help-10

[untold ravine]

i thought it read 3

[short spruce]

if you have something in the form asin(b(x+c))+d, what does the a represent?

[untold ravine]

the a represents a stretch in the positive y direction

so 3 in this case

[short spruce]

right, but there's a specific word used for periodic functions

[untold ravine]

hm

amplitude

[short spruce]

yep

[untold ravine]

so 3 x larger and 5 spaces above

[short spruce]

now can you tell me sin(x)'s range?

[untold ravine]

hmm

1 and -1

i understand

[short spruce]

right, it goes from -1 to 1

[untold ravine]

so it'll be -3 to 3

[short spruce]

because a = 1

yup

[untold ravine]

but 5 spaces above

[short spruce]

exactly

[untold ravine]

so 8 to 2

[short spruce]

yes

[untold ravine]

ahh

thank you

[short spruce]

👍

(also you normally express the lower bound first, so from 2 to 8)

[untold ravine]

ah yes

[hallow star]

🙂

[untold ravine]

.close

[obtuse pebble]

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[ocean fossil]

There exists a function f such that when f(x) is divided by x² - 3x - 4 and 2x² - 3x + 1, the remainders are 4x - 1 and 2x + 7 respectively. Find the remainder when f(x) is divided by 2x² - 9x + 4.

[ocean fossil]

Please help.

[untold ravine]

i'll try this

solving it

[ocean fossil]

Thanks, I may need to go for 25 minutes, so if you wrote anything important, please ping the statement next to it.

[untold ravine]

sure

i'll try keep it simple

[ocean fossil]

No, its' fine.

There is bound to be complexity in this.

Thanks so much,.

[untold ravine]

hmm i reckon someone else should do this

im bad at this it seems

i cant get the answer

[ocean fossil]

Oh golly gosh.

[untold ravine]

sorry

[ocean fossil]

Well, that's all fine.

[untold ravine]

i got two functions that can be used for either but i cant find one that fits both

4x^(3)-13x^(2)-13x+4 4x^(3)+8x^(2)-19x+7

[ocean fossil]

It's still all fine.

[untold ravine]

good luck

[ocean fossil]

Thanks.

Alright.

<@&286206848099549185>

Please help.

Here question again.

There exists a function f such that when f(x) is divided by x² - 3x - 4 and 2x² - 3x + 1, the remainders are 4x - 1 and 2x + 7 respectively. Find the remainder when f(x) is divided by 2x² - 9x + 4.

<@&286206848099549185> ?

[obtuse pebble]

@ocean fossil Has your question been resolved?

[ocean fossil]

<@&286206848099549185>

[obtuse pebble]

@ocean fossil Has your question been resolved?

[untold ravine]

<@&286206848099549185>

[obtuse pebble]

@ocean fossil Has your question been resolved?

[ocean fossil]

<@&286206848099549185>

<@&268886789983436800> My question has not been answered for 2 and a half hours. Should I close this help thing?

[timid silo]

i can help

@ocean fossil

so uh f(x)=x²-3x-4Q(x)+4x-1

and also f(x)=2x²-3x+1Q'(x)+2x+7

were gonna factor them alright?

f(x)=(x-4)(x+1)Q(x)+4x-1

f(x)=(2x-1)(x-1)Q'(x)+2x+7

so we can get

f(4)=15

f(-1)=-5

f(1/2)=8

f(1)=9

now we look at the question

f(x)=2x²-9x+4Q''(x)+ax+b

so

f(x)=(2x-1)(x-4)Q''(x)+ax+b

f(1/2)=1/2a+b=8

f(4)=4a+b=15

a+2b=16

8a+2b=30

-7a=-14

a=2 and b=7

so the final answer: 2x+7

@ocean fossil

[timid silo]

howd u get that

[ocean fossil]

Thanks so much!

.close

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[craggy cairn]

arccos(\sqrt((((1+cosx))/(2))))

[craggy cairn]

How to simplify this equation?

[idle thunder]

$\arccos(\sqrt{\frac{1+\cos{x}}{2}})$

[crimson berry]

That is so many parenthesis

[idle thunder]

dw i TeX'd

[craggy cairn]

yes

[warm shale]

sills

[craggy cairn]

I just don't know where to start

And how to simplify it can anyone help?

[mental solstice]

hint: the thing inside the square root is what a certain double-angle formula looks like if you move things around

[craggy cairn]

arccos(sqrt((1+cos²(x)+2cos(x))/2(1+cosx))?

I am dumb so not so sure about that...

[mental solstice]

do you know the double angle formulas?

[craggy cairn]

bad at english but

cos 2A = cos2A - sin2A (or) 2cos2A - 1

???

[spiral maple]

cos^2A

not cos2A

[craggy cairn]

yes

[safe spade]

double angles

[mental solstice]

right, so one of these formulas, if you move things around, will look something like the thing underneath the square root

bear in mind that a is not necessarily the same as x

[craggy cairn]

is it (sqrt(sin²(x)+cos²(x)+sqrt(1-sin²(x))/2)?

or should I put like x=2b?

so by replacing x by 2b

I obtained sqrt(1+cos(2b)/2)= sqrt(cos²(b))

then arccos|cosb|

which means

it's x/2???

is this it?

[mental solstice]

assuming cos (x/2) >= 0, yes

i don't know what range you're carrying it out in

[craggy cairn]

x VR

x is real

[mental solstice]

if you're doing it for $x\in\bR$, then you need to consider two cases: $\arccos\qty|\cos\frac x2| = \arccos\qty(\cos\frac x2)$ and $\arccos\qty|\cos\frac x2| = \arccos\qty(-\cos\frac x2)$

[warm shale]

Camilleone

[craggy cairn]

then does that mean it's emm gonna be -b and b?

for the answer?

ahh c bon

it's gonna be arccos(-cosb)=arccos(cos(b+pi))??

so either the answer is x/2 or

x+2pi/2

??

?

<@&286206848099549185>

NO

go to help 35

it's available

[mental solstice]

#❓how-to-get-help

sorry, i just got back from sending some emails

[craggy cairn]

no need to apologize. I am sorry for the bother

[mental solstice]

yes, this is what happens, but you need to be careful about arccos

because arccos usually outputs a value in [0, pi]

[craggy cairn]

ahhh

so i should determine the value of x

(hope that was correct)

which means

-pi/2<x<0

?

[mental solstice]

hmm

rather than saying that

you want to solve it for all $x\in\bR$?

[warm shale]

Camilleone

[mental solstice]

or just for some specific values of $x$?

[warm shale]

Camilleone

[craggy cairn]

for all x in R

[mental solstice]

okay, then this is what you do

for the first case, say $\arccos\qty|\cos\frac x2| = \arccos\qty(\cos\frac x2)$

[warm shale]

Camilleone

[mental solstice]

of course, $\arccos$ is the inverse cosine function, so you need to find the particular value of $y\in[0,\pi]$ such that $\cos y = \cos \frac x2$

[warm shale]

Camilleone

[mental solstice]

and that y will be the result

[craggy cairn]

I c will try it

I c thanks a lot @mental solstice and sorry for the bother.

have a great day/night/afternoon.

[mental solstice]

you too!

🙂

[craggy cairn]

.close

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[spice chasm]

can someone explain how OS=x+8

[timid silo]

It's the radius

u already did it

whats the problem

[idle thunder]

Thats some flawless handwriting

[timid silo]

oh wait nvm

uh

x+8

[spice chasm]

its the andwer key

[idle thunder]

Oh

[spice chasm]

ohhhhhhh

[obtuse pebble]

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[craggy cairn]

how to simplify this?

[obtuse pebble]

Please don't occupy multiple help channels.

[craggy cairn]

1/2(ln((y+1)(x+1)/(y-1)(x-1))

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[obtuse pebble]

Please don't occupy multiple help channels.

@full finch Has your question been resolved?

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[next burrow]

if all of the bounds of an iterated integral are positive, is the value of the iterated integral positive

[next burrow]

?

ill do a quick drawing

it seems to me like its a no, since there are functions that can turn positive numbers negative, like inverse trig functions?

does anyone have an example that disproves this?

[timid silo]

Negative functions

[next burrow]

lol

even simpler

than i was thinking

thanks

[obtuse pebble]

@next burrow Has your question been resolved?

[next burrow]

gonna try this one more time

im trying to switch order of integration

i know this is wrong

i think y upper bound should be 3/e?

and lower 0

pretty sure x lower bound is incorrect

this is a graph of the original function

[crimson berry]

of the original domain, you mean

You have the domain well described here. now just take the inverse of the function.

y=lnx
x = e^y

Then the lower bound of x is the points on the curve. So lower bound of x is e^y. Upper bound is clearly 3.
lower bound of y is still 0, upper bound is the point where the curve and the purple line intersect: ln(3)

So your stuff seems right to me

why do you think its wrong?

i mean, lets just check to be sure

,w Integrate[Integrate[Power[x,2],{y,0,ln(x)}],{x,1,3}]= Integrate[Integrate[Power[x,2],{x,Power[e,y],3}],{y,0,ln(3)}]

[warm shale]

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[obtuse pebble]

@next burrow Has your question been resolved?

[next burrow]

Thank you for the response 🙂 I checked it via comparing the answers of two integral calculators but I must have made an error while inputting them

[obtuse pebble]

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[civic obsidian]

Help , I got still or net income

[civic obsidian]

it’s suppose to be a tips for a name

[unborn valley]

Math Help. Please read #❓how-to-get-help and #rules.

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[elfin siren]

is f(y) = tan(y) the same as f(x) = arctan(x) ?

[leaden ibex]

no

[elfin siren]

okay thank you!

[obtuse pebble]

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[main cargo]

is it incorrect to just say

$160 \cdot (\frac{122.5}{160})^{2} = 93.8cm$

[warm shale]

The Torrent v2

[main cargo]

because thats the correct answer

BUT

question is 8 marks which is a lot.....

and the mark scheme talks about coefficient of restitution

so is my method incorrect and i got lucky or correct and will always work and theres nothing wrong with it?

(asked this the other day too but got no answers and ticket timed out)

[obtuse pebble]

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@main cargo Has your question been resolved?

[obtuse pebble]

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[candid halo]

.reopen

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[coarse flare]

if $ln(16) = ln(4x-6y)$, does it mean that 16 = 4x-6y?

[warm shale]

my mother is earth.i m earth son

[slow forge]

@coarse flare can you explain what a logarithm is in words

[coarse flare]

all i know is that it's used to find the exponent

[slow forge]

Ok a logarithm is a way of counting the number that it's exponent needs to be to get the product

Wait I'm not familiar with the syntax of the math symbols

Let me use example to explain

You know lg

lg10 = 1
lg100 = 2
lg1000 = 3
lg10000 = 4

See the pattern

I understood this from 3b1b so I'll just quote him

"think of a log as a exponent"

Ok you know what I'll just link the video he'll explain far better than I ever could

https://youtu.be/cEvgcoyZvB4

9:00 and 14:45 are relevant to your question

[obtuse pebble]

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[coarse flare]

@slow forge thanks

[obtuse pebble]

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[tacit frigate]

on the second line how did 6500 end up getting divded by 0.5 and 200

[rich goblet]

i mean they’re isolating for v^2

so they just divided all the extra terms on the right hand side

[tacit frigate]

ik but i dont get why moving 625 to the other side ended up dividing everthing

[rich goblet]

?

😭i’m confused what u mean

62500 = 0.5 * 200 * v^2

[tacit frigate]

all he did was move 625 and v to the other side right?

[rich goblet]

if you want you can simplify 0.5 * 200 and you’ll have: 62500 = 100v^2

then v^2 = 62500/100

[rich goblet]

line 2?

[tacit frigate]

yes

[rich goblet]

he didn’t move 62500?

he moved the extra terms w the v^2 to the other side?

[tacit frigate]

ooh ok

[obtuse pebble]

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[cloud jungle]

Loodrecht = Perpendicular

[cloud jungle]

how to make n: perpendicular to p:

this is the awnser but i dont know how they did it

[timid silo]

it has to be -1

when u multiply the slopes

[cloud jungle]

oh, okay

[timid silo]

so if its -3 it has to be 1/3

[cloud jungle]

thank you for the refresher 😄

it was there in my brain but couldnt remember

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[nimble jackal]

how do you solve the shaded area?

[nimble jackal]

thx i did it a similar way

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[signal iris]

can someone explain this to me

how did they get the r=0.83? and how they got the mean and stander deviation

[obtuse pebble]

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@signal iris Has your question been resolved?

[signal iris]

hello?

<@&286206848099549185>

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[proven plank]

can someone show me

how to do b)

[hybrid gull]

You need to find when the boat bumps into the dock (t = ? when this happens)

Then evaluate s'(t) at t = ?

[proven plank]

i tried but idk

[hybrid gull]

The boat bumps into the dock when it's 0 meters from the dock

[proven plank]

yes i get that

[hybrid gull]

Find where s(t) = 0 in that case

[proven plank]

but then ur left with 60-10t=0

t=6

[hybrid gull]

Yup

There you go

[leaden ibex]

Just make sure it is inside the range of possible t values (which it is)

[proven plank]

then i did s prime of 6

and i got -5

answer key says its 10/9

[leaden ibex]

,w evaluate the derivative of (10(6-t))/(t+3) at t = 6

[warm shale]

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[leaden ibex]

what is your s prime?

[proven plank]

answer key says its positive

[proven plank]

-90/(t+3)^2

[leaden ibex]

,w -90/(6+3)^2

[warm shale]

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[leaden ibex]

I don't know how you got -5

[proven plank]

sorry i calculated wrong

but answer ley says ots ppositivre

[leaden ibex]

Alrighty, let's talk about positive vs negative

[proven plank]

okk

[leaden ibex]

The distance function s, is it increasing or decreasing?

[proven plank]

decreasing

[leaden ibex]

So the speed must be negative, right?

[proven plank]

yes

[leaden ibex]

From the frame of reference of the dock

[proven plank]

yes

[leaden ibex]

But from the boat's frame of reference, it has a positive velocity towards the dock.

Myself, I would accept your negative answer.

Since the task specifically places the origin at the dock

[proven plank]

then is the textbook answer wrong then

?

[leaden ibex]

🤷

It can be justified

You just have to change frames of reference

[proven plank]

i see

for 13 iii)

im getting -0.25

not 0.25

can anyone explain?

oh wait nvm

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[marble stratus]

Could someone please help me with this one?

[timid silo]

try and split the shape up into squares and triangles

rectangles*

also you can find the base length of the shape by using Pythagoras

[marble stratus]

It's sqrt(24^2-7^2) ?

Maybe the best thing I could do would be to flip it?

[marble stratus]

Is the volume 1620m^3

[timid silo]

idk haven't checked however

[marble stratus]

🥲

[timid silo]

yes

that's right

once you have the length ps

[marble stratus]

eeeh

[timid silo]

pretty straight forward from there

[marble stratus]

the length

sqrt(527)

🍵

[timid silo]

if you don't know what to do with the incline in height just split the side into a rectangle and triangle

[marble stratus]

I'd still need the length

I think the question is a bit of a wrong one-

[timid silo]

the length (PS)

is sqrt 527

[marble stratus]

yeah-

[timid silo]

smaller than hypotenuse and bigger than height

which is expected for the base in this question

[marble stratus]

:o

[timid silo]

i got 1550 m^3

[marble stratus]

How?

[timid silo]

i found the cross sectional area first (the side)

then times it by the width

[marble stratus]

To find the cross section's area you'd have to work with sqrt(527) 🤔

[timid silo]

yes

since that is the base

length

[marble stratus]

1/2 * (sqrt(527) + 24) * ??

[marble stratus]

Is this wrong?

[timid silo]

instead of + 24

it is * 24

[marble stratus]

1/2 * (8 + 1) * 24 * 15

[marble stratus]

no-

[timid silo]

area of a 2d triangle is 1/2 base * height

[marble stratus]

OOH You're doing the triangle, why not do it directly with the trapezium?

[marble stratus]

🤔

[timid silo]

a trapezium is used when the sides are both perfectly horizontal or vertical

[marble stratus]

But they are if we flip it?

[marble stratus]

Like this?

[timid silo]

wdym

[marble stratus]

naaah

24 is the slanted part

So it can't be

[timid silo]

that is the wrong shape sry

for your picture

[marble stratus]

Yeah you're right

[marble stratus]

I flipped it-

[timid silo]

shape this

[marble stratus]

Just rotated -90 clockwise

[timid silo]

the only thing you need to do

is split it into a rectangle and a triangle

[marble stratus]

ooooh

[timid silo]

you don't need to do that ever

[marble stratus]

So when should I use the trapezium area?

[timid silo]

when it is a shape like that

[marble stratus]

aaah

[timid silo]

were two of the sides that are opposite to each other are slanted

[marble stratus]

Now it makes more sense, thank you :D

[timid silo]

np

[marble stratus]

.close

[obtuse pebble]

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[timid silo]

HI

[timid silo]

I got a question

what will the algebraic pattern rule be for this:

5,25,625,390625

[drowsy girder]

Ummm bases of 5?

,w is 390625 a base of 5

[timid silo]

oh

[drowsy girder]

Not bases but exponents i think

[timid silo]

whats a base

oh

[drowsy girder]

,w factors of 390625

[warm shale]

Results provided by WolframAlpha

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Requested by Pluton#6301

[timid silo]

so what will the algebric pattern rule be

[drowsy girder]

$$5^x$$

[warm shale]

Pluton

[drowsy girder]

They all have only 5 as prime factors

[timid silo]

so is x the term?

[drowsy girder]

Ye

[short spruce]

don't do people's work for them

[timid silo]

no thats not true then

cuz the 4th term is 390625

not the 8th

[drowsy girder]

Well your x is in some weird pattern

@timid silo write all numbers as 5^x and you will see tha pattern

[short spruce]

think about it, maybe fiddle around with a calculator or something

[short spruce]

don't do this misread, thought you were meaning list the first few numbers for 5^x

[timid silo]

term: Number:
1 5
2 25
3 625
4 390625

[short spruce]

your pattern isn't 5^x

[drowsy girder]

I mean thats the best hint that works in all scenarios. Write as much info as you know

[timid silo]

wait maybe its 5^(x-1)

[drowsy girder]

No

[timid silo]

no nvm

[drowsy girder]

Just write everything you know

[timid silo]

alr

do I close it?>

[drowsy girder]

No

[drowsy girder]

Write something like this but with much more info

Everything you know about this question

[timid silo]

oh

alr

I will

[drowsy girder]

Even if you think something isnt helpful it might help

[drowsy girder]

Is

$$625 = 5^3$$

[warm shale]

Pluton

[drowsy girder]

?

[timid silo]

no it isnt

[drowsy girder]

What is it

[timid silo]

125

[drowsy girder]

No i mean whats 625 equal to

[timid silo]

5^4

[timid silo]

5^4

[drowsy girder]

And what is 390625

Its not 5^4

[timid silo]

I tihnk 5^7?

nvm its 5^8

[drowsy girder]

Ok so write all the numbers you got

And look for a pattern

[timid silo]

OMG

[drowsy girder]

You see now?

[timid silo]

YEAH

[timid silo]

but idk how to make it in to a algbric pattern

[drowsy girder]

Well what is 1 , 2 , 4 , 8

[timid silo]

doubling

[drowsy girder]

By

Oh nvm

[timid silo]

2

[drowsy girder]

So what can you write 1 , 2 , 4 , 8 , 16 , 32 , 64 ...

Using x

[timid silo]

uhh

um

x2?

[drowsy girder]

Not really

[timid silo]

x^2?

[drowsy girder]

Thats parabola

But close

[timid silo]

eeee

idk

x^3?

[drowsy girder]

Remember what you did with these numbers

[drowsy girder]

Now do same here

[timid silo]

square each

[drowsy girder]

No

[timid silo]

oh

[drowsy girder]

But write it like this

Just correct this time

[timid silo]

oh

so on the right its 5^1, 5^2, 5^4, 5^8?

not what it was before

[drowsy girder]

Ignore 5 rn

1 , 2 , 4 , 8 are important now

[timid silo]

alr

hm

1 sec

[drowsy girder]

Like you found pattern in 5 , 25 , 625 ... this is same thing

[timid silo]

x^3?

[drowsy girder]

No

[timid silo]

double

[drowsy girder]

What is 4

[timid silo]

2^2

[drowsy girder]

What is 8

[timid silo]

2^3

[drowsy girder]

And 2 is

[timid silo]

2^1

[drowsy girder]

1 is also equal to

[timid silo]

2^0?

[drowsy girder]

Yes

[timid silo]

so

[drowsy girder]

So now you can write this as

[timid silo]

n^(2^n+1)?

[drowsy girder]

Umm no

[timid silo]

oh

n^(2^5)?

[drowsy girder]

So you know its
$$5^1 , 5^2 , 5^4 , 2^8$$

[warm shale]

Pluton

[timid silo]

yea I know its that

[drowsy girder]

And you know pattern of 1 , 2 ,4 , 8

[timid silo]

yes

[drowsy girder]

So just put it in exponent

[timid silo]

5^ (2^n)

[drowsy girder]

Yes

[timid silo]

alr

[drowsy girder]

$$5^{2^n}$$

[warm shale]

Pluton

[timid silo]

.close

[obtuse pebble]

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[dapper wagon]

I need to find the slope-intercept for of: (x+y)^5 = x^2+2y-4 at the point (-1,2). Than find the form dy/dx of cos(x^2-y)=x+y^2-1.

[obtuse pebble]

@dapper wagon Has your question been resolved?

[dapper wagon]

<@&286206848099549185>

so far I solve for the first one:
5(x+y)^4*(1+(dy/dx)) = 2x+2(dy/dx)

<@&286206848099549185>

<@&286206848099549185>

[dapper wagon]

<@&286206848099549185>

[obtuse pebble]

@dapper wagon Has your question been resolved?

[dapper wagon]

<@&286206848099549185>

[dapper wagon]

<@&286206848099549185>

[obtuse pebble]

@dapper wagon Has your question been resolved?

[dapper wagon]

<@&286206848099549185>

[compact shadow]

Take derivative in terms of x on both sides just like what you did for question 1

[timid silo]

i just realizd that this doesnt work

but √5^(2^n) does work so thanks

u did help alot

[obtuse pebble]

@dapper wagon Has your question been resolved?

[obtuse pebble]

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[sage geode]

If you ignore the 44m^2 part, what would you say the area is equal to?

[high lily]

do you know the formula for the area of a rectangle

[sage geode]

#❓how-to-get-help
• When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[sage geode]

So, wouldn't it be x*11/3 ? (I rewrote 3 and 2/3 as 11/3)

[ocean topaz]

sorry, but this is not how this server works. you will not be given answers. people will be happy to help you, though

[high lily]

this is a question about the area of a rectangle.
if you don't know how to calculate that then you should consider first looking that up

[pine sail]

So

Can you convert these into improper fractions?

[royal basin]

@pine sail this person only wants answers

and they have admitted to only wanting answers

(naturally you should not give them answers)

[pine sail]

Alright, thanks, that saves time.

[pine sail]

Yes, I did not know they won't work for the answer.

[ocean topaz]

.close

[obtuse pebble]

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[vital thorn]

How do I do that one?

so I know I have to put it in correct form but idk how

<@&286206848099549185>

[limber quartz]

these are all different ways of writing a vector

[vital thorn]

yea that makes sense

but how do I make it in the same form like (x,y)

especially the first one feels very odd

[limber quartz]

a line parallel to a vector has same implications as for a pair of parallel lines

[quaint glen]

i don't think you need to "change the form" of any vectors here, all you need is the direction vector of each line, which has been kindly given to you for both of them, and the geometric formula for the dot product

[limber quartz]

what is the slope of the vector (4,-3)

[vital thorn]

idk

[limber quartz]

what does (4,-3) mean to you

[vital thorn]

but the 2nd one in vector form is (5 4 right?

[limber quartz]

yes

[vital thorn]

it is a point throughout it passes

so would it be like (x y)= (5 4)

[limber quartz]

it's a vector in that form too

not quite

[vital thorn]

yes but we need to find b1 and b2

for dot product

[limber quartz]

a vector points to that point

from the origin

...so what is its slope then.

[vital thorn]

4 -3?

[limber quartz]

that's not the format for a slope, what do you need to do with that

[vital thorn]

how are you supposed to find a slope with only a point?

wait it is parallel

[limber quartz]

you don't have only a point

[vital thorn]

so it would be

like

[limber quartz]

vectors start at the origin and point somewhere

[vital thorn]

the opposite or smthng

[limber quartz]

I mean they don't have to but a vector given like that does

[vital thorn]

ok

idk then tbh

[glossy ibex]

why are you trying to find slope. just use the parametric equation for a line

[vital thorn]

I need to find the direction vector for both

[limber quartz]

he needs a point and the direction to define a line

[vital thorn]

because the slope gives you direction vector?

[limber quartz]

the direction comes from the slope of the vector (4,-3)

Pollywog, how do you write slopes

[glossy ibex]

Both are given

[vital thorn]

rise/run?

[limber quartz]

@glossy ibex you are experienced, they are not

right.

Do you see that information in (4,-3)

?

[vital thorn]

yes?

4/-3?

[limber quartz]

yes.-3/4

[glossy ibex]

good luck using slope when the line is vertical

[vital thorn]

fr? thats crazy

so the slope is 4/-3

[limber quartz]

of L1

b.c. it's parallel

[vital thorn]

so then wouldnt the direction vector for the line be (-3 4)

[limber quartz]

oh yeah

dyslexia

You said it in the given order the first time and I didn't notice

it's -3/4

rise over run

[vital thorn]

ohhh so direction vector is (4 -3)

for L1

[limber quartz]

yes.

[vital thorn]

ok now we need the next one

[limber quartz]

the top number is the x-business, the bottom is the y-business, so the slope is the quotient of the bottom with the top

right

[vital thorn]

5/4

?

[limber quartz]

are you trying to say the slope of L2?

[vital thorn]

yes

[limber quartz]

is that the correct order

[vital thorn]

but how do I know what is rise and what is run

[limber quartz]

i is the unit vector in the x axis, j is the unit vector in the y axis

[vital thorn]

4/5 is the slope for L2 then?

[limber quartz]

do you believe that it is?

[vital thorn]

yes

[limber quartz]

ok

we have a direction...we still need a point

what's the point it passes through?

[vital thorn]

we have direction vector for both right?

[limber quartz]

we are past that

the direction vector gives us slope

you have the slopes

[vital thorn]

so we can find the angle now

[limber quartz]

where's hte point for L2

[vital thorn]

we dont need the rest of the info

we can use cos theta

[limber quartz]

hm

I think you are right about htat

[vital thorn]

lets gooo

[limber quartz]

ok

[vital thorn]

lemme try solving it and ill lyk

it works, thanks @limber quartz

.close

[obtuse pebble]

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[strong vale]

.close

.close

[obtuse pebble]

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[civic zealot]

??? none of these relate to the original question

[fickle cave]

oops

sorry

I sent the wrong 1

ignore all of that haha

working on this 1 rn

ok

I finished that 1

but I'm stuck on this question right here

does that look right?

[obtuse pebble]

@fickle cave Has your question been resolved?

[obtuse pebble]

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[brittle swan]

suppose dim(V) = n (V vector space), how do i show that n linearly independent vectors span V?

[raven spire]

Have you learnt the terms "rank" and "gauss-jordan elimination"?

[mental solstice]

how do you define a dimension, i think is the first question

[raven spire]

If yes, that's the cue to your answer

[brittle swan]

cardinality of basis

(assume finite)

[raven spire]

nvm, I should've known you haven't read on matrices yet

[obtuse pebble]

@brittle swan Has your question been resolved?

[brittle swan]

<@&286206848099549185>

[brittle swan]

somebody help ;-;

[serene osprey]

If you admit that the canonical basis then n linearly independent vector can be reduced to rref form which is exactly the canonical basis and so they span V

[brittle swan]

what are rref and canonical basis

[serene osprey]

Row reduced echelon form and canonical basis is basically the columns identity matrix

Well looks like you didn't learn these concept so they are valid in this case

Arent

[raven spire]

:/

[haughty coyote]

That's most likely the definition of dimension, so how have you defined it ?

[haughty coyote]

because most likely you and I also have the same definition of basis

[brittle swan]

definition of dimension is cardinality of basis

i’m trying to show any n linearly independent vectors is a basis too

to do that we prove it spans V

[haughty coyote]

sorry I missed the "any" and its importance

[balmy mortar]

i swear you're going in circles about this

what set of notes are you following that doesn't prove this

[brittle swan]

kennesaw state uni

[balmy mortar]

i dont even know what facts you have on you rn

[haughty coyote]

because the way we said the dimension was well defined in class was that all bases have the same number of vectors

[brittle swan]

yea

[brittle swan]

but this

[balmy mortar]

you state the definition then prove it is well defined right after

[brittle swan]

so we don’t even know (yet) whether the set’s a basis

[balmy mortar]

have you done that?

[brittle swan]

here

since all bases have the same cardinality

[balmy mortar]

then

the then bit, have you done that

[balmy mortar]

is this proven

if yes, this isnt hard to show

[brittle swan]

yes

[balmy mortar]

ok then let V space dim n

S a set of lin ind size n

ok?

consider V - span S

what can you do with stuff in here

Remember the maximal lin ind thm you showed. It also applies to the entire space

[raven spire]

:o

[brittle swan]

nvm

steinitz exchange lemma

suppose S = {v_1, …, v_n} lin indep
B basis

∃ B’ ⊆ B s.t. |B’| + |S| = |B| and S ∪ B’ spans V

B’ empty set

S = S ∪ B’ spans V

S basis

[balmy mortar]

so a lemma

you shud know

if i have V space

dim n

i can construct a basis by

adding linearly independent vectors to my set Si one by one

until it is size n

if the set is Si (has i lin independent vectors)

Then I can keep adding a vector from V - span Si

and Sn will be my basis

[brittle swan]

yey

.close

[obtuse pebble]

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[regal fable]

Does that statement make sense to anybody

The underline one is suppose to be a math form of the original statement where r represent a number

[obtuse pebble]

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[obtuse pebble]

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[still ravine]

help me

[idle thunder]

Make sure you ask your question while opening the channel

[astral parcel]

Split 25 in such a way that the product is 300, is it even possible?

[idle thunder]

@astral parcel #❓how-to-get-help

[still ravine]

help me

[timid silo]

What's your question?

[still ravine]

transalate Ba năm trước, cha hơn con 30 tuổi. Hai năm nữa tổng số tuổi của 2 cha con là 52. Tính
tuổi hiện nay của mỗi người?

[idle thunder]

English only please

[drowsy cosmos]

the answer is 42

[still ravine]

i dont have time ,my homework due 9

o clock

[idle thunder]

We can't help you if us english speakers can't understand the problem

[still ravine]

hmm

i can transalate

3 years ago dad age was more then son age by 30 years

[idle thunder]

There's more to translate right

[still ravine]

umm no need anymore

i solve it

[obtuse pebble]

@still ravine Has your question been resolved?

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[still ravine]

also i got it wrong

and i got an B

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[amber rampart]

.close

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

@coarse river Has your question been resolved?

[obtuse pebble]

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[white stag]

quick question. I'm in Calc III and my textbook states the statement seen in the image. my question is, why can't the maximum also occur when theta=pi, as in when vector u is antiparallel to the gradient vector?

[white stag]

nevermind, figured it out

.close

[obtuse pebble]

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[obtuse pebble]

@craggy pagoda Has your question been resolved?

[spiral maple]

Say what they're used for

Look at examples in your notes

The question is for you to write in your own words... if I just tell you the answer you're not answering the question correctly

[obtuse pebble]

@craggy pagoda Has your question been resolved?

[tacit root]

consider above as a use case

the red curve is always the curve of a quadratic

see how you can use this fact

[obtuse pebble]

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[obtuse pebble]

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[copper latch]

State true or false with proof; “Between two numbers n and 2n there exists at least 1 prime number.”

[copper latch]

For all n > 1

[hybrid gull]

There are probably proofs of this online somewhere

I personally don't know it

[burnt jungle]

between 100 and 200 are more than one single prime number?

providing proof by contradiction should be good

right?

you have 101 and 103

[hybrid gull]

Actually this ^^

I just didn't think about this hehe

[burnt jungle]

yeah

its kind of deceiving to think about small numbers

[copper latch]

It’s atleast*

[hybrid gull]

That's why pictures are so important

[burnt jungle]

makes sense actually

[copper latch]

[burnt jungle]

when you say between 2 and 2n

that means we exclude n and 2n

?

[copper latch]

Including

[burnt jungle]

does n have to be an integer?

[copper latch]

[copper latch]

Does it matter

[burnt jungle]

it doesnt

[copper latch]

I don’t think we can solve it, can we?

[burnt jungle]

i dont really have anything in mind

[copper latch]

<@&286206848099549185>

[raven spire]

._.

[burnt jungle]

i dont think thats a real question

its either false; to prove that you need a case where it happens, which i dont think is likely

or its true; where you need a written proof, and i have no clue

[raven spire]

it's totally true tho-

lol yeah

[burnt jungle]

how come?

lol

[raven spire]

Let n = p_1^a p_2^b p_3^c p_4^d ... p_k^n, 2n = 2p_1^ p_2^ p_3^ p_4^ ... p_k^

mm ._.

[burnt jungle]

$Let n = p_1^a p_2^b p_3^c p_4^d ... p_k^n, 2n = 2p_1^ p_2^ p_3^ p_4^ ... p_k^$

[warm shale]

Kotoboki

$Let n = p_1^a p_2^b p_3^c p_4^d ... p_k^n, 2n = 2p_1^ p_2^ p_3^ p_4^ ... p_k^$
```Compilation error:```! Double subscript.
l.55 ...p_2^b p_3^c p_4^d ... p_k^n, 2n = 2p_1^ p_
                                                  2^ p_3^ p_4^ ... p_k^$
I treat `x_1_2' essentially like `x_1{}_2'.```

[raven spire]

Lmao just giving it a thought

[copper latch]

Lol

[burnt jungle]

heh

[foggy marsh]

https://en.wikipedia.org/wiki/Proof_of_Bertrand's_postulate

[copper latch]

How does it help?

[copper latch]

Lmao I don’t get a single thing

[foggy marsh]

lmao me neither

[raven spire]

then your question probably should not have the "state with proof"

lmao

[copper latch]

Lol

[foggy marsh]

your teacher wanted you to be the next Dantzig

[burnt jungle]

he said at least one prime not at most

how does it even work!!!

[copper latch]

?

[burnt jungle]

besides the proof

what do you think guys?

is it true or false

[copper latch]

Ig this implies to be true

But i too dk

[raven spire]

It's true ._.

[copper latch]

I think proof is based on number theory _cause thats what lecture was about _

Lol

<@&286206848099549185> 🙄

[tardy epoch]

this is essentially the simplest proof

[copper latch]

Why do we take 468?

[tardy epoch]

near the bottom
https://sites.math.washington.edu/~mathcircle/circle/2013-14/advanced/mc-13a-w10.pdf

[copper latch]

Ohh cool

Thanks @tardy epoch

[raven spire]

because 469 is the second smallest number such that the sum of digits is the difference of two consecutive cubes

after 7

$(4 + 6 + 8) = 3^3 - 2^3 - 1^3$

[warm shale]

Ansh

[copper latch]

?!?

[raven spire]

mwahahahaha

[copper latch]

What?

[raven spire]

wdym what lmao

[copper latch]

Why 4+6+8?

[raven spire]

[copper latch]

Why do we need sum of digits here?

I don’t get it?

[raven spire]

I'm jk lol. Found an interesting thing so shared it >_<

The n < 468 comes from the computation above(in wiki / what riemann shared). Please check (@_@;)

[copper latch]

You son of a I really started connecting dots

Lmao

[raven spire]

Lmfao

[copper latch]

Oh

[raven spire]

@tardy epoch lmfao >_<

[tardy epoch]

helpers give'th, helpers take'th

[copper latch]

Anyways thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[drowsy girder]

Question?

[proper coyote]

Given is the function f(x) = 6x - 2x √ x
See the graph. The tangent of the graph of f is horizontal. Calculate the coordinates of T.

Here is what I have done:

[drowsy girder]

Oh thats easy at least if you use calculus

[proper coyote]

Is this correct?

[long sinew]

f = f(x) = 6x - 2x √ x?

[drowsy girder]

I mean we can see if it is

[proper coyote]

Yes

[proper coyote]

Oh okay

How?

[chrome mesa]

Use the product rule

[proper coyote]

U mean to differentiate?

[long sinew]

Do you want to know if you are right?

[proper coyote]

Yes

[long sinew]

You are

[proper coyote]

Oh okay

Thnx

Have a nice day!

.close