help-10

[obtuse pebble]

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[small sand]

Hello, I need help with this phyisic problem; A projectile is launched from a height of 50.0 m. It hits the ground 5.30 seconds later. Knowing that the range of this projectile is 127 m, determines the initial velocity vector.

[teal turret]

Is it launched horizontally

Or at an angle

@small sand

Please say horizontally 🙏

https://tenor.com/view/uh-oh-worried-emoji-drama-gif-24999384

[obtuse pebble]

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[shadow lava]

Domain and Range is correct?

[thick gyro]

Why is the range from 3 to infinity. Can't you put in 0

[shadow lava]

Good point

.close

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[proper coyote]

Whatt did i do wrong lol

[latent walrus]

third line from the bottom where you split the integral: the second integral should still have a 1/2 in front of it.
second line from the bottom: the 3 from the 3/2 has disappeared somewhere?. then 1/2 moves into the log as a power which leaves it as 3ln(t+1)=3ln(e^x+1)

ah you wrote 1 1/2, but still, that wasnt the best way to leave it

im not really a fan of mixed fractions

[proper coyote]

sorry me neither but my teacher forces us to use mixed

Thank you for your help once again

Have a nice day!

[latent walrus]

you too

[proper coyote]

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[wicked epoch]

Evaluate
1/(1 x 2) + 1/(2 x 3) + 1/(3 x 4) ... + 1/(99 x 100)

[wicked epoch]

I got 99/100 using partial fractions - I simplified it to x/x(x+n)

where n is the final number and x is the first number

but idk if its correct

[tardy epoch]

Did you telescope?

[wicked epoch]

Yeah

wait no

Since its not an infinite series

[tardy epoch]

You can still telescope a finite sum

And get something like 1 - 1/100

[wicked epoch]

is my answer correct tho

[tardy epoch]

Where's your work

[wicked epoch]

i just used partial fractions for a series somewhat like this

i did it for everything from k+1 to k+5

and i noticed a pattern

the solution was always smth like n/k(k+n)

[swift saddle]

You can use induction to formally prove your answer

[wicked epoch]

How would I do that

[swift saddle]

Are you familiar with induction?

[wicked epoch]

I am

[tardy epoch]

I mean you're probably right, but you haven't given a proof.

[wicked epoch]

Proving smth for n and then using that to prove smth for n+1 as an example

[wicked epoch]

Yeah

[swift saddle]

Yes suppose that for n it is true then prove it for n+1

[wicked epoch]

uhhhh so like

using that formula

isnt induction just like

if its false

it dont work

so
it has to be true'

[swift saddle]

Have you tried?

It is very simple

Almost immediate

When formally writing, you first need to prove that it works for n = 1

But this is trivial

[wicked epoch]

Ok so I should say

For n = 1, it works <because>...
Then for n+1 it works as well?

[swift saddle]

For n = 1 it works, then let's suppose that for n it works, we prove that for n+1 it works

Have you done induction before?

[wicked epoch]

A while ago yeah

Last year

I vaguely remember how you do it

[swift saddle]

The crucial step is saying :
It works for n => it works for n+1

[wicked epoch]

Wait here do i do it for

n=2 as well

[swift saddle]

No

No need

[wicked epoch]

but n=1 is just 1/2

ok for n=1

it just becomes n/n+1

[swift saddle]

But you need to find a way to go from n to n+1

[wicked epoch]

now for n+1

it becomes

It becomes

(n+1)/1(n+1)

Ok i think I have figured it out

I will now write my solution formally

[swift saddle]

You know that f(n) is sum of 1/(n(n+1))

[wicked epoch]

Yes

[wicked epoch]

i just worked it out like this

i proved it

[swift saddle]

Well no

This wrong

And you want to prove f(n) = n/(n+1)

I mean the last result is false

@wicked epoch

[wicked epoch]

How

[swift saddle]

For n=1 it is true you proved it

Then let's suppose for n integer >0 it is true

How can we write f(n+1) ?

@wicked epoch

[wicked epoch]

f (n+1) = n+1/n+2

[swift saddle]

No not really

[wicked epoch]

wait i gtg now for lunch

[swift saddle]

f(n) is a sum

[wicked epoch]

ill continue solving this sum after

[obtuse pebble]

@wicked epoch Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[spark field]

could someone help me understand what this means?>

i understand this

[spark field]

but idk wtf this is

[sweet edge]

so it's saying that p is 5<3 and q is 2>6 and r is -5<-2

[spark field]

ok

that has nothing to do

with teh above?

[sweet edge]

well no... they're seperate

[spark field]

oh

and what about the last one

its just

regular truth tables?

[sweet edge]

well yeha

[spark field]

ah

ok

do u understand this?

[sweet edge]

it's just a truth table with an example

[spark field]

as well

I am very conufsed on how they solve this

[sweet edge]

hmm

[spark field]

this is the venn diagram i use

[sweet edge]

so they are shading the areas that would be what is described

yeah

it's just that but with 3 circles

[spark field]

we need to describe (C v a) and B?

for number 1

?

[spark field]

?

[sweet edge]

(C or A) AND B

so first they shade where C or A is

so they shaded C and A, all of it, and the overlap

but then the "AND B" part is shaded, and u just see where they are all overlapping

"all" being the first condition AND the second

[spark field]

would it not be this

[sweet edge]

hold on, lemme grab my ipad and draw out the steps

[spark field]

AORB here they color all of it

so they should color all of A OR C

here ?

[sweet edge]

this is what A or C should be

ur excluding some parts of A and some parts of C in ur image

[spark field]

how is it like this?

im confused

[sweet edge]

and the center

bc the circles are A and C

u fill ALL of A

and ALL of C

[spark field]

but that would go into b circle

[sweet edge]

so?

when we want A, we want ALL of A

[sweet edge]

that's A or C

[spark field]

okay so this is A OR C

[sweet edge]

yup

[spark field]

so how do we do

the last part

[sweet edge]

now from here we have an "AND B"

so that would be wahtever we have shaded here AND the overlap of B

which would be this:

[spark field]

i dont understand this part quite well

[sweet edge]

we didn't shade in all of B here since we need BOTH the left AND right sides to be true

[spark field]

the pictuer here A AND B

colors the sectiosn they both share

[sweet edge]

but if we include that part of B that isn't currently shaded then we are breaking the left side therefore the statement with "AND" isn't true

[spark field]

so AND would cover the sections A B AND C would share?

[sweet edge]

no, it would cover whatever the left AND the right cover

aka the overlap of the left condition and the right condition

[spark field]

im so confused

[sweet edge]

maybe a video with animations would make this clear-er

brb

https://youtu.be/cJkqxQeviik

https://youtu.be/oTTTNpMSc7k

https://youtu.be/TeV5UP7dWdc

[spark field]

what is

U?

[sweet edge]

U is OR

V is same as U

and upside down V is same as upside down U

I just like U bc it's smooth lol

[spark field]

i kin'dve get it

but not really

[sweet edge]

what's giving you troubles?

[spark field]

the questions they did

were different than what i have

[sweet edge]

that's fine, ur only caring about how to use the venn diagrams

[obtuse pebble]

@spark field Has your question been resolved?

[obtuse pebble]

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[steel snow]

hello, i need help if am doing it wrong or right

[steel snow]

our teacher haven’t discussed it yet

[quaint sequoia]

in general yeah
any 2 lines that aren't parallel will intersect at some point, and parallel lines never intersect
the best definition would be that parallel lines are lines which share the same slope (y=mx+b)

but maybe you haven't got there yet

[steel snow]

okay thank you but how do i find the hypothesis and conclusion?

[quaint sequoia]

idk it's a weird question
usually the hypothesis is also in if-then form

[steel snow]

ohh

so like the hypothesis is the if?

[quaint sequoia]

it seems like you just write the same thing 3 times

[steel snow]

ohh okay

[quaint sequoia]

there are no other instructions?

[tropic linden]

hypothesis can be if you draw 2 lines endless lee they will not meet

[fiery birch]

Hypothesis is the first part

Conclusion is the second part of your if else statement

Did you get it ? @steel snow

[steel snow]

OHHH okayy

[steel snow]

yes

im stuck at the cebuanos are peace loving people

[fiery birch]

First think of how you can write it in if else form

Then take the first part as hypothesis and the remaining as your conclusion

[fiery birch]

Are you able to do this? @steel snow

[steel snow]

No

But ill try

[fiery birch]

Hint: If people are...

[steel snow]

if people are Cebuanos, then they are peace and loving people

is that right?

[fiery birch]

Just peace - loving , 'peace' and 'loving' doesn't make sense grammatically

However you got the general idea, well done

[steel snow]

alrighty

also what is a converse, inverse, and a contraposotive ?

[fiery birch]

Right , do you agree that every if else statement can be generalized to something like 'if a then b' where a is the hypothesis and b is the conclusion?

[steel snow]

Yes

i guess

[fiery birch]

Okay, now Converse is basically the opposite. You tell that b is the hypothesis and a is the conclusion.

So what will the if else statement be here ?

Hint: we are doing something similar to taking a mirror image or as we say in English 'vice-versa'

[steel snow]

if two lines intersect to form right angles, then they are perpendicular

[fiery birch]

No, forget that statement, let's do this in terms of a and b now

You are given a statement,' if a then b'

Once you get the general idea all of your questions can then be easily solved

[steel snow]

oh

if b, then a

[fiery birch]

Correct, very good

[steel snow]

oh

[fiery birch]

This is your converse

[steel snow]

that was simple

[fiery birch]

Yes, now shall we move to inverse?

[steel snow]

Yup

[fiery birch]

Ok , so inverse means you negate all of the statements. By that I mean, if there is a hypothesis 'a' it would become 'not a' and conclusion 'b' would become 'not b'

[steel snow]

got it

[fiery birch]

So what will be the if else statement now assuming that you are originally given 'if a then b' again?

[steel snow]

alright

if not a, then not b

[fiery birch]

Bingo!

[steel snow]

Yehey

Then the contrapositive?

[fiery birch]

Yes, the contrapositive is basically the converse of the inverse. So can you tell me what the if else statement will be now again assuming that you are given 'if a then b'?

In other words, contrapositive is the mirror image of the inverse as we had converse being mirror image of the original statement.

[steel snow]

alrightyyy

[steel snow]

If not b, then not a

is it right?

[fiery birch]

Exactly, you know everything you wanted to know now , great job!

Shall we try your first question then?

[steel snow]

yes please

[fiery birch]

Ok you already have your if else statement, what will be the converse then?

Remember that a and b are now getting substituted by something but it's still a and b

[steel snow]

if two lines intersect to form right angles, then they are perpendicular

[fiery birch]

Ok let's take this one step at a time, what is 'a' in the statement given and what is 'b'?

[steel snow]

uhh

[fiery birch]

If 'a' then 'b'. If 'two lines intersect' then 'they are perpendicular'

[steel snow]

Ohh

wait ill be afk

[steel snow]

okay im back

[fiery birch]

Ok let's continue where we left off then. What is a and what is b?

[steel snow]

a is the hypothesis

and b is the conclusion

[fiery birch]

So what are the actual portions in your original statement that corresponds to a and b?

[steel snow]

can we discuss this tomorrow? i gotta sleep

since I understand whats the converse, inverse and contrapositive

[fiery birch]

Sure

This channel can be closed then for now. You can reopen a new one tomorrow.

[steel snow]

okay

[obtuse pebble]

@steel snow Has your question been resolved?

[obtuse pebble]

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[sharp sapphire]

I'm trying to figure out how this solution works esp in line 4 I'm confused on that part

[timid silo]

welp if you look in the denominator of the third line

cotx*tanx

that would equal to 1

bc cotx = 1/tanx like the solution already says

[sharp sapphire]

Ohhhh okay okay that's why, thanks a lot

ok yeah I get it now

thanks 🫶

.close

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[iron rover]

Hi! Can someone explain to me how I can attempt this? The topic is vector calculus.

[obtuse pebble]

@iron rover Has your question been resolved?

[iron rover]

<@&286206848099549185>

[iron rover]

.close

[obtuse pebble]

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[frank hamlet]

if P(1,2) Q(4,6) R(5,7) S(a,b) are vertices of a parallelogram, find a,b

[frank hamlet]

where am i going wrong?

[civic zealot]

what is the question

[primal geyser]

Approach I thought: Use the diagonals bisect each other property.

[frank hamlet]

.

[frank hamlet]

wanted to try with complex numbers

• that would be a lengthy method i think

[civic zealot]

the change in the y-coord of S and R should be the same as P and Q
the change in the x-coord of P and S should be the same as Q and R

because parallel

[frank hamlet]

2,3

oh

well that was a waste of time

thanks

[frank hamlet]

could you still help to find the mistake in this

@civic zealot

[civic zealot]

i don't understand where your tan(theta) came from

[frank hamlet]

angle between lines

tan x = m2 - m1 / 1+m1m2

m --> slope

nvm

got it

thanks

.close

[obtuse pebble]

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[gloomy ermine]

Hi! Can someone help with the blank answers? I'm not sure what it could be this is for the pinching theorem.

[unreal musk]

What does sin(x) have to be between? 🥪

[gloomy ermine]

-1 and 1

im not sure how to get from -1 and 1 to g(x) when it has the +1 in it..

[unreal musk]

Well, if $\sin(x)$ has to be between -1 and 1, then what does $e^{-2x} \sin(x)$ have to be between?

[warm shale]

@unreal musk

[gloomy ermine]

-e^-2x and e^-2x

[unreal musk]

So then, from there, what must $1 + e^{-2x}\sin(x)$ have to be between?

[warm shale]

@unreal musk

[gloomy ermine]

-e^-2x +1 and e^-2x+1

i think..?

[unreal musk]

Yep, there you go

[gloomy ermine]

OH!

it doesn't have to be multiply-

oml

tysmm

also

for this one i got the right answer..but i dont understand why its the case...

the second one

|t|

[unreal musk]

Assuming that the point $C$ is the base of the triangle? But you know the formula for the arc length being something like $r\theta$ for radius $r$ and angle $\theta$

[warm shale]

@unreal musk

[unreal musk]

Here we have the angle being t (when t is nonnegative) and the radius being 1

[in the case t is negative, just take it to be positive as that's the angle BAD]

So then in both cases you'd have that your arc length is |t|*1 = |t|, if that helps?

[gloomy ermine]

could you explain how the angle is t?

isnt point B t?

oh wait-

OH!!

tysm!!!

.close

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[simple laurel]

Hello, Can someone explaing to me how to do this?

[simple laurel]

RM is the currency in my country

[royal basin]

have you done problems like this with the matrix method before?

[simple laurel]

im actually trying to help my brother study for his exam... and ive forgotten on matrix method

[royal basin]

maybe get your brother on the line?

but ok, if it didn't say to use the matrix method, what would you do?

[simple laurel]

i probably do trial and error... and got the answer... 4 packets of 5kg and 5 packets of 10kg

[royal basin]

... do you know your way around algebra?

bc trial and error is bad

you would do better to make two variables, say x for the number of 5kg bags and y for the number of 10kg bags, and write equations for the total cost and total mass...

[obtuse pebble]

@simple laurel Has your question been resolved?

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[simple laurel]

thx

i got it

[obtuse pebble]

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[royal basin]

such channels are unreopenable

[trim portal]

feel free to claim new channel

[obtuse pebble]

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[neat owl]

The third one. The fourth one is similar and I was able to do. In fact I was able to finish the rest of the chapter without any problem but I keep getting stuck on that one.

[neat owl]

My answer iss 90

While it should be 60

[ruby path]

How many possibilities exist for the unit's place?

[neat owl]

3

[ruby path]

And for the ten's place?

[neat owl]

I caught my mistake

Thank you

[ruby path]

All good

[neat owl]

.close

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[sullen elm]

Acc to ne all of this is in parallel connection

Then the ans should be 6c but howw is it 4C/3???

[frosty spoke]

they're not all in parallel

[sullen elm]

Dudee this chapter is making me cry 😭

Can u explain

Which is in series ??

[frosty spoke]

definition of parallel

is that their beginnings are connected by wires

and their ends are also connected by wires

definition of series is that to get to one end from the beginning of the series, you have to go through the elements

[sullen elm]

Then 1 and 2 aree in series with each other

[frosty spoke]

no they are not

I suggest you review what series and parallel are

[sullen elm]

I have done that I am not able to apply it

[frosty spoke]

or I guess you might call them in series, but that information is useless, because you cannot replace them with an equivalent capacitor

[frosty spoke]

you literally just said all of the capacitors are in parallel, which is blatantly false

[sullen elm]

Ya cause there is another in between them

[sullen elm]

Exactly i am not able to apply it

I know the theory

[frosty spoke]

no you don't

if you said something like that, then you don't actually know the definitions

[sullen elm]

In series the negative of one is connected to positive of another while in parallel each of negatives have one connection and positive have one

[frosty spoke]

yeah no

[sullen elm]

😭😭😭😭

Bruh but you never help

[obtuse pebble]

@sullen elm Has your question been resolved?

[whole dock]

That's what happens when you use sl arora

[obtuse pebble]

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[delicate lion]

How to do this?
GIven $2+\sqrt{7}$ is the root of $x^2 + bx + c= 0$. Find b and c.

[delicate lion]

We only have 1 equation but there is 2 unknowns

[warm shale]

Kin

[kind hawk]

the root or a root?

[obtuse pebble]

@delicate lion Has your question been resolved?

[delicate lion]

a

Create the thread again

.close

[obtuse pebble]

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[sage dagger]

Not sure how to do question 2

[sage dagger]

The only thing I can think of is adding or subtracting for part A

[tawny fog]

Use vectors

💀

a and b are just multiplying sqrt shit

C is a real question

[tawny fog]

You can construct a parallelogram and use parallelogram law

[sage dagger]

dont you skull emoji me

i just started this topic

[sage dagger]

what the hell is the parallelogram law

[sage dagger]

but how do i use that to help me with part A

[frosty spoke]

vector addition

[sage dagger]

i dont quite follow

600 + 100?

[frosty spoke]

surely you've gone over an example of this

vector addition

https://www.physicsclassroom.com/class/vectors/Lesson-1/Relative-Velocity-and-Riverboat-Problems

here are a few problems if you need a refresher

[sage dagger]

Ohh this

so i am supposed to draw a diagram?

[sage dagger]

wouldnt part A be a straight line

because tailwind is just a straight line and im assuming is facing the same direction of the plane

[frosty spoke]

all of the vectors are straight lines

but the tailwind is pointing in the direction the plane is moving yes

[sage dagger]

like this?

[frosty spoke]

yes

[sage dagger]

and i just add those up right

oh

would part be 500kmh-1

[obtuse pebble]

@sage dagger Has your question been resolved?

[obtuse pebble]

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[woven shore]

Circles with centres $A, B$ and $C$ have radii $r, s$ and $t$, respectively. The circle with centre $A$ is externally tangent to the circle with centre $B$ at $X$. The circle with centre $B$ is externally tangent to the circle with centre $C$ at $Y$. The circle with centre $C$ is externally tangent to the circle with centre $A$ at $Z$. Prove that $X Z=\frac{2}{\sqrt{\left(\frac{1}{r}+\frac{1}{s}\right)\left(\frac{1}{r}+\frac{1}{t}\right)}}$

[warm shale]

;)))))

[woven shore]

I have no idea where the 2/root ... is coming from, hoping someone can help me with the approach to take

this is what i cam thinking, then similar triangles

but i dont think thats correct

[obtuse pebble]

@woven shore Has your question been resolved?

[woven shore]

@ruby fulcrum

[winter cargo]

wait

[woven shore]

whats the approach you have choosen for this question?

i dont think similar triangles is the way to get the square root

<@&286206848099549185>

[woven shore]

@thick gyro sorry for the ping, but any help will mean a lot at this point 😦

[obtuse pebble]

@woven shore Has your question been resolved?

[rare sedge]

I tried inversion on y with radius 1, trying to use the inversion distance formula it yielded no results unfortunately.

[woven shore]

i tried pythagorean theorem but no luck, maybe you have another approach?

yeahh i know what you are talking about, the lines dont seem to be parallel thats why i was not sure of similar triangles 😭

[rare sedge]

Wait this is actually easy we are just overthinking it.

Just use cosine rule

On triangles AXZ and ABC

Consider angle BAC

[woven shore]

no its actually from a waterloo contest I have the main contest in April so this is a practice problem

tho i dont have the answers to the questions

[woven shore]

ohh okay wait

yeahh i equate both cosine rule formulae on angle BAC

[rare sedge]

From triangle AXZ we have XZ^2=r^2+r^2-2r^2cos(angle BAC)
and from triangle BAC we have (s+t)^2=(r+t)^2+(r+s)^2-2(r+t)(r+s)cos( angle BAC)

Yeah just equate on angle BAC

And you are done

[woven shore]

okay wait, let me try this, and send you my working

[rare sedge]

Uhh I think its just expansion, I believe you can definitely get the answer from there

No need to send it to me, its just a matter of simplifying

[rich hemlock]

Did you actually get it using cosine rule

[woven shore]

i am still doing it, ill update this channel once i get a solution

,rotate

[woven shore]

i think its correct before i start expanding everything

@rare sedge how have i managed to mess this up now 😭

[rare sedge]

Urm x^2 is not cosA

2r^2-2r^2cosA is not equal to cosA

[woven shore]

waitt OMG there was a multiplication

[rare sedge]

lol

[woven shore]

i should take a break, forgeting basic math

[rare sedge]

Also in the srt thing you forgot the -2 while dividing

[rare sedge]

Yup lol, I should take a break too, its like 12.30 am

Imma go hit the sack lol,

[woven shore]

loll you totally deserve it !

[woven shore]

ill get some water strech around and try this again

[rare sedge]

Alright lol

[woven shore]

ayt, fixing everything now

@rare sedge you should just sleep, i will figure this out M sure

thanks a lot tho, great help indeed

[rich hemlock]

Lol

I think you call these problems Sangaku. They are Japanese geometry problems that are supposed to be kinda hard. I am not very good at geometry but I guess using trigonometry is fine since it all comes geometry anyways

[woven shore]

loll but @rare sedge was right, this is cosine formula, my unsimplfied = to the simplified form they want

its just a matter or simplifying now

ill probably close this channel, its just simplifying from here

[tight ice]

what is 2 + 2

???

[rain forge]

it's equal to 5, georges orwell said that you can trust him

[obtuse pebble]

@woven shore Has your question been resolved?

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[spice chasm]

what do i even do

.close

[obtuse pebble]

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[naive fossil]

Would anyone be able to help me out with this problem?

[naive fossil]

I have taken the first derivative (du/dx & du/dy) for x and y, then the second derivatives from that (d^2u/dx^2 and d^2u/dy^2).

I know that for them to be harmonic it should be satisfy u_xx + u_yy = 0.

However, it doesn't = 0 when I add the 2 second derivatives together.

What am I doing wrong?

[unreal musk]

What do you get as those derivatives?

[naive fossil]

I'll upload - one second.

This is what I got for the first and second derivatives with respect to x and y

[unreal musk]

,w diff e^(-x) * ( x cos(y) + y sin(y) ) - y + y/(x^2 + y^2) wrt x

[warm shale]

Results provided by WolframAlpha

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Requested by chartbit#3171

[unreal musk]

,w diff e^(-x) * ( x cos(y) + y sin(y) ) - y + y/(x^2 + y^2) wrt y

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by chartbit#3171

[unreal musk]

Your u_x and u_y are looking fine at least [what a pain that they made you do this manually ]

,w second partial derivative of e^(-x) * ( x cos(y) + y sin(y) ) - y + y/(x^2 + y^2)

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by chartbit#3171

[naive fossil]

Oh, I completely agree. I used a derivative calculator to check my work, but I was just hoping to get some fresh eyes on it to see if maybe I made a mistake and my sleep deprived eyes just weren't seeing it. lol

[unreal musk]

,w second partial derivative of e^(-x) * ( x cos(y) + y sin(y) ) - y + y/(x^2 + y^2) wrt y

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by chartbit#3171

[unreal musk]

Hmm, seems when you add those two together

These should cancel to zero

[naive fossil]

So, it looks like I did the derivatives correctly. That would lead me to believe that u isn't harmonic, right? Because they don't cancel out completely? Or is that where I'm blanking....

[unreal musk]

This new layout

[naive fossil]

But there's an 8x^2y and then an 8y^3...how can that cancel out?

omfg...is it the lcd.

Do I need to combine them?

[unreal musk]

Saves me from that typesetting pain haha

[naive fossil]

My. dumb. ass.

UGHGHGHGHG

Thank you for helping me see that. I literally never would have.

I appreciate you!

.close

[obtuse pebble]

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[obtuse pebble]

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[fathom flicker]

is the x-intercept where x=0 or where y=0 ?

not the best strategy

x-intercept is where y=0 and y-intercept is where x=0

if you have a function, you should be able to plug in and solve for each (in two separate equations)

factoring $$ -x^2+x+0$$ ?

[warm shale]

AustinU

[fathom flicker]

yes it looks like there is a small error

if you factor a negative out, obviously the negative one becomes positive, but you forgot to account for how that would affect the positive x

that would atleast be true

but also

you could lose the habit of writing the 0

[warm shale]

AustinU

[fathom flicker]

can be rewrote as

[warm shale]

AustinU

[fathom flicker]

which is not equivalent to x-x^2=0

that statement isn't wrong, but I don't see exactly what its relation to your question is

this is true because, if g(x) = 0 the result would be undefined (not equal 0). So therefore g(x) has to equal some number (not zero) , and if you have f(x) / (some number) = 0 then you know that f(x) must be 0

np

Could you let me know what exactly you are trying to figure out?

[warm shale]

AustinU

[fathom flicker]

that is f(x) right?

yah so what do you get for the y-intercept now?

you can also think of it like this

if the bottom equal 0

we can't divide by zero, but if we wanted to see kind of what f(x) would equal as we get close to the bottom being 0, we could try =.01 -> =.0001 and so on

and when you start dividing by something really small , the function jumps up to become very large

or if you had =-.01 -> = -.000001 it would jump down to be really small

[obtuse pebble]

@waxen fossil Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[lean spear]

how did he get the ln

<@&286206848099549185>

[tardy epoch]

That's the function definition in consideration

[tardy epoch]

It's the very first line in the top left

[lean spear]

but that says ln x

[tardy epoch]

So?

ln(x) is the same as ln x

sin(x) is the same as sin x

cos(x) is the same as cosx

[lean spear]

so the (x+h) is the x part of ln x ?

[tardy epoch]

x+h is the argument to the log function

if x=e, then ln(x) = 1

If h=e, then x+h=2e and log(x+h)=?

[lean spear]

how do you know if h=e

[tardy epoch]

I'm testing your knowledge, not this problem

Just answer the question

[tardy epoch]

@lean spear are you unable to calculate this?

[obtuse pebble]

@lean spear Has your question been resolved?

[lean spear]

isnt it already solved?

[tardy epoch]

If you're done, close the channel

[lean spear]

was i right?

im not sure how you got h=e

[lean spear]

.

[tardy epoch]

#help-10 message

[tardy epoch]

Right about what? You just posted a screenshot

Nowhere did you calculate f'(e)

[lean spear]

about log(x+h)

[tardy epoch]

What about it

[tardy epoch]

.

[lean spear]

it stays how it is?

[tardy epoch]

As opposed to what?

Or during what step?

[lean spear]

idk you put log(x+h) = ?

[tardy epoch]

That was a concept question that you kept ignoring

[lean spear]

oh

i didnt know that

[tardy epoch]

.

It's important to read messages and ask questions when you don't understand.

[lean spear]

so what is the answer to log(x+h) ? or is it a trick question?

[tardy epoch]

...

[tardy epoch]

Read the full message

Are you able to plug in numbers for variables?

[tardy epoch]

In the problem I gave, x=e

[lean spear]

so its log(e+h) ?

[tardy epoch]

.

[tardy epoch]

Shouldn't be any h

[lean spear]

it should be log(2e) ?

[tardy epoch]

Yes

[tardy epoch]

Do you understand this now

[lean spear]

kind of

ln x = ln(x+h) ?

what does h = ?

[tardy epoch]

no

[tardy epoch]

it's a variable.

you're supposed to learn limits before derivatives

[lean spear]

i did

where are they talking about limits in the example?

[tardy epoch]

$\lim_{h \to 0}$ means limit as h goes to zero

[warm shale]

riemann

[tardy epoch]

you should read this
https://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx

[lean spear]

how will i know which one im using

[tardy epoch]

they're equivalent

[tardy epoch]

compare it to your problem and see which one is correct

[lean spear]

how did they know to use the bottom one?

something about tangent and secant?

[tardy epoch]

.

you look at the limit

[tardy epoch]

does this look more like the first or second one you screenshotted?

[tardy epoch]

here

[lean spear]

2nd one but idky why they picked it

[tardy epoch]

.

[tardy epoch]

you can do either one.

do the first one if it makes you happier

[lean spear]

but we do not solve for h?

[tardy epoch]

no

why would you think you need to solve for h

there's no h on the left side of f'(e)

[lean spear]

we dont know what h is

[tardy epoch]

you need to do this

and read this as well

https://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx

your knowledge of limits could use some refreshening

[lean spear]

oh

so these are the forms of the final answer?

you dont solve past this? thats the derivative/ instant rate of change ?

[tardy epoch]

no

[tardy epoch]

yes you do

you need to evaluate the limit

[tardy epoch]

you should do these problems for practice

[tardy epoch]

and ones here

[tardy epoch]

so you understand the relationship between derivatives and limits

[lean spear]

.close

[obtuse pebble]

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[vast locust]

hi question about lin alg. If i say L is a linear transform, does that mean that there is some matrix such that L(vec x) = A * vec x, where A is a matrix?

[vast locust]

Like if I am talking about a linear transformation, that mean there is some matrix invovled?

[candid stirrup]

yes each linear transformation has a matrix in a base

[brisk matrix]

once you pick an ordered basis yes

[vast locust]

Ok cool. So given that L is some linear transofmation, I can always say that L(x) = Ax, where A is a matrix, x is a vector?

[brisk matrix]

do you have a more specific question in mind?

[vast locust]

its a assignment so I wont share it, but im using that fact in my proof

you know 😩

[candid stirrup]

you can always say let A = matrix(L) in a base B

[vast locust]

woah. that is the form that i need

[candid stirrup]

noice

[vast locust]

perfect. What is B though? dimension?

[brisk matrix]

you need ordered basis for the domain and codomain of the linear transformation

[vast locust]

Yea, im working with Fn -> Fm

so thats cool ig

Thanks guys

.close

[obtuse pebble]

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Use .reopen if this was a mistake.

[timid silo]

Help

[obtuse pebble]

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[crisp linden]

How to you evaluate $$\lim_{x\to\infty^+}{(\sqrt{x^2-5x})-(\sqrt{x^2-3})}$$

[warm shale]

abr

[crisp linden]

idk what to do

[dark stirrup]

Are you familiar with hospital rule?

[crisp linden]

no i havent learned it

yet

[dark stirrup]

I think you need it here

[crisp linden]

oh

[dark stirrup]

I think..

Ah yes you can use it here

If you haven't learned it yet tho, I don't know what else you can do

[crisp linden]

oh okay

tysm

.close

[obtuse pebble]

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[timid silo]

Help

[timid silo]

Hellllllllppppppp

[tardy epoch]

Needs more e,l,p

[robust sleet]

Yep

[timid silo]

This is confusing me badly

What do I do exactly I tried everything

[candid stirrup]

thing is

that y is horizontal bud

the symetry is up to down not left to right

[timid silo]

How

It says across the y

[candid stirrup]

yes but

y is the horizontal line

[timid silo]

Ok

[candid stirrup]

you do across the horizontal one

[timid silo]

Like this?

[candid stirrup]

yes

[timid silo]

Then what?

[candid stirrup]

then B is (-2,5) if i remember corretly

and y=-1

so B is 6 over that line

[timid silo]

So the answer is 6?

[candid stirrup]

the symmetry, it would be -6 -1 since the line is y=-1

[timid silo]

Oh ok

[candid stirrup]

i think drawing the lines and coordinates porperly would be great help

[timid silo]

So the answer is -6 -1 what is there something else we should do?

??

[candid stirrup]

no

it's all good

because the x coordinate does'nt change

[timid silo]

But I don’t think the answer is -6 -1

It’s saying it’s wrong for some reason

[fierce lagoon]

Why would the x value change

You're reflecting it over a horizontal line

[timid silo]

?

[fierce lagoon]

That translation alone has no effect on the x value

It only effects the y value

Find the vertical distance from B to y = -1

[timid silo]

So what do I do?

[fierce lagoon]

_ _

Do this first

If you need to, draw the triangle and the line on a graph

Show me your diagram afterwards.

[timid silo]

Is is -5-2?

[fierce lagoon]

No

graph the line of reflection

[timid silo]

I did

[fierce lagoon]

You did not

All I see are the x and y axes

You did not graph y = -1

[timid silo]

How?

[fierce lagoon]

Have you never graphed functions before?

[timid silo]

I have I think

Wait

Like this?

[fierce lagoon]

That's x = -2

They said y = -1

I really hope if you're doing coordinate geometry you know how to graph functions and equations

[timid silo]

Like that?

[fierce lagoon]

You just drew a point

[timid silo]

Ik

That -1

[fierce lagoon]

y = -1 is a line

[timid silo]

Oh ok

[fierce lagoon]

,w graph y = -1

Have you done functions before

Eh that's a shit graph

[timid silo]

I think

[timid silo]

My teach like giving us hw she never thought

Ok ok

So I draw that

[fierce lagoon]

They should still have patterns that make sense

[timid silo]

Like this?

?

[fierce lagoon]

Not quite

[timid silo]

I’m so confused

[fierce lagoon]

What's the vertical distance from B to the line

[timid silo]

5

[fierce lagoon]

No

That's the distance to the x axis

[timid silo]

2

[fierce lagoon]

...

Literally the vertical distance between the red point and the blue line

[timid silo]

1

No

6

[fierce lagoon]

Yes.

So now you go 6 down from y = -1

[timid silo]

?

Wait

You mean

[fierce lagoon]

-1 - 6

[timid silo]

So is that the answer?

[fierce lagoon]

(-2, -1-6)

Just simplify it

[timid silo]

How?

[fierce lagoon]

...

[timid silo]

Like

[fierce lagoon]

You don't know how to do -1 - 6?

[timid silo]

Why do we have to simplify?

[fierce lagoon]

Because your program will have a meltdown

And it's always nice to simplify unless told not do

[timid silo]

My teacher never taught me this bro

Ok

[fierce lagoon]

You've done reflections across the x and y axes right

[timid silo]

So is is -1, -3?

[fierce lagoon]

-1 -6 is not -3

[timid silo]

You said simplify

Oh wait

[fierce lagoon]

Surely you know subtraction

[timid silo]

So what’s the answer?

[fierce lagoon]

I'm not gonna give out the answer straight and you're literally one step away from it

[fierce lagoon]

Again, simplify -1 - 6

[timid silo]

Ok

How?

-7

Is that it?

[fierce lagoon]

(-2,-7)

[timid silo]

Damn I’m dumb

[fierce lagoon]

So like

You've done reflections across the x and y axes right

[timid silo]

That’s the final answer or more steps?

[fierce lagoon]

Final

[timid silo]

So this should be the answer right?

[fierce lagoon]

Yes

[timid silo]

That’s was good

One more question

I swear my teacher never taught me this

What do I do?

[fierce lagoon]

Work backwards

The fundamentals are the same

As the last problem

[timid silo]

What do you me the fundamentals are the same

?

Nvm

I got it

@fierce lagoon

Thank you for helping

Sorry for bothering

.close

[obtuse pebble]

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[thick hare]

How would you solve this?

[obtuse pebble]

@thick hare Has your question been resolved?

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[noble hemlock]

For fraction decomposition?

[noble hemlock]

Is this how you start the problem off

[fierce lagoon]

Do long division

The leading power for the numerator and denominator is the same

So long division will suffice

[noble hemlock]

Ohhh

Ok brb lemme do that rq

Like this?

[noble hemlock]

Where do I go from this point?

[fierce lagoon]

3 - 5/(t+1) is what you got right

So you just replace the integrand with that

They're equivalent

[noble hemlock]

Can I pull 3 out

Wait

Can’t you also pull our

The -5

To get -15 pulled out?

[fierce lagoon]

$\int (A + B) \dd x= \int A \dd x + \int B \dd x$

Integrals are a linear operation

[warm shale]

Umbraleviathan

[noble hemlock]

Oh

Integral 3

And integral -5/t+1

[fierce lagoon]

Yeah

Those aren't too hard

[noble hemlock]

Ohhhhh ok

Like this right 🙂

+C

[fierce lagoon]

Mmhm

[noble hemlock]

Got it thanks so much for your help!

.close

[obtuse pebble]

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[versed dust]

Can someone explain what I am doing wrong here?

I tried several approach

[versed dust]

I tried to get 4.5% of 42.1 which gives me 1.89 L

I then found 12% of 42.1 and then substracted 5.05 with 1.89

I also tried to do 12 x 42.1 / 4.5

I'm not sure whether it's the approach or is it the 2 decimals that I am not entering correctly

[obtuse pebble]

@versed dust Has your question been resolved?

[versed dust]

.close

[obtuse pebble]

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[timid silo]

i ..

.close

[obtuse pebble]

Channel closed

Closed by @tepid locust

Use .reopen if this was a mistake.

[timid silo]

small mistakes always man

.reopen

[obtuse pebble]

✅

[timid silo]

i got 0,1,-9

on the last row would it not affect the answer matrix?

<@&286206848099549185>

what level math is that

lin alg

I just peeked in here and I was like gobsmacked

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

.close

[obtuse pebble]

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[dry echo]

Differentiate

Ans: -1

So I've tried doing

$$
\frac{dy}{dx} \cdot \sin{(x + y)} = 0
$$

[warm shale]

dannylewastaken