity?
I guess that would make sense
Because the proof clearly makes sense for the sequence elements greater than N
But I guess I don’t get why if we can just write off the elements before N Why can’t we do the same for the elements after N
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can someone help me with arithmatic and geometric sequences
A or b
both
3
Okay and what is d
an=a1+d(n-1) for arithmetic sequence
N-1 tells us how far away we are from n1
When it’s 1 1-1 is 0 since we’re at n1
N2 is 1 away from n1 so 2-1 = 1
Since it is +5 for every n away from n1 we need to multiply n-1 by 5
An=3+(n-1)times5
Yup
is that it
Yes
(b) is just a25
Can you send a clearer pic
Are you sure you subbed in n=25 in the formula you wrote for an?
Still can’t read it ha
find the 25th term
I meant the equation
Oh
First you get the equation we just calculated and then plug in a25
The 3 was not in the bracket
It’s 3 + (25-1) * 5
Yeah
i think i have it
the next question is
12,10,8,6
write an explicit formula
i got An=12+(n-1)*-2
is it -2 or 2
...
Yeah your good
-2, since the common difference is -2
ok thanks
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Can someone please help me understand how I can solve #49
Do you know what topic this is under
I can't even find a video to help me. The videos I find are doing very simple questions
I am trying so hard to understand what to do but I can't find a video to help me
Fantastic this is under differentiation
What does the derivative of a function tell you?
The slope
Of?
The important thing is it tells you the slope of f(x) at its corresponding x value
Okay so, I have x value, I sub x into f(x) to get y value
So f’(2) tells you the slope of the tangent at x=2 for the function f(x)
Then to get m I just derive
Then I sub everything into y-y1 = m(x-x1)
Would this be the goal?
Yes
This is a the formula to find the equation of a line that passes through a known point and the slope
By differentiating you can find the slope at the point (“where x = ???” Part of the question)
And by subbing in that x value into f(x) you can find that point
Doing these 2 steps give you a slope and a point
Then use this formula to find the equation of said line
Ok I am going to try and do 49, I will probably have mistakes, and it would be nice if you can tell me if something is wrong
Please
Of course, send your working out through
2x
Ohh oops
The top seem to cancel out
So would f'(x) = 0
The slope = 0?
Oh I made a mistake
Should be 2x^2(e^(2x))
Look again
Im gonna try to derive it again
Yeah mb
Yeah
Now look at x=1
Find the slope of F(x) at x=1
It also passes through the point (x, F(x))
I sub in x=1 into f'(x) now
Yes
I simplified the f'(x)
So im trying again
My final answer
According to the textbook this is the correct answer. I just want to make sure I did not skip any steps or break any rules
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idk how to do this question can someone pls help
what's giving you trouble with the question?
i dont understnad how to find the domain and range
first thing: do you know what a domain and range is
yes domain is like the x value and range is like the y value of the function isnt it
The domain of f^-1 is the range of f, and the other way around for the range of f^-1, because f and f^-1 are y=x symmetry
ok so i have to find the domain and range of f(x) to solver this?
ok thanks
and question b what does it mean find an expression for f-1(x)
is it just to find out what f-1(x) is?
yep
@grave turret Has your question been resolved?
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Which is the expanded form of (x + 1)3?
you mean (x+1)^3?
yes
expand to (x+1)(x+1)(x+1), then distribute
if you are learning binomial theorem, then use it
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How can I do part b for this question?
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How can this be simplified?
Try doing a substitution, let k=arcsin(x), then try using a double angle identity to solve
Hint: u want a double angle identity that’s entirely in terms of sin
(To get rid of the arcsin)
@plucky carbon Has your question been resolved?
Yea that looks good
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I Need help in maths
which question?
all of them
@flint plinth
i'll let @crimson sedge take over, obviously he's itching to solve these
NO
I smell a troller!
Please help
I don’t want mayo
Mayo is bad at maths
I Need Bingo
.clothesfirst
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hey
,rotate
Weird question but it basically wants to start with an answer and create a question
how do i do that
In other words create a question that when solved ends with x=2
Shouldn't be hard, just add/subtract and divide/multiply some stuff from both sides. For example
x = 2, (add 3 both sides), x + 3 = 5 (divide both sides by say 5) then (x + 3)/5 = 1
mk so
Then solve it by reversing the steps and you'll be able to get x=2
x = 2, x + 3 = 5, (x + 3)/5=1
You can make it more complex by adding some x-terms also but this should suffice
im sorry math isnt my strong suit ☠️
You should try to come up with your own similar answer to numbpy's answer.
Just solve it normally
2 + 5 / 4 - 9 x 6
Also, I'd suggest you make your own question to get a better idea of what's hapenning
what is this?
ill do it then show u
my equation
How is this an equation when there's no equal "="
okay, lemme guide you
write down x=2
add or subtract some number from both sides
Then divide or multiply some non-zero number from both sides
Ta-da you have an equation
I don't think that evaluates to 2
I tried it in the calculator and it gives 36.4
I mean 5 divides neither 3 nor 5 so it will give a decimal number
ah, you misplaced the brackets then
Did I?
It should be (- 9 x 4 + 7 - ( - 3 x 4))/5 - 9
Yes after you correct the placement of bracket
So copy and paste what u sent?
(- 9 x 4 + 7 - ( - 3 x 4))/5 - 9
Correct?
Bottom one
Shouldn't it be 9 not -9?
Just solve it normally
What I do first
Use the pemdas rule
Okok
but evaluate the brackets first
Good?
You were supposed to do the innermost bracket first
As in, (-3 x 4)
Just a small error, you perform all multiplications first
So, you should have "(36 + 7 + 12)/5 - 9"
In the second stage?
yeah or you can add more stages
I’ll slide it in the middle of the both
Like -> (36 + 7 - (-12))/5 - 9, then (36 + 7 + 12)/5 - 9
yep
Why did you reverse it again?
Wym
you wrote 12 in third step
Yeah
Then again wrote -(-12) in forth step
yep
yep
yes, five part first
After you're done evaluating the bracket, the bracket is automatically removed
So, in the previous step itself you'd have 55/9 instead of (55)/9
correct, maybe finally write x=2
I meant writing x=2 after 2=x but it's good anyway
show the questions
That's a rectangle right?
Ya
Thiis one first
Mk
What's the area of rectangle
120 cm2
no, no as in what's the formula for area of a rectangle?
L x W??
L, W?
what is L, what is W?
yeah so write is properly
area = length x width
Okay
now, what's the length and the width?
yes, solve it
You don't know how to solve linear equation?
hmm... you have to isolate the x
how do i do that
first thing you do is remove anything outside
So, there's a 6 as product
to remove it you do reverse of product, ie divide
So, divide both sides by 6
How do I do so
write this
yeah, now you have 6(4x + 8) = 120
6 is multiplied by (4x + 8)
Mhm
so, to remove it you divide by 6 on both sides
ohh
I hope you remember how to perform 120/6
= 20
what is that weird thing?
Just write it normally
6 x (4x + 8) = 120
4x + 8 = 120/6 = 20
I okay
Then subtract 8 from both sides, after this
you have 4x + 8 = 20 right
Yes.
I hope you performed the subtraction and didn't leave it as 20 - 8
ok, good
Division?
yes
no, you have to remove 4
So, you divide both sides by 4
on the lhs the 4/4 would cancel
4 / x
on the rhs you'd get ___
yep
3?
yess
This is also a linear equation that shouldn't be too hard to solve
write the question first
LMAO
then that
by mistake did you miss the - sign before 18?
then perform the bracket
remember that number next to bracket means that they are multiplied
take note of the - sign
just write 36
?
-(-36) is the same as (-1) x (-36) = 36
So what do I write
How did we get that tho
I thought it was gonna be negative
Cause neg and pos equal nrg
Neg
I'd be 3y + 36 - 18 = 0
yeah, I think you should be fine noe
It’s answered?
Just get the value of y
WHY DID YOU AGAIN WRITE -36
WYM?
Look at the 3rd line you've written
Yea??
numbpy
OH
You need to pay attention smh
subtract 6 from both sidesw
how'd you get -3y?
3-6
why did you do that?
I meant both sides of the equal sign
Do you know how to proceed from here?
There’s more?
Nah, how do still not understand
You can't just remove 3 directly on only one side
You HAVE TO DIVIDE both sides by 3
Wait a damn minute
how did you go from 3y + 18 = 0 to 3y +6 = 0
by what?
Then why didn't you also divide the 3 in 3y
oh.
The division happens everywhere
$3y + 18 = 0 \implies \frac{3y + 18}{3} = \frac03 = \frac{3y}{3} + \frac{18}{3} = 0$
numbpy
yep, correct
can I dm you if i ever hit a roadblock w my homework again?
how we go from positive to -
Yeah, we all are here to help but you'll really need to work more
we had y + 6 = 0
yea
-6
OHH
WTFG
WWTF
OHH
OK
I GET IT NOW
OKKK
TY
that was awfully horrid learnign experience for u
mb
Okay.
And see what exactly is happening
yeah
Like why does each step happen etc.
alright then
bye bye
Closed by @clear berry
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hey if there is no p outside an event is the question just asking for the sample space
@steel mural Has your question been resolved?
I think i would need more context on where it is being used, If this is for a venn diagram then its just the sample space yeah (all natural and integer values)
Closed by @steel mural
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I was given this example by my teacher but I think I copied sth wrong
,w 6x^2-13x+6