help-0

[solemn geyser]

Each term can be written as X^i * X^j and I+j=k the power of the term

[plush pebble]

How many ways can you form X^k?

[solemn geyser]

K way I think

[prime badge]

almost

there's more than 1 way to form 1 for example

i mean X^1

so X

not like tim said

[solemn geyser]

?? I don’t understand

[prime badge]

(1+X)(1+X) = X² + 2X + 1

one X comes from 1×X, and another X comes from X×1

[solemn geyser]

Yes

There are two ways to have x in here

[prime badge]

well that's it

you get 3 from 0+3, 2+1, 1+2, 0+3

k+1 ways

[solemn geyser]

Yes

[prime badge]

oh okay that doesn't actually work all the way oops

[solemn geyser]

You’re right, but that only covers the first half for example
(1+x+x^2)^2

That would stop at 3x^2

And then it would be descending the same way it arrived there

The coefficient of 1 and X ^4 would be the same

Kind of like triangle going up until the middle power

But idk how to write this mathematically

[errant herald]

<@&286206848099549185>

[solemn geyser]

How many terms do u have

And does k vary

[errant herald]

Both k and n can vary

The amount of terms is dependent on k though I think

[solemn geyser]

I think that it will be a double sum

[errant herald]

N is number of elements in a list and k is number of lists and each list is if length n/k

[errant herald]

What’s a double sum? Two separate summations?

[solemn geyser]

It’s like the sigma of another sigma with each having different variables sometimes depending on each other

[prime badge]

@solemn geyser

[errant herald]

Sorry I rarely use anything involving sigma notation, what would that look like?

[prime badge]

so you could write it like n+1−|k−n|, i don't know if that's appropriate

[solemn geyser]

Thank you ,I’ll try and see what i’ll get

This is an example of what a double sum is though it’s not the one appropriate to your problem

[solemn geyser]

@prime badge

Is this correct

[errant herald]

Got it… hmmm I was told I would see some pattern when combining one element at a time I.e. n/k + n/k = 2(n/k) then adding another list if there is one would be 2(n/k) + (n/k) = 3(n/k) and continue for size of k

[solemn geyser]

Alright that means that u should multiply by the number of terms and also that n and k are not the variables of ur sum

[errant herald]

K(n/k) ?

[solemn geyser]

Yes

[errant herald]

That’s literally it? 😂

[solemn geyser]

Yes

Though what is the placement of your first term

[errant herald]

I’m not sure?

[solemn geyser]

If it’s 0 then it would be k+1 if it’s 1 you would have to multiply by k

[errant herald]

How do I know?

[alpine sable]

What’s the Pythagorean theorem?

[solemn geyser]

A^2+B^2=C^2 for reactangular triangles

[solemn geyser]

Also it’s the latter

[alpine sable]

Help @naive valley

[solemn geyser]

I was wrong with the first supposition

[errant herald]

So n/k + n/k + n/k …. Looks like sigma with k on top I = 1 below and k(n/k)?

Or maybe n =1 instead of I

[solemn geyser]

No l is the right one

And yes it’s what u’ve done

[errant herald]

How does I play a role as it increments?

[solemn geyser]

@prime badge i searched some more and found the answer

[solemn geyser]

It doesn’t since k and n are not variables and so we are able to just multiply by k

If it were to have a role k or n or even both may not be constants and so the sum would become much more difficult

[errant herald]

That makes sense, does it ever increment then?

[solemn geyser]

If k or n is dependent of l

[errant herald]

Ok I don’t believe it is , think k decides everything

[solemn geyser]

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[coarse charm]

Help

[coarse charm]

I need to solve

[tawny crown]

What have you tried?

[coarse charm]

Multiplying by n times n-5

But it leaves a 4 on the denominator right?

[tawny crown]

Yes and you can multiply the equation by 4 as well

[coarse charm]

Oh I made a mistake with my algebra. I see that now.

It would be n-5 times n^2-6n/4

=1

Do the subtraction to get -n^2*10n-20 equals 1

And then you can cross multiply to solve for x

Do you mind if I ask another question?

[tawny crown]

Go ahead

[coarse charm]

Thanks

For this it’s just simplify

I had tried u-6 times 5 but I always get confused on denominator

[tawny crown]

For the denominator you would want to multiply (u+1)(u-6)

[coarse charm]

Does that account for the 5 because of 30 as a common multiple?

[tawny crown]

I don't understand your question?

[coarse charm]

What happens to the five when you multiply it by that that

[tawny crown]

The numerator of the bigger fraction would become [10+(u-6)]/ 5(u-6). So you could say the 5 gets multiplied by (u-6)

[ocean seal]

Radiation 𝕏

[coarse charm]

I multiplied everything except the right upper term

[mellow grail]

It's (u-6)^2 - (2n - 2)

In the numerator

Then that reverses..oh it's right sry

[mellow grail]

Have u tried compacting this by letting u-6 = some variable

[coarse charm]

I could but it’s just the one messy term. I wonder if I put (u-1)(u-6) over 5 and then multiply out

[mellow grail]

Hmm..well it's ur wish

[coarse charm]

I’ll try your way. I have to go now. Thanks for all the help

Might be a useful strategy for fortune use to

[mellow grail]

Np

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[alpine sable]

I don't even know how to model the first equation
this situation is so confusing
I can see similar triangles, so it's obvious that some ratios will be used

[alpine sable]

Can you guys help me?

[alpine sable]

#❓how-to-get-help

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[peak pecan]

How do I solve y = 2x = 4z and x = y 😒

[peak pecan]

.close

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[clear cobalt]

Two forces, 15 N and 17 N act at an angle of 100° to each other. Find the magnitude and
direction (from the larger force) that will keep the system in equilibrium.

[clear cobalt]

i have no clue how to solve this

i cant figure it out

[alpine sable]

Well, a good tip is to draw the situation.

Start by doing that.

You'll need an Oxy plane, and the 2 forces the problem is giving you.

[clear cobalt]

i was on a trip the whole class so im trying to learn it and its such a pain so thank u

im gonna draw it rq

[alpine sable]

Sure.

I'll be waiting.

[clear cobalt]

ok i cant figure out how lmao

[alpine sable]

Well.

[clear cobalt]

i had to google an oxyplane

lmao

[alpine sable]

It's a plane.

With and x axis.

And a y one.

I'm sure you've used that at least once in your life.

[clear cobalt]

yeah

this is

what i have

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[little anchor]

I completetly forgot bearing

ik all of trig but bearing smhow

[west girder]

this should be sufficient

[little anchor]

?

wha

[west girder]

basically the angle from North

its always 3 digits

[little anchor]

Ye ik that

it has to be 3 digits

LIKE HOW DO I DO MY QUESTION

mb caps

[west girder]

so in the question it says

Bearing of P from B is 102

so B to P is 102

but the question asks P to B

[little anchor]

ye'=

whats the catch

[west girder]

nothing really
you just need to make some lines and find angle

[little anchor]

can u show

how to

[west girder]

this is step one(example)

and since you now have 2 parallel lines

you can find the other bearing

[little anchor]

hm?

still dont get it

do i have to plot the acc graph

and stuff

[west girder]

wdym by acc graph

[little anchor]

draw the actual bearing and stuff

i can do it mentally?

[west girder]

yes

it doesnt look like you have to draw those things

but its best if you draw

@little anchor

[little anchor]

wow

[little anchor]

it seems simpler to draw it

[west girder]

it is

[little anchor]

lemme try

give a sec

mine barely curbes

uhh what should my ans be?

[west girder]

i expect it to be ||282||

[little anchor]

mhm

i measure the angle here

right

[west girder]

ye

[little anchor]

299

298

approx

cuz of pencil thickness

[west girder]

why measure

there's always going to be human error

[little anchor]

then what do i do to calc

im stupid again

istg

oh wait

180-102

[west girder]

remember these?

[little anchor]

ye

ye

180-102

[west girder]

thats progress

[little anchor]

78

360-78

=

282

typos

[west girder]

cool

[little anchor]

so i got it right

and we used this for all the other

questions

that are related to bearing

[west girder]

remember to understand the wording of the question

[little anchor]

mhm ye

theyre usually gon ask for the opposite angle

[west girder]

the one you sent
the language is quite tricky

id expect the other questions to be like that

[little anchor]

ye its the only one in my hw

the rest was easy

cuz it was trig , area and stuff

thanks a lot

u can close

[west girder]

you close it

[west girder]

no worries

.close

[little anchor]

.close

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[west girder]

type this

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[stable warren]

Is my answer also correct?

My Teacher's Answer

I just direct applied the cube formula

:/

[whole shell]

@stable warren you can literally just pick 2 numbers for x and y

and plug them both

in to the two formulas

and see if you get the same answer

[stable warren]

ok

But

I actually mean

Is it satisfying the Question?

The question was to

Simplify

Soooo

[whole shell]

id say the teachers one is better

[stable warren]

Ok

:)

THanks

Also

wait

So if i have x^12 i do square formula first then the cubes?

Ok

Understandable, As it simplifies more

Thanks

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[earnest laurel]

ok so the question is: A​ mail-order gardening equipment business shipped 123 packages one day. Customers are charged ​$4.50 for each standard delivery package and ​$10.00 for each​ express-delivery package. Total shipping charges for the day were ​$801. How many of each kind of package were​ shipped?

[ocean seal]

Spanconstant5
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[earnest laurel]

i guessed 4.5y+10x=801

ok so the question is: A​ mail-order gardening equipment business shipped 123 packages one day. Customers are charged ​$4.50 for each standard delivery package and ​$10.00 for each​ express-delivery package. Total shipping charges for the day were ​$801. How many of each kind of package were​ shipped? compiler error?

[ocean seal]

Spanconstant5
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[gray isle]

set up another equation that represents

business shipped 123 packages one day.

[earnest laurel]

123=4.5y+10x?

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[earnest laurel]

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[final badge]

Whats the steps to solve for the roots?

[ruby current]

factoring

or quadratic formula

[final badge]

Show me how?

[inner path]

identity remarquable

[ruby current]

https://youtu.be/qeByhTF8WEw

[inner path]

$-(x-3)^{2}$

[ocean seal]

phoestaclies

[final badge]

Stil confused

[inner path]

it's a remarquable identity

but with minus

[final badge]

Dunno what dat means

[inner path]

ah sorry maybe it's not that in english, sorry for my traduction

remarkable identity like $(a+b)^{2} = a^{2}+b^{2}+2ab$

[ocean seal]

phoestaclies

[whole shell]

who writes it as a^2 + b^2 + 2ab, and not a^2 + 2ab + b^2

[inner path]

here you can see you have perfect square but it's with minus and a + in 6x so it will gives $-(a-b)^{2} = -a^{2}-b^{2}+2ab$

euh sorry for the sign

[ocean seal]

phoestaclies

[inner path]

is it remarkable identity in english ?

[final badge]

Huh.

Wait is finding the roots basically the same like finding the zeros?

But its just under a different name?

[whole shell]

@final badge yh

same thing

[final badge]

Ah i see. Thz! :D

[whole shell]

wait, you said it so yourself?

[final badge]

Ye

[inner path]

[final badge]

Basically roots is just another name for finding zeros

.close

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[final badge]

How to find the x-intercepts of 2x^2-8x

[jade hollow]

the roots will be the x intercept

[final badge]

Yes but how do i find the x-intercepts?

When i can factor the problem into something like this; (x-2)(x+4)

I can find the x-intercepts easy

x-2=0
+2 +2
x=2

[polar mist]

You've already written it like that though? (2x)(x-4)

[final badge]

?

[polar mist]

2x^2-8x = (2x)(x-4)

(x-4)=0 ?
2x=0 ?

[final badge]

Oh

I think the 2x threw me off since it was out side of the ()

So i just treat the 2x kinda like the 4?

[polar mist]

You can almost think of it like (2x-0) if that helps you see how it works the exact same

Or 2(x-0)(x-4) as the full thing

[final badge]

Ah kay

[final badge]

So like this?

[polar mist]

Yeah pretty much. Normally I would just write 2x=0 => x=0. But what you've written is same thing just in a few more steps ^^

[final badge]

Ty!

.close

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[livid flame]

Can someone tell me how to do 3 and 6

[dry swift]

3. Polar coordinates are a coordinate system that uses an angle and a distance from a fixed point (the origin) to describe the position of a point in a plane. In this system, the distance from the origin is denoted by r, and the angle between the positive x-axis and the line connecting the point and the origin is denoted by theta (θ)

To convince ourselves that the polar equation for a circle of radius 1 is r = 1, we can start by considering the definition of a circle in Cartesian coordinates. In the Cartesian coordinate system, a circle with center (a,b) and radius r is defined by the equation

(x - a)^2 + (y - b)^2 = r^2

now if you express x and y in terms of r and theta using the conversion formulas

x = r cos(theta)
y = r sin(theta)

you can substitute these expressions into the equation for a circle and simplify

(x - a)^2 + (y - b)^2 = r^2
(r cos(theta) - a)^2 + (r sin(theta) - b)^2 = r^2
r^2 cos^2(theta) - 2ar cos(theta) + a^2 + r^2 sin^2(theta) - 2br sin(theta) + b^2 = r^2
r^2 (cos^2(theta) + sin^2(theta)) - 2ar cos(theta) - 2br sin(theta) + a^2 + b^2 = r^2
r^2 - 2ar cos(theta) - 2br sin(theta) + a^2 + b^2 = r^2
-2ar cos(theta) - 2br sin(theta) + a^2 + b^2 = 0
2ar cos(theta) + 2br sin(theta) = a^2 + b^2

this is the equation of a line in polar coordinates, with slope -a/b and intercept (a^2 + b^2)/2b. it describes all the points that lie on a circle with center (a,b) and radius √(a^2 + b^2)

now, if you consider a circle with center at the origin (a = b = 0) and radius 1, the equation simplifies to

2r cos(theta) = 0

this equation holds for all values of theta when r = 0, which is the origin, and when cos(theta) = 0, which means that theta is either π/2 or 3π/2 (i.e., the y-axis and the negative y-axis, respectively)

so the equation describes a circle with radius 1 centered at the origin, since for all other values of r and theta, the equation does not hold

finally you have shown that the polar equation for a circle of radius 1 is r = 1

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[lunar palm]

do the areas underneath this graph between the green and purple lines sum to 1?

[lunar palm]

peaks are all at y=0.25

[velvet cliff]

what's the function

[alpine sable]

no

[velvet cliff]

also yes they don't, because 3x 0.3 = 1 but this is clearly less than that

[velvet cliff]

sheesh

[lunar palm]

i'm trying to adjust the constant (1/48) such that 'area underneath between -1 and 2' sums to 1

[velvet cliff]

interesting

what's it for?

[lunar palm]

wave function normalisation

the middle part is a wave function

normally i'd do this by just like

computing the integral

but that is very hard

[velvet cliff]

wolfram ? :D

[lunar palm]

so i'm wondering if there's some kind of graphical pattern i'm supposed to notice, here

[lunar palm]

hmm i did use symbolab.. maybe wolfram will be better

[velvet cliff]

wolfram 🐐

[lunar palm]

💀

[velvet cliff]

lol

yeah chief idk

[lunar palm]

okay it worked but

hmm

this is a little concerning

ah

i'm stupid

we did it

thank you wolfram alpha

truly goated

.close

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[potent meadow]

Hey, how can I do this question?

Ik
t = d/s
So
t = 256/192
= 1.33333333

[potent meadow]

But now what?

[alpine sable]

90 minutes before 19:15

[jagged cobalt]

(80)

[alpine sable]

oh

yeah ^

[potent meadow]

Oh thanks!

So

17:45

Lemme recheck that lol

17:45
17:35

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[wheat isle]

For part E do I just replace x with the surd?

[vale wigeon]

yes, just as you would do if it was any other number in place of the 'surd'.

[wheat isle]

3(sqrt(1 + sqrt(2))^2 - 3(sqrt(1 + sqrt(2)) - 2?

[vale wigeon]

doublecheck that

you missed something

[wheat isle]

Oops

[vale wigeon]

better.

[wheat isle]

So from here I simplify the surd?

[open hound]

i mean you can

but the question doesnt ask for it?

[vale wigeon]

well you could do some cleanup yes

it's... good form to do that generally

[open hound]

^^^

[vale wigeon]

idt you can do much to the $\sqrt{1+\sqrt{2}}$ that appears on its own but you could at least clean up the remaining $3(1+\sqrt{2})-2$

[ocean seal]

Ann

[wheat isle]

I see

[wheat isle]

Wait wouldn’t there be a radical where the 1 is

because everything is still inside the sqrt

[vale wigeon]

you have $3 \paren{\sqrt{1+\sqrt{2}}}^2$ as your first term

[ocean seal]

Ann

[vale wigeon]

idk about you but i allow myself to rewrite $(\sqrt{a})^2$ as $a$

[ocean seal]

Ann

[wheat isle]

Is that part of the surd laws

Oh wait I think I remember

[vale wigeon]

it's

[wheat isle]

sqrt(x) • sqrt(x) = x

[vale wigeon]

the definition of square root

if you need that phrased as a "surd law" and cant understand it otherwise, somethings gone wrong somewhere down the line

[wheat isle]

Alright

Anyway

[vale wigeon]

yes

[wheat isle]

So after cleaning that up what should be the next step

[vale wigeon]

submit the answer, presumably.

[errant herald]

does this work as a proof by induction?

[lone heart]

@wheat isle Has your question been resolved?

[wheat isle]

You know you can get your own channel right

[errant herald]

Oh I thought the help-0 is like a community channel that redirects everything

[errant herald]

<@&286206848099549185>

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[vale mulch]

how do i prove this

[alpine sable]

Try to prove ABC is congruent to DCB

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[errant herald]

Please help me know if this is correct

[errant herald]

I

[lone heart]

@errant herald Has your question been resolved?

[errant herald]

<@&286206848099549185>

[tacit arch]

does your equation for T(n) satisfy T(n) = 2 * T(n/2) + n?

[errant herald]

like if i plug in 1?

[errant herald]

im unsure what you mean here

[tacit arch]

you have a formula for T

If T(n-1) = (n-1) * log(n-1) + (n-1), then T(n) = ?

[errant herald]

nlogn + n

[tacit arch]

right. now verify if that satisfies this recursive relation

simplify T(n/2) first

[errant herald]

hmmm got that oh oops subtract the n not add from rule of logs

so yeah it equals nlogn + n

[tacit arch]

looks good. as long as it's clear to your class that log means log base 2

[errant herald]

yeah log is base 2 for all our uses

[errant herald]

so is this the answer or the original post?

[tacit arch]

yea you verified it

[errant herald]

so not this

[tacit arch]

both are important

[errant herald]

oh ok

thank you for your help!

[tacit arch]

i think there's one more thing as well

[tacit arch]

You didn't really do the induction here

You just went in a circle

or did the same work i said to do for T(n)

[errant herald]

Oh for some reason I thought I needed that , I kept hearing mention of prove for numbers less than n

[tacit arch]

Going from your 2nd equal sign to the 3rd equal sign, you used the inductive hypothesis for n/2

so if you want to use strong induction, then that proves it true for all n = powers of 2

if you need to prove it for all integers, then you'll need to do some kind of flooring argument somewhere

[errant herald]

What about all numbers less than n?

[tacit arch]

You'll have to use Master Method

https://www.cs.cornell.edu/courses/cs3110/2012sp/lectures/lec20-master/lec20.html

Example 1 in section 1.3.1
https://web.stanford.edu/class/archive/cs/cs161/cs161.1168/lecture3.pdf

If you've never seen it, here's the proof
https://www.cs.cornell.edu/courses/cs3110/2012sp/lectures/lec20-master/mm-proof.pdf

[errant herald]

Hmmm gotta see what exactly is asked haha

this is what you had me do right?

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[native furnace]

i need help with probability smh

[lone heart]

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[red shuttle]

Help I don’t have a clue

[serene junco]

,rotate

[red shuttle]

.close

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[sage pond]

hi guys, we're supposed to express this without absolute value signs

[sage pond]

with cases

https://i.imgur.com/uKw57Lz.png

the answer is this

one thing that's confusing me is how in the answer

line 4 and lin e2

are both checking against a is less than or equal to -b

the 2nd item is checking if b is less than or equal to 0

and the 4th item is checking if b is greater than or equal to 0

how are they both checking against the b is equal to 0 case

but have different answers?

shouldn't one be greater than or equal to, and then the other one just less than or vice versa?

ok I mean the -2(0) case doesn't change anything so the answers aren't "different" so I guess I'm asking if for my answer I only checked the equal to 0 case for one of them and the complement I just checked greater than / less than

is it also correct?

or is the book answer somehow more "general"

and better

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[alpine sable]

So here you'll see the answer is given, but I don't know how to solve it.

[alpine sable]

For now I just want help with a

[whole orchid]

hello, please could you help me with this exercise. Thanks . A girl weighing 35kg stands on a surface. Determine the sum of the surface modulus exerted on the surface for both cases shown in the figure. The area of the sole of each shoe is 3.5 x 10^2m^2 .(g=10m/s^2).

[strong compass]

#❓how-to-get-help

[alpine sable]

.close

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[outer escarp]

Someone explain for d why it doesn’t follow 1/b-a integral of a to b pattern; why don’t they divide by the time and instead by the number of people in the auditorium

[outer escarp]

Nvm I think I got it

.close

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[violet grotto]

can someone help me with these questions? happy to pay if you help (its for homework and due in 30 mins)

[open hound]

Damn

GL

[violet grotto]

<@&286206848099549185> pls 🤲

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[rocky axle]

Hey I need help creating a a frequency distribution table, my situation is I gathered 3 information from a questionnaire, the student level, gender and interested in football (yes or no)

They are a 100 students from each form

So eg. Form 1 has a 100 and 60 says interested 40 male and 20 female

How do u put that info on a frequency distribution table

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[rocky axle]

<@&286206848099549185>

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[eager mesa]

<@&286206848099549185>

[eager mesa]

so how does dis work?

ik what the answer is

i just dont know what to do here

like

its x=7

wait

its now wrong

when i type x=7

so idfk

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[ionic sedge]

lol

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.close

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[vast cradle]

related rates problem

got no idea what to do for a

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[vast cradle]

<@&286206848099549185>

[vast cradle]

.close

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[lone heart]

@storm tree Has your question been resolved?

[storm tree]

<@&286206848099549185>

[lone heart]

@storm tree Has your question been resolved?

[serene junco]

What did you try?

@storm tree how did you get those values for M?

[storm tree]

using projection

[serene junco]

Doesn't seem quite right, can you show your work?

[storm tree]

i already erased it cause it wasnt working

[serene junco]

I guess you can calculate the projection of the vector CB onto CA, and then add it to C

is that what you mean?

[storm tree]

yes

i did that

[serene junco]

I haven't worked it out but yeah that should work

not sure where it went wrong

[storm tree]

let me try again

[serene junco]

you could also find an equation of the line CA, and then find an equation for the line that passes thru B and is perpendicular to CA

and solve the system to find the intersection

[storm tree]

Not sure its still wrong

[serene junco]

uh

that's what I got too

hang on

yeah I'm pretty sure that's correct

Yeah solving the system gives the same result

and desmos agrees

[serene junco]

wait did you use angle brackets like this?

Try entering it with square brackets. That's how they formatted the vectors in the problem

[storm tree]

ah square brackets

sorry new to this notation

cause other questions ask for < >

[serene junco]

I'm just guessing, because that answer appears to be correct

[storm tree]

yeh it works

ty

[serene junco]

awesome 🎉

np 👍

[storm tree]

.close

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[dim plaza]

I need help with 2c:

[dim plaza]

we have already proven the sum is not direct

[vale wigeon]

you should have gotten that dim(W1) and dim(W2) are both 3

and that they are of course not the same as each other

this doesn't leave many possibilities for what their sum could be

[dim plaza]

are you saying the dimension should be 3?

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[lunar lintel]

can someone help me solving this with element arguments

its really confusing

[strange meadow]

Just show if k is an element of the LHS it is also an element of RHS

and the converse of that as well

[lunar lintel]

yea thats what i have a problem with

we cant use de morgan's laws

and i get really confused

with the wording and stuff

[tawny crown]

Are you allowed to do this proof with venn diagrams?

[lunar lintel]

i rather not

💀

[tawny crown]

Why tho, it's extremely easy using that

[lunar lintel]

its jsut a textbook question

[lunar lintel]

because on the midterm he will ask in that specific way

[tawny crown]

I see

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[wet lagoon]

yo someone me and my friend got a hw and the question was 24g^2-39gh+51h^2
his answer was 8g^2-13gh+17h^2

[vale wigeon]

are you sure you did not miss anything in the question

"24g^2 - 39gh + 51h^2" is not even a question, it is just an expression. you haven't told us what needed to be done with it.

[wet lagoon]

oh yeah I forgor

factor

we factor it

[vapid shuttle]

it seems like all your friend did to arrive at their answer is divide all the coefficients by 3

[wet lagoon]

my problems are the

variables

why is it the same variables

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[wheat isle]

how does completing the square work with a non monic

[ivory fern]

Either divide everything by 4 before doing anything, or make a square of the form (2x + a)²

[echo socket]

If you are efficient with completing the square when the coefficient is 1, then, in this case, you can substitute for 2x

[vale wigeon]

or 4(x+a)^2...

[echo socket]

Let's say, some t is 2x, then the quadratic expression becomes t^2 + 3.5t - 1

Or, since here you have it as an equation, you could simply divide both sides by 4, like d suggested

[wheat isle]

uhm. like (2x + 3.5)^2 - 1?

[lone heart]

@wheat isle Has your question been resolved?

[ivory fern]

Not exactly

You have 4x² + 7x - 1
And want it to equal (2x + a)² + b

[wheat isle]

hm

[ivory fern]

In particular the linear terms must be equals in both expressions

[ivory fern]

So what is the linear term in the second expression?

[lone heart]

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[light torrent]

int 6 -inf , 1/(x-4)^2 dx

[light torrent]

i missed a day of zoom and were on this diverging shit for calc 2

idk what i’m doing lol

[echo socket]

$\int_{-\infty}^6\frac1{(x-4)^2}dx$ is this what you mean?

[light torrent]

i did u substitution but apparently it was wrong

other way

the 6 and -inf

[ocean seal]

A Lonely Bean

[light torrent]

ya

[echo socket]

Firstly, a discontinuous function wouldn't be integrable, right?

[light torrent]

sure

[echo socket]

And are you sure that 1/(x - 4)^2 is continuous on that interval?

[light torrent]

it diverges

[echo socket]

Right

[light torrent]

and i get that’s the answer but like

don’t i need to show proof

mathematically

[echo socket]

1. What you could do is break the integral up into $\lim_{a\to{4^-}}\int_{-\infty}^a\frac1{(x-4)^2}dx + \lim_{b\to{4^+}}\int_b^6\frac1{(x - 4)^2}dx \$
2. There is nothing mathematically wrong with the first argument

[ocean seal]

A Lonely Bean

[echo socket]

Post your question in an available help channel

[echo socket]

And showing that both of those integrals diverge*

[light torrent]

ok great

and the lim is to 4 because that’s where it’s 1/0 right

[echo socket]

Yeah

[light torrent]

fasho

preciate it man

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[boreal shadow]

How can i

[boreal shadow]

$\int_{0}^{\pi} x*\sin(x) dx$

How can i solve this?

[pseudo ice]

Integrate by parts

Differentiate the x to make your life easier

[ocean seal]

Noir

[boreal shadow]

like, u* sin(u) du ?

what am I missing?

[gray osprey]

You know about integral by part?

Or just don’t know how to apply

[boreal shadow]

I jsut googled it and as I applied found the solution pi-2

which's wrong

[gray osprey]

Can you show me the step

So I can have a look

[boreal shadow]

lemme rewrite it, it's pretty messy now

[gray osprey]

No problem

Take your time

[boreal shadow]

but based on

u*v = int(u * v' dx) + int(u' * v dx)

it's true right?

[gray osprey]

Yea

By integrating multiplication of differentiation rule thing as I remember

[proven tapir]

its u*int v minus int(differentiation u *v)

[gray osprey]

Umm umm

I see

[boreal shadow]

could you put ` around it?

asterisks lost

now it's pi

only lower half

[gray osprey]

Correct

[boreal shadow]

oh

I missed the 2 pi multiplier

[gray osprey]

2pi?

[boreal shadow]

question ask me to calculate the volume for solid of revolution

2 pi int(x*f(x) dx)

f(x) happen to be sin(x)

it's right this way

thank you

.close

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[soft pagoda]

hi

[soft pagoda]

i kinda forgot how to solve this exactly

not sure what to start with

[heady pollen]

log(x/y)=log(x)-log(y)

this is true for all bases afaik

so we can rewrite
log9(108)-log9(4) as log9(108/4)

when is log9(8y-9)=log9(27)

[soft pagoda]

i just got to this point right here

but idk what to do then

like how do i solve after that to find x

[heady pollen]

apply 9^() to both sides

as in
if we apply 9^() to abc, we get 9^(abc)

then, 9^log9(x) cancels and gives us x

that is why if
logx(y)=logx(z)
then
y=z

[soft pagoda]

uh

so we just cancel out the log?

[heady pollen]

yes

[soft pagoda]

so

8y-9=27

8y=36

[heady pollen]

🙂

[soft pagoda]

36/8

so 9/2

thanks

.close

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[soft pagoda]

okay confused

[soft pagoda]

1 more example

so for this would it be

[heady pollen]

ah this is nice

even more logarithm rules

[soft pagoda]

$$ log_2 8 * log_2 (a-2) $$

[ocean seal]

Stellarch

[heady pollen]

well

we have a plus there, not multiplication

[soft pagoda]

oh i thought it would equal * cause of the +

like how - = division

[heady pollen]

it actually does 🙂

$\log{x}+\log{y}=\log{x\cdot y}$

[ocean seal]

~Martin

[soft pagoda]

so would the above work then

[heady pollen]

well no

you wrote

$\log x + \log y=\log x \cdot \log y$

[ocean seal]

~Martin

[heady pollen]

which would imply "+ = *"

[soft pagoda]

ohhh

so $$ log_2 8(a-2) $$

[ocean seal]

Stellarch

[heady pollen]

yes^^

on the left hand side we can use another logarithm rule

do you know which?

[soft pagoda]

not sure about that side, never multipled a log with a real number

[heady pollen]

$\log (a^b)=b\cdot\log a$

[ocean seal]

~Martin

[heady pollen]

@echo socket there you have your parenthesis haha

[soft pagoda]

so $$ log_2^12 $$

?

[ocean seal]

Stellarch

[soft pagoda]

oh

thats

weird

[heady pollen]

uhm

this is weird

[soft pagoda]

no i meant

$$ log_2 2^6 $$

[ocean seal]

Stellarch

[heady pollen]

yes ^^

2^6=64

now we cancels the logs

[soft pagoda]

yep

and then solve

[heady pollen]

64 = 8 * (a-2)

[soft pagoda]

a = 10

nice

[lone heart]

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[lone heart]

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[torn forge]

instead of x-2 maybe x+2?

[tardy rock]

OOHHH thanks

that was a silly mistake

.close

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[upper ibex]

Let S be the sphere around (0, 0, 0) in R

3 of radius √

3. Then find the
   equation of the plane which passes through the point (1, 1, 1) and is tangent
   to the sphere S.

[upper ibex]

O

I'm tryinf to understand how you would use the gradient in this question, and why you would use it in that way

[lone heart]

@upper ibex Has your question been resolved?

[lone heart]

@upper ibex Has your question been resolved?

[lone heart]

@upper ibex Has your question been resolved?

[upper ibex]

.close

[lone heart]

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[mellow grail]

How should I simplify?

[mellow grail]

I can't simplify the surds further (I think)

[lone heart]

@mellow grail Has your question been resolved?

[rich quiver]

$\sqrt{2+4\sqrt{5}}+\sqrt{28-12\sqrt{5}}$

[ocean seal]

Anagh

[rich quiver]

Is it this you have to simplify?@mellow grail

[mellow grail]

No oo

The last fraction

[rich quiver]

3rd one?

What is your original question?

[mellow grail]

Uhh one sec

[mellow grail]

Yeah

[rich quiver]

Send me the original question

I am getting confused by what you have written above

[mellow grail]

9th

[rich quiver]

See

Now square both sides and then simplify

And then find value of α

You will get a simplified value

@mellow grail

[mellow grail]

Tried that

I wanted to see if i could get a solution that way

[mellow grail]

1

[rich quiver]

Wait

Isn't α=$\sqrt{2}$

[ocean seal]

Anagh

[rich quiver]

I am getting this

[mellow grail]

Wait

It's two solutions

1 of them is 1

[rich quiver]

can you show your working

[mellow grail]

Ignore the top part

The xy thing

Ignore it

[cobalt badger]

can you guys help me on a question

[rich quiver]

Create your own channel

[rich quiver]

See m>0

[mellow grail]

Yeah?

[rich quiver]

so there will be only one value of m

[mellow grail]

Ah right that's 1

[rich quiver]

Yes

@cobalt badger #❓how-to-get-help

[mellow grail]

Is there any way of simplifyimg the last fraction to 1 tho

[rich quiver]

I didn't understood how you get that

[mellow grail]

Simplify the first fraction without squarimg

[rich quiver]

But how?

[mellow grail]

Here

[rich quiver]

You multiplied and divided by $\sqrt{\sqrt{5}-1}$?

[ocean seal]

Anagh

[mellow grail]

Yesh

[rich quiver]

See your calculations again

Here

[mellow grail]

What?

I don't get the problem

@rich quiver i don't get the problem...

[rich quiver]

Wait for a few mins

[mellow grail]

Ok

[rich quiver]

I will explain

[mellow grail]

Aight

[rich quiver]

@mellow grail

[mellow grail]

Ohhh

Shit

[lone heart]

@mellow grail Has your question been resolved?

[lone heart]

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[junior warren]

was wondering if someone could let me no what more i may have needed when doing this proof

it mustve been a seemingly big thing missing to have lost half the marks on the question

only marks i lost on the midterm so wanted to see if i could possibly get some back (:

obviously it is subjective to marker but was just looking for opinions

[mortal trellis]

well you said that because 1/a is not integer/integer then b cannot be rational

but what about for example 1/0.5

or what about something like (2pi)/pi which is irrational/irrational but gives a rational number

[last tendon]

You should also explain why b = 1/a is well-defined, although you got away with it from the looks of it. I think 4 is generous for this.

[lone heart]

@junior warren Has your question been resolved?

[junior warren]

ah ok i see

so it wasn’t enough to just say b is irrational because A is

or i guess just defined things in a poor/incorrect way

[junior warren]

this explains it very well i see how what i said is not sufficient

[lone heart]

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[alpine sable]

how do I find the base of the rectangle

[lone heart]

Please don't occupy multiple help channels.

[tepid elk]

anyone need help?

[alpine sable]

yes lmao

[tepid elk]

okkkk

[alpine sable]

^

[tepid elk]

was up

hmmm

[alpine sable]

I know the height is 4

[tepid elk]

have u tried doing it yet

[alpine sable]

bro what

yes

I don't know how to "do it"

[tepid elk]

ok so wat do u hav

[alpine sable]

that's why I'm here

[alpine sable]

bro

what

[whole shell]

b is the base of the parralelogram, base of the rectangle is b - 3

[alpine sable]

I don't know the base of the parallelogram

how do I find it

[whole shell]

unless you are given the actual area

you cant

[alpine sable]

I'm not given the area

[whole shell]

then you cant, b can be anything

[alpine sable]

I'm only given the base of 2 triangles and the height

but I need the base of the rectangle

[modern sedge]

||Impossible||

[alpine sable]

fuck you connexus

💀

(talking about my school)

wait