help-36

[tranquil pine]

how to i slove this one? i tired doing it in a logic way

"he got each 3 for 172" so I did 172 X 3

A year has 12 months so I know there's X 12 somewhere

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[clever elbow]

Is this correct way of solving number 8 part 2

[final tangle]

no

integral of a quotient isn't the quotient of the integrals of the numer and denom

[clever elbow]

How do I do it then

[final tangle]

consider splitting the fraction

[clever elbow]

It would be 1 bracket and a divide

?

Is the e correct doe

[final tangle]

It would be 1 bracket and a divide
vague and unclear

[final tangle]

no, that's exactly what I said you should NOT be doing

[deft ravine]

You can't move out factors that aren't constants (out of the integral)

[clever elbow]

Wdym

How do I split it then

[final tangle]

(a+b)/c = a/c + b/c

[clever elbow]

e^x /e^x

3/e^x

[final tangle]

and integrate those terms

[clever elbow]

How do i integrate a fraction

Split the fraction?

[final tangle]

well can you simplify e^x/e^x

if your fraction is simple enough then a combo of power/exponential rules and chain rule will work

[clever elbow]

Simplify it to 1?

[clever elbow]

That is = 1 right

[final tangle]

yes

[clever elbow]

Now I got 3/e^x

Is it gonna be 3x/e^x

OR

3x/ 1/2 e^x

[deft ravine]

Note that 3/(e^x) = 3e^(-x)

[final tangle]

neither

again your attempting to commit the same math crime again

[clever elbow]

I'm a math criminal

[clever elbow]

Wha

Lemme

Switch it rq

Then I can make it that the 3 goes outside then i would add a negative inside and outside

Therefore

-3e^-x?

[deft ravine]

Yes

[clever elbow]

And the derivative of 1 is x?

So jt will be x+3+c

[final tangle]

no

[clever elbow]

What did I do wrong then

×@£/

I meant

X-3e^-x +c

[final tangle]

integral of 1 is x + C, don't get those words mixed up

[clever elbow]

Wait wait wait

Do I add 2 +c?

[final tangle]

whut

where's 2 coming from

[clever elbow]

I means

Two + c

+c + c

[final tangle]

you only need one constant

[clever elbow]

Is this the correct formulq

[final tangle]

not a formula,

if that capital X was lower ase it'd be the correct result

[clever elbow]

Lemme right jt and send pic

THIS IS THE 3RD PEN TO FINISH ON THIS PAGE

[final tangle]

yes

[clever elbow]

Finally

I got another question that says e^x/2 + e^-x/2

[deft ravine]

Your e^x in the denominator looks like ex

[clever elbow]

In that case do I directly integrate

[final tangle]

yes

[clever elbow]

e^x integration is the same rigjt

[final tangle]

no

you're committing the same crime again

integral of a quotient isn't the quotient of the integrals of the numer and denom
no, that's exactly what I said you should NOT be doing

[final saddle]

@clever elbow Has your question been resolved?

[clever elbow]

What crime

What is quotient

U just told me to integrate directly

[final tangle]

a quotient is one thing divided by another

integrate directly (properly)

[clever elbow]

How do I integrate directly properly doe

Sorry but sometimes my brain is below 0

[final tangle]

note that e^x/2 is the constant 1/2 being multiplied to e^x

[clever elbow]

1/2e^x

????????

Waaa

[clever elbow]

.

1/2e^x -1/2e^x+c is the answer?

I'm having a problem that jm trying to solve many problems at once

[final tangle]

integral of e^-x isn't -e^x

[clever elbow]

What

I keep getting stunned

And realizing my math crimes

[clever elbow]

-e^-x

?

[vital crag]

yes

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[coral root]

How prove it?

[void valley]

have you tried induction

[coral root]

Mm i dont get nice thing

[tranquil pine]

yeah induction should work here

[void crest]

this is why we cant have nice things

[coral root]

I try but nothing

[void crest]

so

whatve u done so far

[coral root]

Mmm i try bernuli inequality

<@&286206848099549185>

[magic totem]

https://artofproblemsolving.com/community/c6h625369p3748317

[coral root]

Thanks

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[frosty mauve]

Find the sum of all positive integers n for which |2^n+ 5^n–65| is a perfect square.

[covert marsh]

can somebody help me out please?

I literally have no idea like does if it’s 25 cm, shouldn’t that just mean OA is 12.5?

[frosty mauve]

if AC is 12.5cm then the semi circle would exceed the triangle

[covert marsh]

But how tho?

It’s already given AC is 25 cm

[frosty mauve]

i mean AB and BC would be tangents

to the semicircle

[covert marsh]

ohh yeah

So how would we calculate the length OA?

[frosty mauve]

i didnt try that

lemme see

[covert marsh]

Alr thx!

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@covert marsh Has your question been resolved?

[frosty mauve]

try by joining o and b

i got the answer that way

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[keen depot]

yo

[keen depot]

if you have 324000

and 230

how can you say how many percent 230 is

of 324000?

[void valley]

230/324000 * 100%

[keen depot]

so (230/324000) *100%?

or 230/(324000*100%)

[void valley]

1st

[keen depot]

alright thanks 👍 b:

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[clever elbow]

Is it gonna be ln| sqrt x|

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[clever elbow]

Number 9 at top

Sorry for bad quality

I don't have the book and I took it from someone quickly

Integrate e^sqrt x/sqrt x

[manic herald]

make a u-substitution

[clever elbow]

I didn't take that

I don't know how to use it

[manic herald]

are you supposed to know?

[clever elbow]

I'm supposed to solve it without u substitution

[sweet summit]

are you 100% sure about that? U-sub is the first instinct to try

in fact yeah all of these problems in the top portion are solvable with u-sub

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[clever elbow]

Yes im

[clever elbow]

The teacher never told us about it so it means we shouldn't know it

[dry light]

#9 is clearly a u-sub

I don't see any other way

[sweet summit]

yeah same

I would double check with your teacher if you can. All of these problems scream u-sub

curious, did you solve any of the other problems in that section? If so how did you solve them?

[clever elbow]

Lemme show u a picture

Wait weong one

[final tangle]

regardless, chain rule is being applied
explicitly doing the u-sub just makes it clearer

[sweet summit]

yeah those are not correct

[clever elbow]

What

What

WHAT

[sweet summit]

are you trying to solve the integrals or just simplify their expressions?

[clever elbow]

Solve it

The teacher said that is how to solve it

[final tangle]

apart from the x for multiplication, those are fine

[sweet summit]

oh wait you're right

my bad

I misread them

[final tangle]

$\int f'(x)e^{f(x)} \dd{x}= e^{f(x)} + c$

[clever elbow]

The teacher said if the number beside e is the derivative of the e power then just remove it

Is there a way to make

[soft zealot]

ℝamonov

[clever elbow]

Is there a way to solve number 9 without u substitution

[final tangle]

consider the derivative of sqrt(x)

[clever elbow]

1/2sqrtx

Can I take the e^sqrtx outside the integration and multiply 2

Down

[final tangle]

don't take anything with x outside the integral

you could however express your integral as
$$2 \int \frac{e^{\sqrt{x}}}{2\sqrt{x}}\dd{x}$$

[soft zealot]

ℝamonov

[clever elbow]

Okil

Lemme do that

Now I need to have a 1

On top

[final tangle]

wdym

[clever elbow]

Instead of e^sqrt x

I need 1

Can I turn it into e^(x^1/2)

[final tangle]

wdym by
"need 1"

[clever elbow]

If

If the thing at the top is derivative of down

Then I can switch to len

[final tangle]

there's no need to overcomplicate

$\frac{e^{\sqrt{x}}}{2\sqrt{x}} = \frac{1}{2\sqrt{x}} \cdot e^{\sqrt{x}}$

[soft zealot]

ℝamonov

[clever elbow]

Huhhh

1/2 sqrt x is derivative of sqrt x

Is the answer gonna be

2 e^ sqrt x

[final tangle]

+c

[clever elbow]

YAY

Thanks alot

U r an integration pro

What does the dx at top mean

Number 10

[final tangle]

that's just another way of writing

[clever elbow]

So what does jt mean

Like

What is on top

[final tangle]

$$\int \frac{1}{\sqrt{x}e^{\sqrt{x}}} \dd{x}$$

[soft zealot]

ℝamonov

[clever elbow]

Ohhh

Doesn't that mean

Sqrt x e ^ - sqrt x

Is the answer - e^ - sqrt x +c

Am I correct doe

Or I can't flip it

Wait

I realized my math crime

How do I make the root x into 1 / 2 root x

.close

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[daring heart]

Factorise

[daring heart]

-3x^2 - 20x - 12

put it in quadratic formula

i get -1/6

and 3/2

which is wrong

why does this happen

i send my calc

Pls ping when replying

,rotate

[daring heart]

,rotate

Finr

[wraith crater]

,rccw

Uh

[wraith crater]

Bruh bot so slow

[wraith crater]

Occupied

@daring heart a=3 not 12

[daring heart]

my god

[daring heart]

U can have this channel

i'll get my dumbass out

.close

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[rapid elm]

How do I solve e^(2x)+x+1=2 ? I dont understand the exponential part. I simplify to e^(2x)+x=1 , but then I dont understand the algebra involved in solving for x.

[exotic hill]

Are you sure this is e^2x +x =1?

[lethal totem]

I don't think its possible

[faint locust]

https://math.stackexchange.com/questions/409185/prove-that-xe2x-1-have-only-one-solution?noredirect=1

[lethal totem]

At least not without busting out special functions or taylor series

Obviously it's easy to verify that x=1 works but formally solving for x doesn't seem doable

[rapid elm]

Ok perfect thanks.

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[haughty sonnet]

so ive gotten P(A) + P(B) - P(A union B)

and i think the answer to 1 is 47/80 but im not entirely sure or confident

P(A) is 18/40 or 36/80
P(B) is 10/40 or 20/80
P(notB) is 3/4
I THINK P(A n B) is 9/80

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[echo grove]

Help number 2

I set derivative equal to 0

And got 2 answers

4 and 12

Not sure where to go from there or what that means

[tranquil pine]

I'm not quite sure if I understand correctly, but you need to get a box by cutting pieces out of a cardboard

the cube has 6 faces but since the top of the box is open you need to cut 5 equal square pieces

[shy wren]

Find the derivative of the derivative

For a maxima that'll be negative

For a minima that'll be positive

[echo grove]

So I have to do the derivative test for extrema

[shy wren]

Ye

[echo grove]

Is there no other way to solve without doing that

[shy wren]

I don't think so

Another thing you can do is find the value of both the answers you got

The greater one will be the answer

But still differentiating would be a better method because if you're checking the value of both, you're assuming that at least one of them is a maxima

[final saddle]

@echo grove Has your question been resolved?

[echo grove]

Wdym by this

Are u saying there could be another maxima that isn't those 2 values

[shy wren]

Getting 0 as the derivative can mean 3 things

It can be a maxima minima or inflection point

If 1 of them was an inflection point and 1 was minima none of them would be a maxima but both would give you 0 after differentiating

[echo grove]

I just did the first derivative test for extrema

Also how can f'(x)=0 be an inflection point

Isn't that f''(x)

I think its just either maxima or minima

Is this correct?

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[tranquil pine]

...

need help

[tranquil pine]

how to solve this question

[scarlet sequoia]

Ever heard of euler's formula ?

[tranquil pine]

in integration?no.

it was in complex number

i have heard it there

can we solve it using the reduction method?

i am getting the value of A

but facing issues with B and C

[scarlet sequoia]

Still

It helps with euler's formula

Write (sinx)⁵ using euler's formula

Then expand

Wait it's even worse than what I thought as first

I thought the right hand side would be something with sin(5x) and stuff, not some cosine in factor

Don't worry, we can still try to find A,B and C

Derive the RHS, it should be equal to (sinx)⁵

Then apply euler's formula to everything that is in sine or cosine

Expand everything

Identify the terms in exp(aix), with "a" integer

Gives you a system of equations in A,B and C

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@tranquil pine Has your question been resolved?

[tranquil pine]

still can we do it using the reduction method of integration?

[tranquil pine]

how will we get that iota term here?

[tranquil pine]

.close

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[marsh turtle]

can anyone do a Time Complexity analysis in forming a Huffman Tree (not a Huffman code for each character)?? Make a pseudocode and do the analysis.

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@marsh turtle Has your question been resolved?

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@marsh turtle Has your question been resolved?

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[queen spindle]

Hi

[queen spindle]

I do not understand this

[tranquil flume]

Two of the angles in the triangle are s-3 and s

What is the third angle?

[queen spindle]

S

Right?

[tranquil flume]

No

[queen spindle]

Oh

180-(s+32)

???

[tranquil flume]

Yes

[queen spindle]

Ok

[tranquil flume]

All the angles in the triangle add up to?

[queen spindle]

180

[tranquil flume]

Yeah

So add all the angles and find s

[queen spindle]

?

Whats s

I s it

[tranquil flume]

(s-3) + s + [(180-(s+32)] = 180

Solve for s

[queen spindle]

?

Whats the answer

35?

.close

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[solemn sage]

what did you try?

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@spring rover Has your question been resolved?

[spring rover]

i got leave bruhh

.close

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[tranquil pine]

Hi guys, can anyone explain me why this relation Is true (solution given by the text)?
I tried to represent by below diagram but according to It, for me It Is false

[tranquil pine]

I mean, green space Is different from Blue space, but i don't understand where I make the mistake

[deft ravine]

Your diagramm is false

You need to mark x's area blue, too

[tranquil pine]

Thank you @deft ravine, but if I mark X's are as Blue, also Z and Y areas should be Blue? Because the Union takes all the element. So I obtain Orange area.
And the intersection between these two Orange areas Is the Blue area that I represented.

I don't understand what wrong whit my think

[deft ravine]

No, if we have an element in x it is in the left and the right bracket.

Therefore, it is in the intersecting set

If an element is just in y and not in any other set, it is just in one of the brackets. So it's not in the intersecting set

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[tranquil pine]

Everithing clear, thanks @deft ravine

. close

.close

[deft ravine]

You're welcome

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[strong swallow]

this is KS4 I think btw also I think it may be from a past GCSE paper

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[strong swallow]

NO

😭

I didn't mean to close it

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[rancid condor]

Please check if my answer is correct thanks 🙂

[boreal bluff]

you can think of it as having 6 letters when you group 2 i's and 2 s's

ii is one letter, ss is another

so you have 6!/2! where the denom. comes from the two p's

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[sleek slate]

can someone help?

[sleek slate]

,rccw

[sleek slate]

Can someone help with the first question?

<@&286206848099549185>

[rancid condor]

.reopen

but they are adjacent to each other so wouldn't it make them as one group 🤔

[sleek slate]

what

[rancid condor]

was replaying to my question

[sleek slate]

???

[heavy loom]

aren't all 3 transversals?

[sleek slate]

on which one

1 2 or 3

[heavy loom]

for 1

a b and c are all transversals

[sleek slate]

yeah ik

its so confusing

and same with 2

they are all transversals

[heavy loom]

I think so

i'm not entirely sure if concurrency is allowed though

[final saddle]

@sleek slate Has your question been resolved?

[sleek slate]

It says 'obvious transversals' so maybe it just means what is shown and not the lines extending indefinitely

[hollow pasture]

what is x square divided by 67 plus 63864874538 - 989787?

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[rain star]

Can someone explain to me how we get this second derivative? Is it the chain rule plus the product rule or is it just one of them. A step by step sequence of equations would really help. Thanks!

[thorn grotto]

just the chain rule, because sqrt(g / L) is a constant

[rain star]

right, and since its a constant, the first derrivation would be sqer(g/L) and in the second derrivative it would go away no?

[thorn grotto]

lets set sqrt(g / L) = a, because it's just a constant and its easier to write

we have theta(t) = cos(a * t)

then theta'(t) = -a * sin(a * t), by the chain rule

[rain star]

makes sense

[thorn grotto]

and theta''(t) = -a * a * cos(a * t)

[rain star]

right, thanks

.close

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[clear scarab]

does anyone know the trachtenberg method of math. I am quite confused on some parts of it

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[sonic olive]

hi

[sonic olive]

anyone here?

oh mb

[fossil geyser]

Yeah, just post your question

[sonic olive]

just wanna clarify something

f:x --> 3x-5
g:x ---> 1/2x (half x)

hence, write an expression for (gf)^1

should i do the composite of gf, then inverse it?

what should i do here

?

[spiral quail]

I believe composite then inverse it. I see it as the inverse is being applied to a composite

[sonic olive]

ok

wait

but whats with the brackets lol

usually with brackets and exponents, you do apply the exponent to everything in the bracket

so for example

(3-2)^2

= 1

because the exponents distributes

wait

idek what im saying anymore

im just gonna do the composite of gf then inverse it

so 1/2(3x-5) = 6x-10?

since u have to multiply the 2 on both sides?

anyone

please

i gotta go soon

https://tenor.com/view/arima-ichika-ichika-loading-waiting-thinking-gif-21829545

<@&286206848099549185>

you're the only hope

@vestal yacht can i dm you

yeah ima use another channel. its been 15 mins

[final saddle]

@sonic olive Has your question been resolved?

[shy wren]

What did you do here

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[vestal yacht]

don't ask just do it

[vestal yacht]

.close

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[sage fiber]

can someone check if my answers are right?

[serene cradle]

Looks right to me

[gaunt star]

can someone help

which inequality match the region?

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[zinc fractal]

How do I do #2?

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[tranquil pine]

Is this JL = ZX

[final saddle]

Please don't occupy multiple help channels.

[spiral quail]

Yes

Or angle Y equals angle K

[tranquil pine]

I would help

If I knew

nope

Sorry

[final saddle]

@tranquil pine Has your question been resolved?

[vestal yacht]

mean

and you just can't unless you spend 60 hours in your calculator trying to code thousands of words worth of code

which is not worth it

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[tranquil pine]

need help

Is it like R is congruent to Y

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[clever elbow]

Number 18

If I take out thr constants 5 and 7

Is it gonna be 5 +7 or 5*7

[fossil geyser]

Neither. x is not a common factor of the numerator and denominator, so you can't cancel it out.

Instead, divide the entire (5x+7) by x

[clever elbow]

Uh

The teacher said never divide by functions

If I take the constants out I can have x/x

Which is one

[fossil geyser]

No, you can definitely divide each term in the numerator by the denominator.

I think your teacher was referring to something else

$\frac{5x+7}{x} = 5 + \frac{7}{x}$

[soft zealot]

tatpoj

[fossil geyser]

You just have to be careful if there's more than one term in the denominator.

You have to divide each term in the numerator by the entire denominator

I think that's what your teacher was warning you about

[unborn roost]

this is not a true equation, right?

[fossil geyser]

um, yes? As long as x is not 0

And if x is 0, then the original expression was undefined anyway

[unborn roost]

had the x been in both 5 and 7, then yes, you can certainly factor it and remove the denominator

[fossil geyser]

What?

[clever elbow]

I'm back

I solved it in a very none correct way

[fossil geyser]

Yes, this is very much true

I don't know what you're talking about

[unborn roost]

(5x+7x)/x = x(5+7)/x

[clever elbow]

So I uh

[unborn roost]

but this only applies if 7 contained x

which it doesn't

[clever elbow]

Divided the equation over 7 and multiply 7 outside to get rid of the 7 in plus

[fossil geyser]

What

Dude

[clever elbow]

Then I took the 5 outside

And had x/x

Ended up with 35x

I think that is wrong

[fossil geyser]

yes

Please look at what I did up here

[fossil geyser]

.

[clever elbow]

How did the x go out

[fossil geyser]

let me show you in one more step

$\frac{5x+7}{x} = \frac{5x}{x} +\frac{7}{x} = 5 + \frac{7}{x}$

[soft zealot]

tatpoj

[fossil geyser]

I just distributed the division by x

[clever elbow]

OHHHH

I forgot about splitting fractions

[fossil geyser]

Just like combining fractions with common denominator, only backwards

Or, in other words

you can distribute division just like multiplication

I just divided both terms by x

It cancels with the 5x

But not the 7

[clever elbow]

Do they take 2 integration brackets

Or 1

[fossil geyser]

Now just integrate the function as

$\int\left(5 + \frac{7}{x} + e^x\right)\dx$

[soft zealot]

tatpoj
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[clever elbow]

Is this correct

[fossil geyser]

Yes 👍

[clever elbow]

Can you help me with number 9

There is 4 questions I don't understand with is 9 10 11 12

[fossil geyser]

Hint: $\ln(x^n) = n\ln(x)$

[soft zealot]

tatpoj

[clever elbow]

I said that but none responded

I can make it lnx^4

Then divide them

And have 1/lnx^2

Right

[fossil geyser]

no

I mean

$\ln(x^2)$ becomes $2\ln(x)$

[soft zealot]

tatpoj

[fossil geyser]

and same with the ln(x^3) in the denominator

[clever elbow]

Hmmm

Is jt

3xlnx

Or x 3 lnx

[fossil geyser]

Just 3*lnx

[fossil geyser]

See this

[clever elbow]

But there is a lnx

Xlnx

X ln x^3

[fossil geyser]

Oh

I'm sorry, yes

The denominator can be expressed as 3x*ln(x)

[clever elbow]

The answer is 2/3 ln x

[fossil geyser]

Yes

[clever elbow]

Perfect

[fossil geyser]

$\frac{2}{3}\ln|x|+C$

[clever elbow]

Thanks alot

[soft zealot]

tatpoj

[clever elbow]

Now my question is

Number 10

I got many questions tbh

Can i do anything to the sqrt

[fossil geyser]

Sqrt(x) is the same as x^(1/2)

So you can use the same property we used before

[clever elbow]

So can I like

Take jt as a hald

Half

Outside

[fossil geyser]

Yes

[clever elbow]

2 ln x + c

Is that correct

[fossil geyser]

Yeah exactly

[clever elbow]

Thanks

In number 11 is there a way around with the e and x

[fossil geyser]

2 ln|x|+c

[fossil geyser]

You should put abs values around the x in the ln

[fossil geyser]

Like this

[clever elbow]

I put it in paper

Idk where is absolute on keyboard

[fossil geyser]

Oh ok

[clever elbow]

2e/x

X/e

Is there some way around this

[fossil geyser]

e is just a constant. Treat it the same way you'd treat any other constant, like 2 or 6 or something

[clever elbow]

I can get the e out?

[fossil geyser]

Not really in this case. The first term is 2e(1/x). The second term is (1/e)x

[clever elbow]

I got now

2e lnx + 1/2e x^2 + c

How do I add the 2e to the lnx?

[fossil geyser]

You dont

[fossil geyser]

This is good

Just leave it like this

[clever elbow]

Oh ok

Last one I'm struggling with so far is 12

Xlnx

Xln3

[fossil geyser]

Again just treat both terms seperately

[clever elbow]

I mean

How do I integrate ln3

Or x

Can I take the ln out

Or do I leave it

[fossil geyser]

ln(3) is just a constant

So is e^3

[clever elbow]

Is it gonna be

e^3 ln x +1/2 x ln 3 + c

[fossil geyser]

Yep, you got it

[clever elbow]

Thanks qlot

Alot

Those questions made me have a headache yesterday

[fossil geyser]

No problem 👍

[fossil geyser]

Wait

That second x should be x^2

(1/2)x^2 ln(3)

[clever elbow]

Ohhhh

I forgot it

Thanks

Is number 21

Can I directly remove the x^2-4

[fossil geyser]

Hm

No

[clever elbow]

Split it?

[fossil geyser]

Try factoring the numerator and denominator

[clever elbow]

2 questions

Like 2 brackets

X+2 and x-2

?

[fossil geyser]

In the numerator, yes

What about the denominator?

[clever elbow]

(X^2+2) (x-2)

[fossil geyser]

Hm

I think thr denominator can just be x(x-2)

[clever elbow]

I'm not really that good with factorizing

Oh

Take common factor

[fossil geyser]

Yes

[clever elbow]

But

In that case

We r left with 3 brackets and I can't get rid of any

Do I like return it to its original state without factorizing

So I can have x2-4 over x(x-4l

Then remove x-4 with x^2-4

[fossil geyser]

Its $\frac{(x-2)(x+2)}{x(x-2)}$

[soft zealot]

tatpoj

[clever elbow]

And end up with x/x

[fossil geyser]

Then the x-2 cancels

[clever elbow]

OH

I wrote it wrong in the paper

Can I take the 2 outside

X+2/x

[fossil geyser]

It'll be $\frac{x+2}{x}$

[soft zealot]

tatpoj

[clever elbow]

I do have that

But

Is it possible to take the 2 outside

[fossil geyser]

Distribute the division and you get 1+(2/x)

[clever elbow]

Wot

I have an idea

Can i divide by 2 to have x+2/x+2

Then end up with 1

And add an 2 outside

To not mess up

Is the answer 2x+c

[fossil geyser]

Dividing by 2 would have the effect of multiplying the denominator by 2, not adding 2 to it

Instead

$\frac{x+2}{x} = \frac{x}{x} + \frac{2}{x} = 1+\frac{2}{x}$

[soft zealot]

tatpoj

[fossil geyser]

Distribute the division

[clever elbow]

I qlmost

Always

X+2ln x + c

Is this correct

[fossil geyser]

Yes

👍

[clever elbow]

Uhhh

I saw number 22

And it

Seems abit confusing

Can I disturb the power on both

[fossil geyser]

So just try like we did before

Distribute the division

[clever elbow]

Before splitting

Like

Can I split the power

Both will have power 2 right

[fossil geyser]

No

[clever elbow]

Then

Uh

[fossil geyser]

Oh wait I was looking at 20, one sec

[clever elbow]

Oh

Take your time

[fossil geyser]

Try expanding (foiling) it first

[clever elbow]

Expanding jt

Isn't it expanded

2 brackets?

[fossil geyser]

Yeah

Like that bracket, times itself

That's what the second power means

[clever elbow]

Basically

3-x

Or x-3

I pretended it is cross multiplication

Im confused

I tried solving it as numbers but it got confusing

[final saddle]

@clever elbow Has your question been resolved?

[ashen shadow]

@clever elbow what's
${(\sqrt{x}-\frac{3}\sqrt{x})^2}$

[soft zealot]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[final saddle]

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[chilly kindle]

I try integration by subtition but i cant seem to get rid of t

[strange rune]

separate it into two integrals first

or do it in your head

then you can apply u sub to the exp one

and integrate the t^k like you would normally

[chilly kindle]

how

[final saddle]

@chilly kindle Has your question been resolved?

[chilly kindle]

What I have so far

I'm not sure if it's right

[final saddle]

@chilly kindle Has your question been resolved?

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[severe marsh]

idk how to do this

its an olympic exercise so

[vapid hare]

Can you translate the problem into english?

[severe marsh]

yes

determine the number n so the square root of that belongs to natural numbers

natural numbers are the postive numbers including zero

so [0, ∞)

[vapid hare]

What I would do here is first answer the question: what needs to be under the root for it to be a natural number?

(Not even looking at the expression)

[severe marsh]

i wrote this but this is real for all real numbers

wait

[vapid hare]

Think about it like this

What is the difference between 4 and 5 when you take the square root?

[severe marsh]

uhhh

i should google the exercise

[summer isle]

the prime factorization! 😄

[severe marsh]

ohh yes great idea

[vapid hare]

I can say what I think if you want but dont want to give you the answer

If you want to find it yourself

[severe marsh]

wait i will search it

[summer isle]

roughly speaking, people in this channel know everything google knows, but will help you understand and answer your questions too

[vapid hare]

Its a bit unclear what you mean, but what I will say is that the thing under the root has to be a perfect square

$4=2^{2}$ for example, so we can take the root of 4

[soft zealot]

Tech support

[vapid hare]

Trying to be as clear as possible here

[vapid hare]

Ping me if you still wish for help when you see this

[severe marsh]

@vapid hare

i didnt find anything

[vapid hare]

Okay lets return

[summer isle]

if you want my help explaining, ping me. but i'm sure you got it.

[vapid hare]

Read what I wrote earlier

[severe marsh]

yes i understand but there are infinite possibilities

[vapid hare]

Infinite possibilities in solutions or perfect squares?

[severe marsh]

perfect squares

[vapid hare]

Its quite easy to narrow down

[severe marsh]

im guessing i have to factor the quadratic right

[vapid hare]

With high numbers of n, the rate of change gets so high you are missing esentialy every square, that would be quite improbable for this kind of test

[severe marsh]

but 2 perfect squares multiplied result another perfect square

[vapid hare]

Think of what perfect squares exist

1,4,9,16,25...

Then try to relate them to the functions outputs for different real values of N

[severe marsh]

hmm

let me write something and ill brb in 2 seconds

[vapid hare]

Ow

[severe marsh]

what

i don’t understand

this equation cant be factorised?

[vapid hare]

You can factor the polynomial under the root, but it is not necessary (atleast not for my 2 min solution)

Its more about narrowing it down to a small set of numbers and testing those numbers

[severe marsh]

so youre saying i should equal the equation to the perfect squares

[vapid hare]

Yes, but instead of trying everything you can reason a bit

You may not find my solution the best or fastest, but it worked for me with minimal effort and did not involve any fully random guessing

[severe marsh]

i still dont understand your solution

[vapid hare]

I have not finished it

This is what I did
Rule out 1,4,9,16,25 as the functions minimum is 28 for x<0

We can then look at the squares 36,49,64,81,100

Instead of looking at $x^{2}+6x+28=81$ for example, we move 28 to one side and get $x^{2}+6x=53$

[soft zealot]

Tech support

[severe marsh]

alright so x^2 + 6x + 28 > 28

[vapid hare]

Then we get the values 8, 21, 36, 53, 72

[vapid hare]

Yes, it has a positive derivative x>0

[severe marsh]

and from this list only 36 is a perfect square

so x could be 6

[vapid hare]

This is a list where we moved over 28

[severe marsh]

yes

[vapid hare]

So we need to compare it to x^2+6x for different x

We get the values 7,16,27,40,65,72

72 matches (for n=6) matches, so n=6

[severe marsh]

interesting, so 6 is the only answer?

[vapid hare]

It is 1 answer, and it can be deemed improbable another one exists, but I have not confirmed it

[severe marsh]

well 1 answer is enough for me

thanks for the help!

.close

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[odd parrot]

David made a square with play-doh but his little brother Daniel came over while David wasn't looking and cut out a square. With what's been left behind, David decides to make another rectangle. Determine the dimensions of his new rectangle.

[odd parrot]

Is the correct answer (2x+10)(4x+6)?

Simply because you find the unshaded area and factor that out

Which I can use difference of two squares here

because (3x+8)^2 - (x-2)^

gives ((3x+8)-(x-2))((3x+8)+(x-2))

which simplifies to 2x+10 times 4x+6

I'

I'm not sure if this approach is correct however

It's just asking the two side lengths

so it would be 2x+10 and 4x+6, right?

[final saddle]

@odd parrot Has your question been resolved?

[odd parrot]

<@&286206848099549185>

[odd parrot]

bruh

[torpid tartan]

The approach and the result are correct

[odd parrot]

thx

is there anything wrong tho

[torpid tartan]

nope, seems prefect to me

[odd parrot]

thank you

.close

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[topaz yacht]

Where did I go wrong? (question 2)

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[topaz yacht]

YES

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[topaz yacht]

I always end up finding the answer before I get help :[

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[sonic cairn]

how do I simplify 1.06(tan(71.5))=tan(71.5+deltax)

[vital crag]

can you show the whole problem

[sonic cairn]

A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 71.5 degree. How accurately must the angle be measured if the percent error in estimating the height of the tree must be less than 6%? Round the answer to the nearest hundredth of a degree.

wait if I do (tan^-1)(tan(x)) is it just x

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[summer isle]

How tall is the tree if all info is assumed to be correct? What angle do you get if you change that tree height by 6%?

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[unkempt swift]

hi can someone explain to me why QQ^-1 = I ?

[trail mango]

how does that question relate to the image? 😕

[unkempt swift]

umm

omg

sorry

i meant

Q^TQ = I

brain lag

[trail mango]

https://web1.eng.famu.fsu.edu/~dommelen/courses/aim/aim03/topics/linalg/matrices/inv/node2.html how's this?

[unkempt swift]

can i ask why

so like q3 . q1 is 0?

oh wait

OH

BECAUSE THEY ARE ORTHOGONAL

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

@trail mango thanks maam

[trail mango]

lolll

yep ^-^

[unkempt swift]

.close

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[shell dune]

Im on the verge of giving up lol

[shell dune]

Can you please help me with the following homework question?

Posting question and work below......

Solve the following differential equation by using integrating factors. y ' = 2 y + x^2

dy(x)/dx - 2y(x) = x^2

e^-2x dy(x)/dx -(2e^-2x)y(x) = e^-2x x^2

e^-2x dy(x)/dx = d/dx (e^-2x) y(x0 = e^-2x x^2

e^-2x dy(x)/dx + d/dx (e^-2x) y(x) = e^-2x x^2

integral e^-2x x^2 dx

-1/4e^-2x(2x^2+2x+1)+C

1/4 (-2x^2-2x+4Ce^2x - 1)

Final answer - > [(-x^2-x)/2] + [Ce^(2x)] - [(1/4)]

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[safe elm]

Hello, desperate for help with this question (Parts 3 and 4). I've used a parameterised the equation of a superellipse into something similar to polar form to draw the superellipse in part 2.
x = R cos(t), y = R sin(t), where R is a function of t as well.
For a given axes, what I've done is calculated the angle of rotation with respect to the Cartesian x-axes and used a rotation matrix on the superellipse to get a rotated superellipse. Is this the same as what the question is requiring me to do or is scaling along those axes different from simply doing such a rotation