help-0

[ionic jewel]

no

[wild nest]

?

[magic heron]

bc negative + negative is positive i thought

or whatever idk

[ionic jewel]

absolutely not

negative + negative is always negative

[wild nest]

No

[ionic jewel]

negative times negative is positive tho

[wild nest]

This isn’t times

[ionic jewel]

thats true

[glass lichen]

they're talking to soso/ directing it at them

[ionic jewel]

^

[wild nest]

What’s the actual answer

[magic heron]

ok idk sorry

[jade birch]

,w calc -3/12 - 8/12

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[cinder lily]

you still need help on this?

[jade birch]

@cinder lily #prealg-and-algebra

[cinder lily]

oh ok

[calm perch]

N must be 1

since 2 single digits cant sum to any number above 19, even with carries

[sage jacinth]

ok the planet addition problem isn't too bad i think you just need to use logic and the given information to figure stuff out

[fiery adder]

sure, im doing other stuff rn tho, was gonna come back to it later

[alpine sable]

Hey anyone able to help me?

[fiery adder]

dont ask to ask

[alpine sable]

how do I use L'Hospital's Rule to solve lim x-> infinity (x^(9/5)*e^(-5x)

[alpine sable]

^^

Is that done correctly?

(At the bottom)

[noble sinew]

Can use e^(ax) grows faster than x^b (for a>0) so the limit is 0. (can be proven using L’Hopitals a bunch of times)

[noble sinew]

(Since e^(-5x)=1/e^(5x))

[alpine sable]

OH true

appreciate

[lofty ridge]

part b

bisection seems viable yet the function itself has no roots

[wild nest]

Hello

[lofty ridge]

hi

[wild nest]

How do i do this

[alpine sable]

use distributive property

then collect like terms

[lofty ridge]

[wild nest]

How do i distributive property for (x + 3)

[alpine sable]

distribute the negative

[wild nest]

How

[alpine sable]

-(x+3)=-x-3

[wild nest]

Ahhh

So it acts like a -1

[alpine sable]

yes

[wild nest]

Thanks

So should the negative still be there?

Or since I used it, it should be gone now right?

[alpine sable]

you distributed the negative, you don't put another negative around the parenthesis after it's been distributed

[wild nest]

So it is good right?

[alpine sable]

so you should get (6x-15)+(-x-3)=(2x+2)+4

[wild nest]

Why would we substitute with a +?

[alpine sable]

this implies the two things are being multiplied, they should be added

if you write (a)(b) it means a times b

that's not what we want

[wild nest]

Ok

So that’s just a law in math

[alpine sable]

what's just a law in math

[alpine sable]

this is just notation

[wild nest]

Yeah but how can we just add a + in the middle

[alpine sable]

something -(x+3)= something -x -3

=something +(-x -3)

[wild nest]

I’ll just trust you

[alpine sable]

adding a negative is the same as subtracting

[wild nest]

Alright

[alpine sable]

you don't need to write it as +(-x-3) only do that if you find it helpful

you can get rid of the parenthesis after you distribute

6x-15 -x-3 = 2x+2 +4

now just collect like terms and solve

[cosmic stream]

Can I have some help w/ this?

I’m stuck I’m not sure what to do next

[echo pike]

i need help

[covert nacelle]

1. 1 23 24
2. 1 23 24
3. 1 23 24 14
4. 1 23 10
5. 1 23 10
6. 1 23 10
7. 1 23 24 10
8. 1 23 10
9. 1 23 10
10. 22 26 28 18 14
11. 16 26
12. 16 12 24
13. 16 12
14. 16 12 24
15. 1 23 24
16. 1 23 24
17. 1 23 24
18. 1 23 24
19. 28 12
20. 14
21. 6 24
22. 6 24
23. 6 24 18 12 21
24. 6 24
25. 6 24
26. 6 24
27. 6 24 
28. 21
29. 25

What do you see? Do you see any pattern?

[analog meteor]

t = w.

y+w = 180 so w = 180-41 = 139

So t would be 139 degrees.

[worthy crest]

help me

[oak chasm]

@worthy crest Please don't send the same question to multiple channels.

[worthy crest]

bruh i need help man

please

@oak chasm

[sage jacinth]

i just tried doing this, but the something seems off. https://docs.google.com/document/d/1QSpO1tAHDxnmPDpqqXfeC_GNQWs15jTLbknm3V6L5eU/edit?usp=sharing

i may have made a silly mistake though

[worthy crest]

@sage jacinth

helpo me

[sage jacinth]

its not complete btw i stopped once i got E = H = 5, which doesnt make sense

read about the secant-secant theorem and #❓how-to-get-help @worthy crest

[worthy crest]

what does that even mean

[alpine sable]

#help-8

[sage jacinth]

i take that back nitezba, i think it should be done from left to right since numbers are being carried

[lusty hound]

I just don't know where to start. Can someone explain the steps please?

[thorn kindle]

What is normal form?

[echo pike]

can someone explain this to me and help me

[arctic umbra]

a line has 180 degrees

you could do this multiple ways, its really simple and straight foward do you have any notes or anything

[echo pike]

We just started this today

[arctic umbra]

what did the teacher tell you

anything abt parallel lines

[echo pike]

Not that i remember

[arctic umbra]

when a line cuts through two parallel lines (idk the word like bisect or something? idk) angles have a bunch of congruencies

[echo pike]

he has a really strong accent so its sometimes hard to understand him

[arctic umbra]

the y=100 is the same angle as u, v, and s because of exterior angles theorem, and like 2 others

i dont know the formal names of hte theorems i just know them

[echo pike]

Oh Im kind of getting it now

thanks

[arctic umbra]

https://www.dummies.com/education/math/geometry/definitions-and-theorems-of-parallel-lines/

here

[charred heron]

so like

this is better ig

if i have this information

and i pick a random 3 digit code

how do i figure out all of the different combinations of letters?

e.g. 789 - combinations would be ptw, ptx etc

[oak chasm]

@charred heron Take the cartesian product.

[charred heron]

i do not know what that is

[oak chasm]

Well, let's say I have two sets: {a, b} and {c, d}. The cartesian product is all the 2-tuples where the first element is from the first set and the second element is from the second set: {(a, c), (a, d), (b, c), (b, d)}.

You can do a cartesian product with three sets as well, which is what you'd do.

Is this just to list them by hand or to make a program?

[charred heron]

make program

[oak chasm]

Then you have something like:```
let set1 = "abc"
let set2 = "ghi"
let set3 = "tuv"

let results = {}

for (character m in set1) {
for (character n in set2) {
for (character o in set3) {
results.add(m + n + o)
}
}
}

It'll fill up results with all the "words".

[waxen tartan]

if we let n=3 for a sec
1/1 + 1/2 + 1/3 + 1/(1+2) + 1/(1+3) + 1/(2+3) + 1/(1+2+3)
whats the sum notation for something like that
doe stha texist

so i want to calculate for n something like this

[oak chasm]

@waxen tartan Maybe this: $$\sum_{S \in \frak{P}( {x: x \in \mathbb{N}, 1 \le x \le n } ) } \left( \frac{1}{\sum\limits_{s \in S} s} \right)$$

[ocean seal]

Chai T. Rex

[waxen tartan]

thanks!

[oak chasm]

No problem.

[waxen tartan]

just wondering what's the \frak {P}

[oak chasm]

It's the powerset function.

[waxen tartan]

ahh

[ashen wave]

Today my teacher went over this problem and I really didn't understand her- x^2=16 she said that the 4 could be positive or negative? How does that work

x^2=16

sorry

[ocean seal]

Chai T. Rex

[ashen wave]

oh okay

thank you!

[oak chasm]

No problem.

[runic vine]

???

<@&286206848099549185>

[gray isle]

don't ping helpers immediately
pythag

[night blade]

oh i didnt see the lack of a 15 minute wait

[runic vine]

[night blade]

levi, please read the #rules and #❓how-to-get-help

[runic vine]

I already read

[night blade]

then follow the rules

[runic vine]

Ok

[night blade]

thats why they exist...

[runic vine]

can I get help now

[glass lichen]

you already got help

[gray isle]

pythag

[glass lichen]

pythagorean if you need a further hint

[runic vine]

Idk how to use it

[glass lichen]

ok well what does pythagorean say?

[runic vine]

A2 + b2 = c2

[glass lichen]

^2, yes

what do a b and c represent?

[runic vine]

Right triangle

[glass lichen]

yes it's a right triangle

what do a,b and c represent in a right triangle?

[runic vine]

The angles

[glass lichen]

no

[waxen tartan]

pain aleks

i hate aleks

[runic vine]

Uh the sides of the triangle

[runic vine]

Ikr

[glass lichen]

yes, which side is c?

the hypotenuse or a leg? (legs are the sides which form the right angle)

[runic vine]

Legs because 36 is already hypotenuse because it’s longest side

[glass lichen]

c is the hypotenuse

[runic vine]

Bruh

Okay what do I do now

Equation?

[glass lichen]

well you have the hypotenuse and a leg, and want the other leg

so plug in the values and solve for the other leg

[runic vine]

33 squared plus 36 squared = c2?

[glass lichen]

no.. read what I wrote

"c is the hypotenuse"

[runic vine]

[obsidian tapir]

so c is given

[glass lichen]

so given you have the c value, your application of pythag shouldnt be to find c

[runic vine]

What is C then

[obsidian tapir]

here

[glass lichen]

the hypotenuse

[runic vine]

The hypotenuse is the Square that’s in the triangle or is it 36

[glass lichen]

it's 36, the longest side as you said

[runic vine]

So I don’t have a B ?

[glass lichen]

yes

you dont have one of the legs

so pick your favourite letter to solve for out of a and b

[runic vine]

Oki

I got 14.4m

How do I solve this?

[oak chasm]

@runic vine Well, there are three right triangles in that image. Which has two known sides?

[runic vine]

G and f ?

Or h

Idk I’m lost

[oak chasm]

Well, the three right triangles are FGH, FEH, and EGH.

Do you see how those are all right triangles?

[runic vine]

Yes

[oak chasm]

OK, which of those three triangles has two known sides?

[runic vine]

EGH?

[oak chasm]

Right, now if you have two sides of a right triangle, how can you get the third side?

[runic vine]

Pythagorean theorem?

Well I would use a2 b2 and c2

[oak chasm]

Yes, though to write that on here, use ^ for "to the power of".

a^2 + b^2 = c^2.

[runic vine]

Aight

[oak chasm]

So, find the third side and write it in.

[runic vine]

We have a and B right ; so it’s just C we need to find

[oak chasm]

No.

The hypotenuse is the side across from the right angle.

Which side is that?

[runic vine]

41?

[oak chasm]

Yes, that's right.

So, the hypotenuse is the one on the right side, c.

[ocean seal]

Chai T. Rex

Chai T. Rex

[runic vine]

40?

[oak chasm]

Yes, that's right.

Now, fill that in for GH on your drawing and then what triangle now has two known sides?

[runic vine]

FGh

[oak chasm]

OK, do we have two legs or one leg and a hypotenuse?

(that we know the length of)

[runic vine]

2 leg

[oak chasm]

OK, is 40 across from the right angle or next to it?

[runic vine]

Next to it

[oak chasm]

OK, is 85 across from the right angle or next to it?

[runic vine]

It’s above it

[oak chasm]

Right, it's across the triangle from it.

So, that's the hypotenuse.

So, we put the leg on the addition side and the hypotenuse on the length by itself side.

What equation do we have for the Pythagorean theorem?

[runic vine]

I’m kinda lost on what you said

Rn

[oak chasm]

OK, did you understand how I found out which side was a leg and which a hypotenuse?

[runic vine]

yes

[ocean seal]

Chai T. Rex

[runic vine]

yes

[oak chasm]

The two legs are on the side with the plus.

The hypotenuse is on the side without a plus.

Does that make sense?

[runic vine]

Yes

[solar sierra]

jacob went to his girlfriends house at 3:10pm. he got home at 12:40am when he got home he got on his pc and stayed on to play with brad angad and nathan until 7am. how long did he spend at his girlfriends house and how long did he play on the pc for. what grade is this?

[oak chasm]

@runic vine OK, so fill in 40 and 85 to the formula and show me what you have right after you fill them in.

@solar sierra Sorry, busy. #help-9 is open if you hurry.

[runic vine]

Okay so 40^2 + 85^2 = c^2 ?

[oak chasm]

No, remember 85 is the hypotenuse, right?

[runic vine]

Wait

40^2 + b^2 = 85^2

?

[oak chasm]

Yes, that's right.

You put the hypotenuse on the side without the plus.

OK, now find b.

[runic vine]

75

[oak chasm]

Right.

What are the two letters for that side you just found the length of?

[runic vine]

It was FH and 75 was the answer

[oak chasm]

Right, and that's the answer to your problem.

[runic vine]

Thank you!

[oak chasm]

You're welcome.

[shy prairie]

im stumped for this one

[oak chasm]

@shy prairie OK, division is the outermost operation there. What's division convert to in a logarithm?

[shy prairie]

subtraction?

[ocean seal]

Chai T. Rex

[oak chasm]

Let's do the first log. What happens when you take the logarithm of a number to a power?

[shy prairie]

err doing -8^5 wouldnt b correct right

[oak chasm]

No, not exactly.

[ocean seal]

Chai T. Rex

[oak chasm]

The power comes out to multiply it by the log of the the base number.

[ocean seal]

Chai T. Rex

[shy prairie]

5logc?

[ocean seal]

Chai T. Rex

Chai T. Rex

[shy prairie]

1/2logx

[ocean seal]

Chai T. Rex

[shy prairie]

1/3logab?

[oak chasm]

No, don't do the part under the square root yet. Leave that inside the logarithm. What do you take out of the logarithm when you have a logarithm of a square root?

[shy prairie]

err wat exactly do u mean by taht

[oak chasm]

Well, you took out 1/2, right?

[oak chasm]

here

[ocean seal]

Chai T. Rex

[shy prairie]

yea

cuz ik sqrt x is x^1/2

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[shy prairie]

ohh i see

i need to think of ab^3 as one variable kinda

[ocean seal]

Chai T. Rex

[oak chasm]

Yeah, it sort of works like that.

The whole thing is inside the square root, so it's treated as one together thing.

Now, inside the second log, we have a multiplication.

What does log change multiplication to?

[shy prairie]

addition?

[ocean seal]

Chai T. Rex

Chai T. Rex

[shy prairie]

3logb

[ocean seal]

Chai T. Rex

[shy prairie]

oh so u just plug it in now?

[ocean seal]

Chai T. Rex

[oak chasm]

So, what do you get as the answer?

[shy prairie]

-31

[oak chasm]

,w 5*-8 - (1/2)(6 + 3*-10)

Almost 🙂

[shy prairie]

oh oof lemme see wat i did wrong

[oak chasm]

Bah.

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[shy prairie]

oh lol i plugged in -8 instead of -10

whoopsies

appreciate the help

[oak chasm]

You're welcome.

[carmine lion]

i don't understand these types of series

$1^2+2^2+3^2+...+(2n)^2$

[ocean seal]

abe

[runic vine]

Are you helping someone at the moment

[carmine lion]

what am i supposed to find when i plug in n=1

this is for an induction question btw

[shrewd oracle]

Just sub in where there is n and see if the trivial case holds

[carmine lion]

yes but what is the LHS when n=1

[shrewd oracle]

E.g, show 2n is always even, we take the trivial case n=1, then we have 2n=2(1) = 2 which holds true

[carmine lion]

i've only given u LHS

i know how induction works

i don't understand how this series works

[glass lichen]

if it's for an induction question, you'd need what you're trying to prove the sum equals

[carmine lion]

i just don't understand the series

the series is the LHS

[glass lichen]

sum the squares of natural numbers from 1 to 2n

[shrewd oracle]

Its jst a sum of the natural numbers squared

[glass lichen]

$\sum_{i=1}^{2n}i^2$

[ocean seal]

moshill1

[carmine lion]

yeah so i get LHS=1?

[glass lichen]

yes

[carmine lion]

but if i do the same

for the RHS

[glass lichen]

you also havent given a RHS, so im taking your word for it

[carmine lion]

$\frac{n(2n+1)(4n+1)}{3}$

[ocean seal]

abe

[carmine lion]

if you sub 1 here

[glass lichen]

wait no sorry

[carmine lion]

and u get 5

[glass lichen]

if you sub n=1 to the LHS it's 1+2^2

[carmine lion]

yeah

thats what im after

[glass lichen]

so 5=5

[carmine lion]

why is it 1^2+2^2

[glass lichen]

so n=1 is true

[carmine lion]

for LHS when u sub n=1

and not 1^2

[glass lichen]

$\sum_{i=1}^{2(1)}i^2$

[ocean seal]

moshill1

[carmine lion]

$\sum_{i=1}^{n}i^2 + \sum_{i=1}^{n}i^2$

[ocean seal]

abe

[carmine lion]

that?

[glass lichen]

no

sum from i=1 to i=2n, but n=1 so 2n = 2

so sum i^2 from i=1 to 2

(1)^2+(2)^2

[carmine lion]

im still confused a little

is it something to do with how there are 2n terms instead of n terms

[shrewd oracle]

@carmine lion your summing up to (2n)^2

So n=1 means your summing to to (2)^2

[carmine lion]

so S_1 would be 1^2+2^2

[shrewd oracle]

So you need to start at 1

Till yo get to 2^2

So thats just 1^2 + 2^2. =5

As for the RHS, its easy you see that when you place in n=1, you get 5

Just basic arithmetic

[carmine lion]

ye thats why i was only asking for LHS

[shrewd oracle]

So now you have 5=5

[carmine lion]

??

lol

[shrewd oracle]

Lol shh haha

And then you can continue with the induction

[carmine lion]

any way to explain without using sigma concept

or not really

cuz i kinda get it

with sigma

how would you explain this to someone who has never done sigma sum stuff

[shrewd oracle]

I meqn sigma is just a way of shortening how much you write

Like instead of saying $ 1+2+3+....+n-1+n$, we say $\sum_{i=1}^{n} i$, which is just much shorter to write

[ocean seal]

Conor Sheridan

[glass lichen]

sum until the nth even natural number

[shrewd oracle]

Yeah, so your last term is 2n

So the top of the sigma, we put 2n

And then each value is squared

So we put i^2

[carmine lion]

ok

[shrewd oracle]

Giving us $\sum_{i=1}^{2n}i^2$

[ocean seal]

Conor Sheridan

[shrewd oracle]

Reading it takes a lil bit of time but it becomes easy

The bottom is where we start

The top is where we finish

[carmine lion]

rip this is a misunderstanding

[shrewd oracle]

The stuff to the right of the sigma is whar we are doing to each term

[carmine lion]

i already know how sigma work

[shrewd oracle]

Oh lol

[carmine lion]

ye

[thorn kindle]

@shrewd oracle i^2 = -1

So this sum is equivalent to -(2n)

[shrewd oracle]

@thorn kindle The i here is an index, not the imaginary number

[carmine lion]

lol

AMD

don't try and act cool

[shrewd oracle]

I can let it be q if that helps lol

[carmine lion]

mathematics (mathematicians) have weird norms

[shrewd oracle]

Amd pulling moves on me

[carmine lion]

huh

yes

[thorn kindle]

I dont have to try 😎

[carmine lion]

😭

[shrewd oracle]

https://tenor.com/view/sheldon-tbbt-paper-bag-couch-hyperventilate-gif-4992098

[signal wolf]

\int [0,2] ln x^x^2 dx

$\int [0,2] ln x^x^2 dx

[shrewd oracle]

You need the dollar sign to begin and another at the end to end the latex @signal wolf

[signal wolf]

$\int [0,2] ln x^x^2 dx$

[ocean seal]

MrThink15000

$\int [0,2] ln x^x^2 dx$
```Compilation error:```! Double superscript.
l.55 $\int [0,2] ln x^x^
                        2 dx$
I treat `x^1^2' essentially like `x^1{}^2'.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
(./757639076475174922.aux) ) 
Here is how much of TeX's memory you used:
 18264 strings out of 479485
 359566 string characters out of 5871962```

[shrewd oracle]

I assume you mean this

$\int_0^2 ln(x^{x^2}) , dx = \int_0^2(x^2)ln(x) , dx$, then try let u be something

[signal wolf]

Thx bro : D

[ocean seal]

Conor Sheridan

[shrewd oracle]

No bother, in integral, the bounds are done using the _ and ^

[glass lichen]

Log laws then probably u sub

[shrewd oracle]

Yeah

$\int_0^2 ln(x^{x^2}) , dx = \int_0^2(x^2)ln(x) , dx$, then try let u be something

[ocean seal]

Conor Sheridan

[glass solstice]

mind if i slide in

[fleet steeple]

why does $20^20 = 5^20*2^40$

[ocean seal]

Kathullhu

[signal wolf]

$\int_0^2 ln(x^{x^2}) , dx = 8/9(ln(8)-1)$

[ocean seal]

MrThink15000

[shrewd oracle]

why does $20^{20}= (5^{20})(2^{40})$ ? Is this what you wanted?

[ocean seal]

Conor Sheridan

[fleet steeple]

yuh

[glass solstice]

uhh can someone help me

[signal wolf]

$8/9(ln(8)-1)$

[ocean seal]

MrThink15000

[carmine lion]

don't you use the distributive property

[shrewd oracle]

@fleet steeple why does $20^{20}= ((4)(5))^{20} = (5^{20})(4^{20}) = (5^{20})(2^{2(20)}) = (5^{20})(2^{40})$

[carmine lion]

index laws

[ocean seal]

Conor Sheridan

[carmine lion]

wait

do u know

or are u trying to help someone

else

[alpine sable]

hi

[shrewd oracle]

What is each value increasing by as we increase x?

[shrewd oracle]

I was helping someone else

[carmine lion]

its increasing by cubes?

[shrewd oracle]

I was hoping he/she would have answered it lol

[carmine lion]

ah

btw conor

do u know how to factor a non monic

cubic

$8k^3+30k^2+37k+15$

how to factor

[ocean seal]

abe

[upbeat gorge]

first off k=-1 zeroes out, so you have (k+1) as a factor

factoring is mostly guesswork

[carmine lion]

educated guesswork

[upbeat gorge]

but you can limit your guesses with rational root theorem

descartes rule of signs

[carmine lion]

it should involve factors of 15 i think

[upbeat gorge]

etc

[carmine lion]

so you'

[upbeat gorge]

to be more precise, factors of 15/8 can be roots

[carmine lion]

what how

[upbeat gorge]

including negatives

that's the rational root theorem

divide the coefficient of the constant by the coefficient of the highest degree term

actually wait i stand corrected

factors of the coefficient of the constant

[carmine lion]

other way

ye

[upbeat gorge]

factors of the coefficient of the highest degree term

then divide them

[carmine lion]

divide them?

[upbeat gorge]

ye

so for example 15 has factors $\pm 1, \pm 3, \pm 5, \pm 15$

[ocean seal]

CST

[carmine lion]

yes

[upbeat gorge]

and 8 has factors $\pm 1, \pm 2, \pm 4, \pm 8$

[ocean seal]

CST

[carmine lion]

yes

[upbeat gorge]

actually i should insert descartes' rule of signs here

to show that there can be no positive roots

essentially you observe the sign changes in the equation

anyway, trying out smaller values to factor easily helps

again, -1 zeroes out and is thus a root

and then you can factor out (k+1)

leaving $8k^2+22k+15$

[ocean seal]

CST

[ebon relic]

Can someone please help

12 ,14,15

Someone please help me with this

[upbeat gorge]

are these all direct proportions?

huh, i think your teacher's crazy lol

especially for #12

[charred flint]

lol these problems are extremely scary

[alpine sable]

13. 86

I mean 82

[charred flint]

hints:
7 is close to 8
14 and 26 are even
159 is 10 more than 149

[alpine sable]

This is how we do them

Just cross multiply the proportions

[charred flint]

everything besides #13 isn't proportions

[alpine sable]

Oh wait let me see

what the heck are those problems

[upbeat gorge]

ye I was thinking "are they direct, or indirect, or..."

nope they're just crazy

[alpine sable]

I think 14) the answers 15

Not sure

[charred flint]

they're like riddles

[upbeat gorge]

ye

analogy problem ig

[alpine sable]

well in that case any answer for any problem is justified

[upbeat gorge]

secret operation or smth

for example #11 could be 8 since you divide the first term by 13 and add 3

[charred flint]

you have to add the rule of "find the relation of adding/multiplying/dividing that is the simplest"

[alpine sable]

I'd still say that's not well defined

[upbeat gorge]

find the best alternative is very vague lol

[charred flint]

ehhh they're pretty unique given the multiple choice part

[upbeat gorge]

I hate teachers who write "find the best answer" and sabotage their multiple choice so all the choices are wrong

[alpine sable]

I did the explanation

what if someone comes up with a slick relationship that fits but the person who wrote the problem wasn't thinking of that

[charred flint]

[upbeat gorge]

You nag them till they give in

12 can be 90

(n)(n+1)

[alpine sable]

14 is 15

15 is 268

They all have the logical formulas lol

They are like riddled

Riddles

[upbeat gorge]

yep

it's like that riddle where six is three and twelve is six, but ten isn't five

[blazing rose]

$\int_1^2 {x f'(g(x))}$

$\int_1^2 {x f'(g(x))dx}$

[oak chasm]

Ten is obviously four.

[blazing rose]

$\int_1^2 {x f'(g(x))dx}$

[ocean seal]

Josh.

[blazing rose]

can someone help me solve this integral with the given info

[ebon relic]

Yup I could not find a mental ability server so...

[charred flint]

reverse chain rule

[alpine sable]

I think the answer to 11 is 9 because in my opinion the rule is take the first digit and add 3 to it

[blazing rose]

no idea how to do that

[charred flint]

the integral of g' * f'(g(x)) is f

and here you have g' outside because x is close to the derivative of 5-x^2

[blazing rose]

i dont think i learned reverse chain rule

im in calc ab

[ebon relic]

Ok

[alpine sable]

uhh

I was making fun of the nature of the problem actually

don't take that as serious advice

[ebon relic]

Ok

Lmao

I am in 8th yall speakin latin to me

[charred flint]

eh just trust me on that rule then

it's fine to use if you've learned the chain rule

[blazing rose]

wait figured it out

i just set g(x) = u

so u = 5 - x^2

du = =-2xdx

-1/2du = xdx

replaced xdx with du

[charred flint]

looks good

[blazing rose]

yeee

[charred flint]

I forgot it's more known as u-substitution haha

[tawny lion]

can someone help please

[alpine sable]

I am getting these , hopefully I didn't made any mistake in solution

@tawny lion

[tawny lion]

thank you very much

let me see

my teacher just posted these problems in the middle of doing matrices

[alpine sable]

oh

[tawny lion]

I see what you did

I think that's right, thanks again

[alpine sable]

welcome

[tawny lion]

@alpine sable do you have any other practice problems of such nature

that you'd be willing to share

also, if anyone could help with this it would be really appreciated

[spice tendon]

I missed the lesson because I was at the hospital today, can somebody help me with this?

[tawny lion]

quadratic equations have the form ax^2+bx+c

in this one you have b = 4, a = 1

so therefore -b/2a = -(4)/2(1)

then input that value into the function to find y vertex

other part seems self explanatory

[blazing rose]

how do i do this

differentials?

[barren jacinth]

helpp

i'm stuck trying to solve for x

[tawny lion]

@alpine sable thank you

I did that, but is that the correct way?

[alpine sable]

This one??

[tawny lion]

yea

i don't see any other method

[alpine sable]

I’m not sure tho, but that’s how i do it

Did your teacher mention about what she is asking for?

[ionic jewel]

$\ln(\ln(x)) = 2 \to e^{e^2} = x$

[ocean seal]

bunny

[ionic jewel]

the first side is just a constant use a calculator

[tawny lion]

he, and nah

[ionic jewel]

yeah prettys approach looks right

combine the logs and cancel then simplify however you like after that

[alpine sable]

Can someone explain me this?

[vale wigeon]

@alpine sable still here?

[alpine sable]

Yes

[vale wigeon]

i'm a little confused at the wording of the problem as it seems a little redundant.
you say f'(x) ≤ 8, but then you say f'(x) ≤ 3 for all x?

either the latter implies the former, or there's a typo somewhere.

[alpine sable]

It’s both

[vale wigeon]

but why would you state both

if f'(x) ≤ 3 then it's guaranteed that f'(x) ≤ 8 too

are you absolutely sure you copied everything 100% correctly with no typos?

[alpine sable]

No I made a error

[vale wigeon]

see, that's what i'm trying to get at

[alpine sable]

Sorry let me write it again

[vale wigeon]

yes, please do that.

[alpine sable]

The statements are correct

This one is correct

[vale wigeon]

,rccw

[vale wigeon]

so now f'(x) ≤ -3

negative three

yes?

[alpine sable]

Yes

[vale wigeon]

ok

so you're asked to sort those statements into "guaranteed", "possible" and "impossible"

[alpine sable]

Yes

[vale wigeon]

ok, progress so far?

[alpine sable]

I don’t know how to start them

Like how do I determine it

[vale wigeon]

are you familiar with the concept of increasing and decreasing functions?

you might do well to try and visualize what the graph of y = f(x) looks like under the conditions that they state

[alpine sable]

Yes

[vale wigeon]

so given that f'(x) ≤ -3 everywhere, what can you say about f?

[alpine sable]

It’s the derivative of f(x)?

[vale wigeon]

???

read my question again please

so given that f'(x) ≤ -3 everywhere, what can you say about f?

what can you say about f itself?

what property does it have that will significantly simplify matters here?

[alpine sable]

I don’t understand, like is it less than -3?

[vale wigeon]

look i even prompted you with "increasing and decreasing functions"

the derivative of your function is bounded above by -3.

in particular this implies that the derivative of your function is negative.

now what do we know about functions whose derivatives are negative?

[alpine sable]

It’s decreasing?

[vale wigeon]

there we go.

yes.

your function is decreasing.

what's "it"

[alpine sable]

Never mind

[vale wigeon]

you have several "it"s here

idk which one you're talking about

[alpine sable]

This function is decreasing right??

[vale wigeon]

yes i literally told you

your function's derivative is negative

therefore the function itself is decreasing

[alpine sable]

Yes, I understood that part

[vale wigeon]

if you did you wouldn't have asked me about it again

[alpine sable]

Sorry I’m a bit confused on this topic

[vale wigeon]

this function is decreasing

[alpine sable]

Yes I get that

[vale wigeon]

if we have a decreasing function on some interval, at what point does it achieve its maximum on the interval?

[alpine sable]

At -infinity?

[vale wigeon]

on some interval

i didn't say "the whole number line"

i meant a closed interval to be more specific

[a,b]

[alpine sable]

Ahhh ok

[vale wigeon]

we have a decreasing function defined on [a,b]. where does it achieve its maximum?

[alpine sable]

0?

[vale wigeon]

why 0?

who said 0 was even a point in our interval in the first place?

[alpine sable]

Then how do we achieve its maximum??

[vale wigeon]

did it not occur to you to say "at the left endpoint"?

or "at x=a"?

[small stag]

It helps if you visualize it in your head

[vale wigeon]

yeah, imagine a graph of a decreasing function, over an interval

[small stag]

Can be as simple as y=-x if you want

[vale wigeon]

ayewaddup do you want to take this over

[alpine sable]

It’s like this right??

[vale wigeon]

this graph could use some more labels but yes

[small stag]

Uh lemme see the question Rq

[alpine sable]

This is the question

These are the statements

[small stag]

Gracias

[ionic jewel]

no

[small stag]

And these statements are all noted down correct?

[alpine sable]

Yes

[small stag]

Sorry this Channel is busy

It’s just that it says f’(8) is less than 8 and also less than 3 in the next line

[alpine sable]

No don’t mind that part

[ionic jewel]

she updated the statement in the second ss

[alpine sable]

Yes

Only a,b,c,d parts

And I rewrote the question

[ionic jewel]

okay ann pretty much gave you part a

[small stag]

Ah then I apologize

Will reread

Ok so did you understand the reasoning for a?

[alpine sable]

Yes, the function is negative, so it would be decreasing

And it’s possible right?

[ionic jewel]

its more than possible

but that means you dont understand why

[small stag]

It would have to be guaranteed

Yes

Okay so

Hold on I’m tryna

Okay so f’(x) <= -3 right?

[alpine sable]

Yea

[small stag]

And the derivative tells us by what degree the function changes at every point

Or in other words the slope of the tangent line at every point

Now if the slope of the tangent line is always lower than -3

Can we agree that the slope is always negative?

Channel taken

[alpine sable]

Yes

And it’s decreasing

[small stag]

Good

Now it’s forget about that for a second

Say I have another decreasing function

Like y = -x^3

Sorry channel is taken you’re going to have to wait for one to be free

[ionic jewel]

hes also taking an exam so thats very against the rules

[small stag]

And say the interval [-3, 3]

Do you know what -x^3 looks like?

[alpine sable]

Yes

[small stag]

Ok so

Without any math

Where is the maximum

On the interval [-3, 3]

[alpine sable]

3

[small stag]

And why do you say this?

[alpine sable]

Because i think it’s the highest point on the graph

[small stag]

Let’s take another example

Say y = -x

Same interval

Is it increasing or decreasing

[alpine sable]

Decreasing

Since it’s negative

[small stag]

Good work

And what’s it’s maximum

In [-3, 3]

[alpine sable]

-3 ?

[small stag]

And why do you say this

[alpine sable]

Because the function is decreasing and the maximum should be negative?

[small stag]

Think about it this way

If a function is decreasing right

That means as you go to the right, it will go downward

[alpine sable]

Yes

[small stag]

And as you go to the left

It will go upward

[alpine sable]

It goes up

[small stag]

Good

I want you to reword your reasoning for y=-x

First half is correct

[alpine sable]

The function is going right and it’s negative and it’s going downwards

[humble wyvern]

yo i have a question

[small stag]

Ask in a free channel

[humble wyvern]

kk

[small stag]

Better but I think you’ve gotten the conceptualization aspect so I won’t push it

Now for y = -x^3

On [-3, 3]

At what x does it reach its maximum

[alpine sable]

-3

[small stag]

Good

You cannot go more to the left

Which means you cannot go more upward

[alpine sable]

Yes

[small stag]

And that means no matter what -3, our lower bound, is our maximum

That’s gonna be the conclusion we use for a

[alpine sable]

Yes I got it now

[small stag]

With that knowledge explain to me why a is guaranteed

[alpine sable]

The function is increasing since its positive

[small stag]

why is it increasing?

[alpine sable]

5 is the maximum value

[alpine sable]

Because it’s positive?

[small stag]

What is positive

[alpine sable]

Oh wait, so they alr gave the absolute max

[small stag]

The min and max don’t matter yet

You need to classify whether the function is increasing or decreasing

[alpine sable]

How do we draw a graph for this tho?

[small stag]

Do we need a graph?

[alpine sable]

We need it to determine whether it’s going upwards or downwards?

[small stag]

What’s the first derivative of y = -x

[alpine sable]

-1?

[small stag]

Good

[winter bay]

just ask dont ask to ask

[small stag]

And -x^3?

[alpine sable]

-3x^2?

[small stag]

Good

Now is -3x^2 always negative, positive, or both

[alpine sable]

Negative

[small stag]

So do you see how when our first derivative is always negative

Our function is decreasing?

[alpine sable]

Yes

[small stag]

Atleast within a certain interval

That’s all we care about rn

So

[alpine sable]

Ok so since the first derivative is -3 it’s decreasing

?

[small stag]

It’s not -3

It’s <= -3

[alpine sable]

Yeah

[small stag]

Which means it will always be a negative number

[alpine sable]

Yeah

[small stag]

So yeah decreasing

And what did we say about decreasing functions on certain intervals?

[alpine sable]

It would be Guaranteed?

[small stag]

That’s not what we said

It’s about maximums

And decreasing functions

[alpine sable]

Oh yeah, it would be negative??

The maximum would be negative??

[small stag]

What?

Ok we said that the lower bound would be the maximum always

[alpine sable]

Yes

[small stag]

Cause you can’t go higher from that

So what’s our lower bound

For a

[alpine sable]

1

[small stag]

And what’s f(1)

[alpine sable]

8

[small stag]

So is 8 the absolute max?

[alpine sable]

Yes

[small stag]

Now b

If f(x) = 0 at two different x’s

It requires the graph to pass through the x axis and then come back up again

Implying that at some point we have a relative maxima or minima

Or the derivative = 0

Is this possible?

If so is it guaranteed?

Sorry I have to sleep

[alpine sable]

No it’s not possible right?

[small stag]

Hopefully you can get the rest it’s just late for me

Good it’s not possible

[alpine sable]

Yes I will figure them out

Thank you and sorry!

[small stag]

And the final two are the same logic

No problem

[alpine sable]

Yes I got it now!

[small stag]

I’ll leave you with this

If f’(x) at its highest can be -3

That means atmost f(x) is linear

Just see if those points fall on or below the line

If above it’s not possible

If below it is

Gn!!

[alpine sable]

Gn and thanks again!!!

how do i know which function comes first?

[vale wigeon]

you can take their difference, whichever way you want, and check if it's positive or negative in your interval

and if it's negative, multiply it by -1 before proceeding

[foggy onyx]

In 40° right triangle, apply TOA to find the value of opposite having 12m adjacent

a. 10.06
b. 10.05
c. 10.04
d. 10.07

can someone help me rn

btw this is not an exam

its a homework but multiple choiceses

im having some trouble

i tried to answer it but i got 90.09m

[vale wigeon]

one moment

@foggy onyx so how exactly did you get 90.09 m?

it doesn't look like it comes from a degree vs radian mode mishap

[foggy onyx]

i used toa elevation formula

[vale wigeon]

"toa elevation formula"?

[foggy onyx]

mhm

theres toa depression and toa elevation

[vale wigeon]

??

what are you talking about

[foggy onyx]

Angle of Elevation TOA
Angle of Depression TOA

but since its finding the opposite i used the elevation one

[vale wigeon]

???????

why would there be two different formulas for that

[foggy onyx]

im so confused also can u just answer for me

whats your answer

[vale wigeon]

no we don't give out answers

[ionic jewel]

is TOA the trig memorization thing?

[vale wigeon]

i don't know what elevation or depression you're talking about when all you have is A SINGLE RIGHT TRIANGLE

x/12 = tan(40°)

i see no need for this overcomplication with "angle of elevation" vs "angle of depression" which really only make sense when you're considering like... lines of sight in a "physical" setting

[foggy onyx]

okay okay

[vale wigeon]

and even then the only difference is in how the relevant triangle is positioned

[foggy onyx]

so whats the answer

[vale wigeon]

no i'm not telling you the answer

[foggy onyx]

;-;

[vale wigeon]

you can and should calculate it yourself

x/12 = tan(40°); find x

[foggy onyx]

my homework needs to be pass at 3

90.90m

[vale wigeon]

no

tan(40°)*x = 12 is wrong

[foggy onyx]

...

[vale wigeon]

and tan(40°) isn't even 1.32 so your calculator IS in radian mode when it should be degrees

[foggy onyx]

i was just following the formula in my notes

its on deg

[vale wigeon]

tan = opp/adj.

your adjacent is 12

your opposite is x

tan(40°) = x/12

this does NOT give tan(40°)*x = 12.

[foggy onyx]

OOPS OMG YES

[vale wigeon]

just like z/4 = 5 does not give 4 = z*5

[foggy onyx]

I DIDNT NOTICE LOL SORRY

[vale wigeon]

THIS IS WHAT IVE BEEN TRYING TO POINT OUT

[foggy onyx]

I already tried that formula

it comes up at 9.96m

[vale wigeon]

??

can you use your calculator right now and tell me what you get when you calculate 12 * tan(40)

in DEGREE mode mind you

[alpine sable]

e

[foggy onyx]

okayyyy soooo what now lmao @vale wigeon

[vale wigeon]

bruh

[foggy onyx]

im really confused

[vale wigeon]

how in the fuck

do you write

[foggy onyx]

;-;

[vale wigeon]

tan(40)*12 = x

and then IMMEDIATELY AFTERWARDS

turn that multiplication magically into a division

[foggy onyx]

im shorcutting it..

[vale wigeon]

no you're not

you literally took a multiplication symbol and replaced it with a division

[foggy onyx]

im following this method

[vale wigeon]

do you even algebra

[foggy onyx]

dont notice the writting

[vale wigeon]

do you even algebra

[foggy onyx]

kinda

can you give me the formula for solving

written on the notebook

[alpine sable]

They are doing a different problem

[vale wigeon]

it's no use giving you formulas when you're shaky with your algebra

you seem to like. not understand what you're doing algebraically

and i'm not in the right headspace to clear that up rn

[foggy onyx]

I KNOW HOW TO SOLVE I JUST HAVING A HARD TIME ON THE FORMULA

[vale wigeon]

YOU LITERALLY TURNED X = 12TAN(40) INTO X = TAN(40)/12 AND CALLED IT "SHORTCUTTING"

[vale wigeon]

i even told you this

but no

[alpine sable]

He’s blindly following the example

[foggy onyx]

;-;

Okay okay

[alpine sable]

Just multiply tan40*12

[gray isle]

the location of you values changes depending on the question
start with soh-cah-toa
the rest is algebraic manipulation

[vale wigeon]

prettygirl i already told him to do that but he chose to ignore me

or just not read the message

or maybe it wasnt a conscious choice

[foggy onyx]

okay

[vale wigeon]

but still

[foggy onyx]

IM SO DUMB

ONG LOL

ITS 10.06

[alpine sable]

Yes that’s right

It’s 10.06

[foggy onyx]

IM SO SORRY FOR DISTURBING YALL OMG LMAO

[vale wigeon]

no

it's not 10.06, it's 10.07

round properly

[foggy onyx]

but though thanks

[vale wigeon]

,calc 12 * tan(40*pi/180)

[ocean seal]

Result:

10.069195574127

[alpine sable]

Yes by rounding it would be that

[vale wigeon]

10.069 rounds to 10.07

[foggy onyx]

so 10.07?

[alpine sable]

Yes

I think you can do the Pythagorean theorem from here

To get the hypotenuse

Since you have two sides

[vale wigeon]

you dont need that

all that was asked for is the oppoosite

so the correct course of action from here is to acknowledge that we are DONE with this problem and to move on

[alpine sable]

Oh yeah!

[foggy onyx]

Okay i sent my homework, im really sorry for stressing you out from that stupidity of mine lol @vale wigeon

[vale wigeon]

i was already somewhat stressed out

you didnt add much

[foggy onyx]

and though im not kinda into math but im slightly reading algebra book i only know the polynomial methods LOLa

[alpine sable]

is anyone able to help me with d?

[vale wigeon]

are you allowed to use the fact that $t + t^{-1} \geq 2$ for positive $t$?

[ocean seal]

Ann

[vale wigeon]

because i have a feeling it'd be much much easier to do (d) using that than using part c