help-10

[forest sinew]

and multiply it by 1, plus 0.06

1600*1.06

this is the amount you make during the second year

this operation is equivalent to a 6% raise

so how do you get the second 6% raise now?

[autumn lintel]

by raising the power to 2

right

[forest sinew]

yea

wed get a 6% raise on 1696

so 1696 * 1.06

but 1696 is just 1600 * 1.06

so 1600 * (1.06)^2

this is how much were making beginning the end of the 2nd year

so lets say

year n starts

how much are we making

at the start of the nth year, how many raises have we had?

year 0 we had 0

[autumn lintel]

so n year we have n?

[forest sinew]

i think so, yea

we might have off by 1

but we can sort it out

[autumn lintel]

1600(1.06)*n

[forest sinew]

alright

who starts saving first

[autumn lintel]

scheme a left... b right ... so its a right

[forest sinew]

surprising

okay we need to reason out whats going on with that 7.65

with regards to starting saving

then you can answer the second question

[autumn lintel]

what do u mean by that

like it takes him 8 years?

[forest sinew]

yea

so you know when they start saving

and how much they make in any given year

and how much of their salary they save

so should be able to approach the end now

[autumn lintel]

oh okay so thats it i guess

thanks for your help mate

appreciate it

[forest sinew]

nno prob

[autumn lintel]

.close

[obtuse pebble]

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[covert stratus]

Hi, I want to find the values of B0 and B1 from pi 0 and pi 1

[covert stratus]

Shouldnt the denominator for both B0 and B1 be (1+ pi 1) instead of minus

<@&286206848099549185>

[obtuse pebble]

@covert stratus Has your question been resolved?

[brisk matrix]

@covert stratus how did you get that?

the denominator for b1 should be 1 + pi1 like you said

[covert stratus]

For b0 also

i guess it should be 1+ pi 1

?

[obtuse pebble]

@covert stratus Has your question been resolved?

[obtuse pebble]

@covert stratus Has your question been resolved?

[obtuse pebble]

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[frank shell]

i have this function :

f(x) = x^3 - 2x + 5 if x < -1
x+3 if x >= -1

question is to calculate the limit of f(x) as x goes to -1. how can i do that ?

i tried doing the following:
lim(x->-1) f(x) = lim(x->-1) x+3 = -1+3 = 2
but its wrong.

[formal bear]

How to solve this question without a calculator?. The 1st one

[frank shell]

dude use another channel please

[formal bear]

Sorry my bad

[frank shell]

its ok i swear

love you

[frank shell]

.

[rough stratus]

Solve the piecewise func

https://youtu.be/OYOXMyFKotc

If you don't know how to solve piecewise func

@frank shell

[frank shell]

no

i dont need to solve it

i just need limit

[rough stratus]

I'm pretty sure it is included in this video

[frank shell]

okay thanks.

thanks a lot.

love you.

❤️

[rough stratus]

https://youtu.be/JrYmEo6hoiU

Waiit

[frank shell]

oh

[rough stratus]

Here is a separate one

[frank shell]

thank youm

thank you.

[rough stratus]

Np

:)

[frank shell]

really thank you.

i love you.

❤❤❤

[rough stratus]

Thanks :D

[frank shell]

.close

[obtuse pebble]

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[charred solar]

.

hello

[charred solar]

The rectangle ABCD has vertices at A = (1,2,3) , B = (3,6,-2), C = (0,5,-4) Determine the cords. of vertex D

how would you approach this problem?

I just learned about the angle between two vectors so i have to find a vector that is perpendicular to one of the corners

[obtuse pebble]

@charred solar Has your question been resolved?

[charred solar]

<@&286206848099549185> 🙂

do i need to further explain my question?

[dim root]

@charred solar hello

Are you sure its a rectangle? If so D could be anywhere

Normally it says parallellogram

[charred solar]

yes it says rectangle ABCD

i just learned about

i think i have to use cos x = 0

[dim root]

Been a while since last time i did vectors...

[charred solar]

ohh

[dim root]

@charred solar can you show the whole question in its entirety

I feel like some detail is missing

[charred solar]

sure ill make a picture

[dim root]

Thats called the scalar product also

35 right?

[charred solar]

yes

[dim root]

@charred solar does the question assume a rectangle has 4 square corners?

[charred solar]

that's the definition of a rectangle right?

so i think so

[dim root]

I think lmao

Been a long long time since that

Ok then its great i can solve it

[charred solar]

oke cool how would you solve it?

[dim root]

AD//CB

Meaning that dvec x a vec=0

Scalar product rule of 90 degree angles

[charred solar]

what do you mean with '//'?

[dim root]

Parallell

[charred solar]

ok , ok

oke wait let me try somethign

this is 0 but then i can put any scalar in front and it will still work

[dim root]

Here is how you’d solve it

We know that |CB|=|AD|

We know that the angle CAxAD=0

Im just googling how tf you made vectors of two points

[charred solar]

with |CB| you mean leanth of CB right?

[charred solar]

yes

[dim root]

Yes

@charred solar

We know that D is A+CBvector

We can also find it by taking the absolute value+angle

[spiral maple]

You do know you can draw rectangles in 2D right? Just because you have R^3 vectors, you don't need to draw it in 3D

[dim root]

Vectors suck

Only part of math i just dont like

[charred solar]

thanks im looking over it rn

[timid silo]

how to open my help channel

i dont know

[charred solar]

go to the help channels above

[timid silo]

i did not understand -_-

[charred solar]

the cb vector is the sqrt(14) ?

or (3 , 1 ,2) <-i think this

but if i add A (1,2,3) io get (4,3,5)

which give the wrong answer it should be D(-2,1,1)

[timid silo]

I got $ \begin{pmatrix}
-2\
-2 \
-1
\end{pmatrix}?

[warm shale]

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

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

[timid silo]

This is what i got. ^

[charred solar]

i think the answer(-2,1,1) is right

[timid silo]

I must gave made a mistake then

[charred solar]

oh i see you used the wrong vector

(0,2,-6) should be (0,5,-4)

wow it was so much easier then i thought

@dim root and @timid silo thanks for the help!

[timid silo]

All’s good

[charred solar]

.close

[obtuse pebble]

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[burnt solstice]

how would i find the area of the shaded part of the fan shaped- shape (ABC)

[dusk nexus]

8 is the radius

try and find teh area of the triangle and the area of the quarter circle separately

[deft hazel]

Is the curve 8 cm or is the leg

[burnt solstice]

the leg is 8cm

[dusk nexus]

right

[deft hazel]

Yeah so what the guy says

[burnt solstice]

ph wait i understand now

[deft hazel]

Area segment = area sector - area triangle

[burnt solstice]

yeah yeah

I just had to quarter a circle and subtract from it with the triangle

[obtuse pebble]

@burnt solstice Has your question been resolved?

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[civic jasper]

I am close to the answer but I think a minor step away

(The answer I have gotten is 1440 but the answer given is ||2880||)

Considering lions as / and tigers as - -

Possible combinations are:

1. /-/-/-/-
2. -/-/-/-/
3. /--/-/-/ (with /-/--/-/ and /-/-/--/ as iterations)

For the 1st combination:

Total possible combinations must be: 4! x 4! (576)

For the 2nd combination:

Total possible combinations must also be: 4! x 4! (576)

For the 3rd combination:

Internal combinations of the joint-tiger-pair = 2! or 2
Combinations of all tigers = 3! (considering the joint pair as a single item)
Combinations of the lions = 4!

Total possible combinations = 2! x 3! x 4! (288)

Adding all of these up (adding, since they are unrelated) we get:

576 + 576 + 288 (1440)

||The answer is exactly double of mine's, so I suspect there is some kind of flipped version of the arrangements||

Could someone please point out where I forgot something?

Thanks in advance

(Also, I am not too fluent in mathematical terms so please excuse me if I stated anything wrong)

[timid silo]

why would lion and tigers want ice cream

[civic jasper]

my first response was lions are communal animals who would want to stay together instead of tigers (solitary) who would wanna stay apart

biology and animal science isnt really their strong subject

[unborn valley]

-L-L-L-L- there are 5 possible gaps from tigers to choose from

wtf

so 5c4

5c4 4!4!

[civic jasper]

yea, but 2 tigers cant be simultaneously at the sides, right? (since that would allow two lions to get into contact)

[civic jasper]

trying that out, one second

[civic jasper]

it worked

thanks a ton (tho i think i'll have to reread everything again)

[unborn valley]

yes

[civic jasper]

.close

[obtuse pebble]

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[pallid raft]

pls give 2 examples of solving systems of equation by elimination

[cedar lichen]

That seems like something you could find by searching "system of equations by substitution examples"

[pallid raft]

that wont work bc my math teacher checks google everytime

i just need examples no need to solve

[cedar lichen]

Any system of equations can be solved by substituting, so theoretically any system of equations will work

Elimination?

Same thing

[pallid raft]

yeah

[civic jasper]

bring in an equation from google and change the variable names and constants to something appropriate that still works
(although i think cheating on academic things is forbidden here)

[pallid raft]

the thing is that the examples i used in substitution can't be used in elimination examples otherwise it wouldn't count according to my teacher

[pallid raft]

hmm

[cedar lichen]

If you want an easy elimination example, just make a system of equations where the coefficients on x are the same

[pallid raft]

alright ill try doing that

thank you

.close

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[trim island]

Am I allowed to do this ?

[high lily]

,w rotate

,rotate

[high lily]

yes

[trim island]

Idk why it feels so wrong even though it makes sense

Thanks

.close

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[charred solar]

.close

.close

[obtuse pebble]

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[elder lichen]

if A union B equals A, then B is either empty set or A?

[sage geode]

$A \cup B = A \iff B$ is a subset of $A$

[warm shale]

Touch Our Beans

[elder lichen]

.close

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[static patio]

how to solve this limit ?

[mental cloak]

is n a odd number?

[static patio]

n approaches infinity

[mental cloak]

yeah, sry stupid question ^^

[turbid cedar]

not stupid question

[turbid cedar]

the answer would be 0

[turbid cedar]

first multiply by 1/3^n and divide by 1/3^n

[static patio]

hmm

[turbid cedar]

does the rest seem trivial ?

[static patio]

whats next? i know that sinx/x = 1, but x must apprroach 0

[turbid cedar]

yes

so 1/3^n approaches 0 when n approache infinity

so sin(1/3^n)/(1/3^n) approaches 1

got it ?

[turbid cedar]

?

[static patio]

yes i got it

[static patio]

thanks

[turbid cedar]

ok

[static patio]

.close

[obtuse pebble]

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[obtuse pebble]

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[charred solar]

when calculating the distance from the point B why do they use the distance from B to the n

are they the same length? if so why? i don't think they are

[spiral maple]

A to where the projection ends on n will have the sane length as BP

A B P and that point form a rectangle.

[charred solar]

but if you do this in 2d it doesn't make any sense

actually it does

i thought the length was a to p

[spiral maple]

Nope, B will end up somewhere on n.. the projected distance is the same as BP

[charred solar]

yup

thank you for helping 🙂

[obtuse pebble]

@charred solar Has your question been resolved?

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[graceful cliff]

Is it possible to find inverse of the function f(x) = |x|? And if so, what are the steps to find it?

[cedar lichen]

The function doesn't have an inverse, at least, not an inverse function. Since both -1 and 1 give you 1, then the inverse will map 1 to both -1 and 1. A function can't map one x value to two different y values

[graceful cliff]

The inverse one doesnt have to br a function, i just want to find the inverse of this equation

Does it need to be a function to inverse it?

[cedar lichen]

No. You can have an inverse relation

Do you know the piece wise definition of y=|x|?

[graceful cliff]

Yes, for x>0 y=x and x<0 y=-x

[cedar lichen]

So what's the inverse for y=x and y=-x?

[graceful cliff]

Well its the same for y=x

And the same for y=-x too?

So i get two seperate functions when i do it?

[cedar lichen]

Yes

What's going to happen is that for some input x, we're going to get both ys out

So well get both x and -x, aka, ±x

[graceful cliff]

So we get β=±x

Thanks

[cedar lichen]

Yeah. The inverse of y=|x| is y=±x

[graceful cliff]

.close

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[worthy cargo]

https://gyazo.com/f27fe90c0b30783c9ebac97fe7b7cbf0

For this question i made 2 equations

h + w = 2

.36h + .04w = .24

I then looked up the correct way to set up the equations and it was instead for the second equation

.36h + .04w = 2(.24)

can anyone explain why the two is there

[spice bay]

cuz there is 2 cups that have .24% of butterfat

[worthy cargo]

@spice bayya but why need to represent that, wouldnt it be 2(.36h + .04w) = 2(.24)?

which simplifies down

[spice bay]

each cup of heavycream has .36% butterfat
and each cup of milk has .4% butterfat
but you need 2 cups of a mixture of those two, such that each cup has 24% butterfat

[worthy cargo]

ohok i see

thank you

.close

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[mystic saffron]

can someone help on how to find x

[wary vigil]

you have two similar triangles

[astral ivy]

Yeah

[wary vigil]

do you know how the sides of similar triangles relate?

[mystic saffron]

bro

im stupid

thanks

.close

[obtuse pebble]

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[arctic ridge]

can someone explain how to solve this ?

[cedar lichen]

Write a system of equations. Let x be the pricr of a pen and y be the price of a pencil

[arctic ridge]

like this ?

[cedar lichen]

Not just x + y. He didn't buy 1 pen and 1 pencil

[arctic ridge]

29,75 $ for 12 pens and 7 pencils

[cedar lichen]

Yes. x is the price of 1 pen and y is the price of 1 pencil

[arctic ridge]

so how do find how much it will cost to buy 15 pens and 4 pencils

[cedar lichen]

We're gonna get there

[arctic ridge]

okay what do i do next

[cedar lichen]

For now, use the given to write a system of equations. 12 pens and 7 pencils is $29.75. How can we write that in terms of x and y?

[arctic ridge]

29,75 = x + y ?

[cedar lichen]

x + y is the price of 1 pen and 1 pencils, not 12 pens and 7 pencils

[arctic ridge]

x + x + 0,50

[cedar lichen]

Stay on the first thing. If 1 pen is x dollars, how many dollars is 12 pens?

[arctic ridge]

x times 12 pens

[cedar lichen]

Yes. In other words, 12x

Now, if 1 pencil is y dollars, how many dollars is 7 pencils?

[arctic ridge]

7y

[cedar lichen]

Yes

So how many dollars is 12 pens and 7 pencils?

[arctic ridge]

12x + 7y = 29,75

[cedar lichen]

Yes

There's our first equation

We're also given that a pen is 0.50 more than a pencil. How do we write that in terms of x an y?

[arctic ridge]

12x + 7 (x + 0,50) = 29,75

[cedar lichen]

Not quite

That equation is saying y = x + 0.5, in other words, y is 0.5 more than x

This is the wrong way around

[arctic ridge]

x - 0,50

[cedar lichen]

Yes, that'll work

So now we have 12x + 7(x - 0.5) = 12.75

Now we solve for x

[arctic ridge]

thanks i can handle the rest from here i just had trouble writing the equation

[obtuse pebble]

@arctic ridge Has your question been resolved?

[obtuse pebble]

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[untold cave]

\begin{table}[]
\begin{tabular}{lllll}
& D & I & & \

• & u & dv & & \

• & du & v & & \

• & ... & ... & &
  \end{tabular}
  \end{table}

[warm shale]

JSGF

[untold cave]

Ok, so for DI method for integration by parts, how would the notation to write the ellipses be?

Like $d^2 u$, etc. ?

[warm shale]

JSGF

[untold cave]

Or maybe $du du$

[warm shale]

JSGF

[spiral maple]

you'd never write this so... idk what your point is

[untold cave]

To show what DI method consists of to someone epse

[spiral maple]

You'd always have the u and dv functions if you're doing tabular

[untold cave]

Else

[spiral maple]

use an example

or.. words

words exist too

[untold cave]

I mean I don't know If I am allowed to use it in a test so I explain it visually, so that the teacher does not think it makes no sense

I find DI method way more convenient than the udv = uv- vdu

[spiral maple]

DI is just a shorthand for doing IBP..

[untold cave]

This will siffice I think

[spiral maple]

But, have you asked your professor if you can use it or not.....?

[untold cave]

Yeah, but you dont need to remember the formula

[spiral maple]

...

It's a shortcut not a replacement

Tabular is just a way to keep everything in 1 place and neat, you're not replacing IBP with it

Besides, Tabular has it's downsides

[untold cave]

I know

Actually

I asked him if I could use tabular for all exams including the university entrance exam. He said that he had never seen it, thus, to ensure, he told me to use the conventional method.

As you said, tabular is neater-and faster writing wise- than conventional method, that's why I use it.

I thought that maybe if I explained the method during the exam there would be no problem. That's why I asked for the notation doubt.

That's all.

[obtuse pebble]

@untold cave Has your question been resolved?

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[obtuse pebble]

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[mighty ether]

is it wrong to write the perimeter as this to start with?

[mighty ether]

or would i be double counting the x ?

[hushed moat]

yea, you don't include the red x in the perimeter

[mighty ether]

mhm okay thanks

.close

[obtuse pebble]

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[storm wagon]

How can I simplify this: 2a√(1-a²)/1-2a²

[storm wagon]

Orr lemme ask another question
If cos72=a then what's the value of tan36?

I solved like this:
a=cos2.36=2cos²36-1=1-2sin²36 (from formula)

a=2cos²36-1
a+1=2cos²36
(a+1)/2=cos²36

a=1-2sin²36
a-1=-2sin²36
1-a=2sin²36
(1-a)/2=sin²36

sin²36/cos²36=tan²36=((1-a)/2)/((a+1)/2)
tan²36=(1-a)/(a+1)
tan36=√((1-a)/(a+1))

But in my teacher's solution:

I used third and fourth formulas in my solution and my teacher used last one.

<@&286206848099549185>

[zinc flax]

can u tell the question ?

[storm wagon]

@zinc flax

[zinc flax]

use this
cos2A=

since cos72=a

which is cos2(36)

[storm wagon]

Actually, I solved but my answer isn't same with my teacher's solution :,,,)

And couldn't understand what's my mistake

[zinc flax]

k let me look into it

[storm wagon]

Or maybe the answer of my teacher can be simplified

[zinc flax]

both seems to be correct so they are just alternative forms

[storm wagon]

Oh, I understood

Do you think the answer of my teacher can be simplified?

[zinc flax]

yes we can

but I've to try it

[storm wagon]

if you give me a hint about what to do, then I can continue maybe?

[zinc flax]

u mean u need to make the end term same ?

[obtuse pebble]

@storm wagon Has your question been resolved?

[storm wagon]

yup.

[zinc flax]

ig that wud be difficult as what u take here is cos72 and there is sin18
and answer doesn't contain angles to tranform

[storm wagon]

Oki, I got it. I agree with you.

Thank you for your help :3

.close

[obtuse pebble]

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[zinc flax]

np

[obtuse pebble]

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[pallid bolt]

ok

[pallid bolt]

so

i believe that it is A

except i don't know what to fill in the boxes

P(three) = 1/13

i know that much

but
P(three|club) = ?????????

im stuck

on that, and i dont know what it would be, i already tried 1/13 for that as well, beacuse out of 13 clubs there is only a single three card, but its not correct for some reason
unless of course it is B but i am wrong

...........

it was B, my blank fills were correct at 1/13

[unborn valley]

P(three|club) The probability of event A and event B occurring.

[pallid bolt]

keeping channel to myself in case i have another question

i already got the answer for that one @unborn valley

but thanks anyways!

[unborn valley]

oklol

[pallid bolt]

i got .4125 by doing
.75 (is the chance the flight oesnt leave on time)
.75 x .55 = .4125

its not correct

@unborn valley you still there?

might need you

its ur time to shine

[unborn valley]

isn't it only asking for probability that her luggage arrives at denver

[pallid bolt]

yeah

but i dont understand

how to get that

my math teacher isnt good at teaching

[unborn valley]

that is 0.9 and 0.55, the probability

[pallid bolt]

oh i was overthinking it

[unborn valley]

so 1/4 time the probablity is 0.9

[pallid bolt]

yeah i was just boutta do .9 x .55

once i thought it over

[unborn valley]

and 3/4 time it is 0.55 ??

[pallid bolt]

answer is not .9 x .55

i just tried it

i got 1 attempt left.

should i just ping a helper

cuz if ur putting ?? i dont feel that confident

ye ill just ping

<@&286206848099549185> would love some help!

[unborn valley]

yes ping lol

[pallid bolt]

ping me when u arrive helper

this is a link to where my problem starts

#help-10 message

[twilit loom]

@pallid bolt have you tried drawing a tree diagram for this problem?

[pallid bolt]

no i have not

honestly didnt think it would be necessary for it

[twilit loom]

never hurts to be careful

[pallid bolt]

i could try really quick and ping u with what i think the answer is based on that

when im done

[twilit loom]

sure thing

[unborn valley]

avg of (0.25)(0.9) and (0.75)(0.55)

I guess?

[twilit loom]

no need to average

but that's almost there

[pallid bolt]

umm

alright

a few more seconds

[twilit loom]

no rush

[pallid bolt]

so with a tree diagram

it gives me probabilities for 4 outcomes

but i would not know what one answers the question

[twilit loom]

and how many of those four outcomes have the baggage arriving with Sarah?

[pallid bolt]

it

wait

if her flight leaves on time, and connected (it lands with her) its a .225 chance

if her flight is delayed but it connects and lands with her, its .4125 chance

but .4125 i've ruled out already

as wrong

so it's got to be 22.5%

[twilit loom]

no need to rule out everything

[pallid bolt]

well i already entered it thinking it was the answer, website told me its wrong

[twilit loom]

do you notice how if you sum the probabilities of all four possible outcomes together, it's 1?

[pallid bolt]

ill double check that ^

[twilit loom]

that's because those four account for everything that could possibly happen to Sarah

[pallid bolt]

well yeah i know that much

i just suck with understanding wording

sorry if i sound rude

[twilit loom]

but we only care about two cases: if flight leaves on time and the baggage arrives with her, or flight is delayed and the baggage arrives with her

that means we can simply add together the probabilities of those two cases

[pallid bolt]

everything from my tree diagram does add up to 1, so i did do it correct

OH you are supposed to add them together?

that makes sense

[twilit loom]

yup

[pallid bolt]

because it wants to know the TOTAL

not just for 1 situation

.6375 is the answer

[twilit loom]

exactly, there's more than one outcome that leads to what we want

tree diagrams help up see cases more easily

[pallid bolt]

yeah tree diagrams, ven diagrams, two way tables

all pretty helpful

ok i do have

one more problem though

that i am lacking understanding

on

i got a correct, cuz no brainer

but B i am struggling on

i tried .65 x .9

im realizing

that is instantly a mistake

because it feels like something isnt being represented

im confused on how iwould even start a tree diagram

but ill try it rn

[twilit loom]

think about picking a random student from freshmen year when drawing your diagram

[pallid bolt]

yeah that doesnt make sense to me ^

i am terrible, with understanding wording

[twilit loom]

if we pick a random student, what's the probability that they attended a public school?

[pallid bolt]

.7

PS = public school

G = graduate

so

oh wait

this is another one of those

that i need to add the probabilities

it just clicked

[twilit loom]

that colour is so painful to read, but yeah you got the idea

[pallid bolt]

yeah, i used snipping tool :p

it was painful to write in too

.7 x .65 = .455

.3 x .9 = .27

.455 + . 27 = .725

72.5% of freshman graduate

[twilit loom]

,calc 0.70.65+0.30.9

[warm shale]

Result:

0.725

[twilit loom]

noice

[pallid bolt]

thank you tons <3

[twilit loom]

^^

[pallid bolt]

i got 2 more problems in my thing, ill keep the channel open just on the occurence i need help, but i will try everything out before i do that

am i free to ping you in specific if i wind up needing help?

[twilit loom]

sure

[pallid bolt]

<3

[twilit loom]

I'll be upset if you ping me without drawing a tree diagram first though

[pallid bolt]

haha

yeah

i will try to do everything out on my own for the most part

for these last two

[twilit loom]

[pallid bolt]

gotta do the learning process, not the spoon feeding process

my friend said

im really good at understanding things

once i repeat them back

but i suck when im just trying to do it

and i dont speak it out

[twilit loom]

it's always worth it to step back and refresh your perspective when problem solving

[pallid bolt]

yeah

.15*.2 = .03

.85 x .45 = .3825

. 03 + ..3825 = .4125

hmm

incorrect

time to double check

[twilit loom]

think about what .4125 represents

[pallid bolt]

oh

wait

right

its the probability her stuff never made it

i need
P(flight delayed)

which is why im confused because i gurantee the answer is not .85

[twilit loom]

technically you need P(flight delayed | stuff never made it), but I'll explain that later

[pallid bolt]

hm alright

probably doesnt help i missed a day of class the day this was due

[twilit loom]

so the .4125 probability that her stuff never made it is a guarantee by the question right?

within that .4125 is all the possible cases we can examine

[pallid bolt]

yeah

[twilit loom]

so within that .4125 probability, what's the probability that her flight was delayed?

[pallid bolt]

im not quite sure i can answer that

unless the answer is .85

[twilit loom]

not quite

[pallid bolt]

this has me scratching my chin

is there an equation im missing

[twilit loom]

we know that the luggage didn't make it, and we're looking for the probability that her flight was delayed given that we know that the luggage didn't make it

[pallid bolt]

ok so

[twilit loom]

so that would be the probability of the luggage not making it AND the flight being delayed, right?

[pallid bolt]

im trying to think of

how to write it now

gimme a sec

p(A|B) = (.4125 + .85) / (.4125)

would it be that?

[twilit loom]

did you forget some parenthesis?

[pallid bolt]

yeah

[twilit loom]

notice how that would give you a number bigger than 1, which is kinda fishy

[pallid bolt]

usually they would be underneath eachother

and yeah that is

doesnt seem right

[twilit loom]

P(A|B) = (probability of A and B happening)/(probability of B happening)

P(A|B) = (flight delayed and luggage isn't there)/(luggage isn't there)

[pallid bolt]

wait, why would you divide it by B

dont you always divide it by A?

[twilit loom]

hm, I've never seen that

the notation I'm using is P(A|B): the probability of A given B

[pallid bolt]

oh nope

have my equation backwards in my head

thats why

i messed up

P(A given B) = P(A and B)/P(B)

right?

[twilit loom]

yeah

[pallid bolt]

alright

now that i have it not backwards in my head

P(A given B) = (.85+.4125) / (.4125)

simple as that

no

still not

gives greater than 1

[twilit loom]

isn't that what you wrote earlier

I can't type

[pallid bolt]

oh yeah

i just reversed it agian

wait

so the .85

doesnt belong

wait

WAIt

https://media.discordapp.net/attachments/903430332324405288/929650797770342420/unknown.png

flight delayed

and its not there

is

.45

[twilit loom]

nope

[pallid bolt]

wait

.85 x .45

[twilit loom]

yup

[pallid bolt]

its

.3825

so

its

(.3825+.4125) / (.4125)

no

[twilit loom]

.–.

[pallid bolt]

duide

im sorry

im a potato brian

sometimes

[twilit loom]

where did the .4125 in the numerator come from?

[pallid bolt]

its the probability that her luggage never lands

[twilit loom]

that's not what we want on the numerator right

P(A|B) = (flight delayed and luggage isn't there)/(luggage isn't there)

that's only on the denominator

[pallid bolt]

oh

.3825 / .4125

[twilit loom]

correct

[pallid bolt]

i was doing an OR

equation

instead of an AND

idk why

[twilit loom]

you can think about it like the question limited us into the two branches of the tree where the luggage didn't arrive

that's our entire probability space

then we look for a case where the flight is delayed, which is only one of those two branches

so it's that one case (.3825) divided by all cases (0.4125)

[pallid bolt]

i think im just overtired / fried from all the math i been doing. because I actually want to learn so i have been trying so much, isntead of just cheating the answers

so im making careless mistakes

/ being impatient

[twilit loom]

take a break

[pallid bolt]

understood

i mean

i only have

1 question left

so

i dont really want to now

last one

if ur gonna lurk

let me struggle for it

it helps me think smarter, when i dont have a hand me out

.6 x .04 = .024

.4 x .06 = .024

.024 + .024 = .048

4.8% are absent on any given day

im done with it all

finally

that question though

was so much easier

than the other ones

@twilit loom just wanted to say thank you so incredibly much for being so patient with me, i really appreciate you! have a great day, night, whatever it is lol. Again thanks!

.close

[obtuse pebble]

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[wanton tapir]

hello

[wanton tapir]

i need help with this question

[cinder yew]

try with factors of 18

a technique that u probs know

is that if u plug a number into the polynomial and it returns 0

the poly is factorisable by x - number

[astral ivy]

@wanton tapir

[wanton tapir]

oh okay

[obtuse pebble]

@wanton tapir Has your question been resolved?

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[late herald]

.close

[obtuse pebble]

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[rich holly]

can you divide the middle square into 4 just like the one on the right?

[rich holly]

.close

[obtuse pebble]

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[rich holly]

.reopen

[obtuse pebble]

✅

[junior inlet]

i don't get what you're trying to say

[brittle swan]

me neither

[obtuse pebble]

@rich holly Has your question been resolved?

[rich holly]

wait my bad

shouldn't have parted it in the middle

[obtuse pebble]

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[rich holly]

is 5 in a tenths place?

[rich holly]

if so, what about the "3" in "32"?

[misty cedar]

yes

[misty cedar]

that's the "tens" place

[rich holly]

ah

thanks

.close

[obtuse pebble]

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[wispy heath]

Can someone help me solve this ?

[obtuse pebble]

@wispy heath Has your question been resolved?

[balmy mortar]

This reminds me of the contraction mapping theorem 🤔 (maybe not, idk)

[wispy heath]

i solved it, thanks

.close

[obtuse pebble]

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[pastel forum]

from the inequality, x = -10, 6/5 but how do u know whether it will be x <-10 or x>-10

[pastel forum]

is there a way to do it without plugging in?

[spice bay]

what do you mean x< -10 or x>-10?

[pastel forum]

like which one is the answer

idk which side the inequality faces

[spice bay]

i think i understood your question

so you got that x = -10
and x = 6/5 right?

from a quadratic equation

[pastel forum]

yes

[spice bay]

and you wanna know for which x, the inequality holds

[pastel forum]

yes

[spice bay]

your function is > 0 when
x > 6/5
or x < -10

because between 6/5 and -10, it will be negative

[pastel forum]

ohh

[obtuse pebble]

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[obtuse pebble]

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[upper basin]

For what values of m is the matrix A invertible ?

[spiral maple]

what have you tried?

[upper basin]

I really don't know how to start

[spiral maple]

what are the conditions for a matrix being invertible?

dont give answers............

[upper basin]

A * A^-1 = identity matrix

[spiral maple]

yes, what else?

[upper basin]

det(A) /= 0

[olive dragon]

it has to be a good movie, like matrix 1 and matrix 2

[spiral maple]

dont troll.

[spiral maple]

yes, use that

[upper basin]

sry for the translate 😉

[spiral maple]

det(A) is a polynomial in m

[upper basin]

so : m(m-3)^2

[spiral maple]

I doubt that's the polynomial

[upper basin]

I don't understand :/

[spiral maple]

oh it is

Ok, so you have $m(m-3)^2\neq 0$

[warm shale]

Mosh

[spiral maple]

so what values of m is this 0?

[upper basin]

0 ?

[spiral maple]

and?

[upper basin]

3 ?

[spiral maple]

yes

so 0 and 3 make A non-invertible.

[upper basin]

so for the answer, it would be all except 0 and 3?

[spiral maple]

yes.

[upper basin]

Ok, I understood the method, thanks 😉

.close

[obtuse pebble]

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[hybrid thistle]

Can someone please tell me what is the name of this or how to search it
1,2,3,4 1,3,2,4 1,2,4,3 1,4,2,3 1,4,3,2

[spiral maple]

permutations

[hybrid thistle]

thx

[obtuse pebble]

@hybrid thistle Has your question been resolved?

[obtuse pebble]

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[west sierra]

What is a continuous and discontinuous function and how would you prove if a given function is continuous or discontinuous

[cedar lichen]

In a non rigorous sense, a continuous function is a function you can draw without picking up your pencil

There are no vertical asymptotes, there are no holes, and it doesn't suddenly jump to a different value

[west sierra]

Like in a graph?

[cedar lichen]

Yea

[west sierra]

A curve is a continuous function then?

[cedar lichen]

Depends on the curve. If you mean one connected curve without any holes or anything, then yeah

[spiral maple]

a curve is continuous at x=a if $\lim_{x\to a}f(x)=f(a)$

[warm shale]

Mosh

[spiral maple]

a curve is continuous on a domain D if this holds for all a in D

[cedar lichen]

^ Thats continuity in a more rigorous and mathematical sense

[west sierra]

What if the curve stops at a point on y axis then another curve begins from y axis at another point

[spiral maple]

it's discontinuous at 0 then

aka jump discontinuity

[west sierra]

Ohh

[spiral maple]

also assuming one is open and one is closed, cause if they're both closed you dont have a function

[west sierra]

But what if there is a straight line joined between those 2 different curves but y axis blocks that view?

[cedar lichen]

Like a vertical line?

[west sierra]

Yes

[cedar lichen]

It ceases to be a function then

[west sierra]

Ohh

[cedar lichen]

Because there's infinite y values for that one x

[west sierra]

Like this photo

[cedar lichen]

That's a prime example of a jump discontinuity, yes

In a nonrigorous sense, if you tried to draw it, you'd have to pick your pencil back up at x=0 to move it up

In a rigorous sense, the limit at 0 doesn't exist so it can't be continuous

[west sierra]

I see..

You cant draw a straight line with just a pencil?

[cedar lichen]

You can, but as you can see, the graph jumps up.

You can't draw vertical lines since they aren't functions to begin with

[west sierra]

Does that mean x=a is not a function?

[cedar lichen]

Exactly

[west sierra]

Oh

What are open and closed curve?

[cedar lichen]

You know how a curve can suddenly stop, then you have an endpoint?

[west sierra]

Yes

[cedar lichen]

It's closed if the curve includes that endpoint, and it's open if the curve does not

[west sierra]

Ok

[cedar lichen]

It's typically notated with a filled in circle at the endpoint if it's closed and a hollow circle if it's open

[west sierra]

I kinda get it then. Thanks for solving my queries!

[cedar lichen]

Np

[west sierra]

.close

[obtuse pebble]

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[maiden musk]

How do I isolate u with cosu=x/2

[cedar lichen]

What's the inverse of cos?

[maiden musk]

cos^-1

[cedar lichen]

Yes. So how would you cancel out the cos?

[maiden musk]

times both sides by that?

[cedar lichen]

Not times. It's a function. You don't multiply by x² to cancel √x

[maiden musk]

So what would i do then?#

[cedar lichen]

Well, how would you cancel √x?

[maiden musk]

times by rtx

[cedar lichen]

So if you had √x = 2, you would multiply both sides by √x to get x = 2√x?

[maiden musk]

yes?

[cedar lichen]

So how would you isolate x? I mean before the x was only on one side and now it's on both. You haven't really gotten closer to solving for x in this case. There's a much better way to solve √x = 2

[maiden musk]

i'm not sure tbh

its probably very easy but my brain isn't working

[cedar lichen]

What I would do is square both sides

In other words, we plug √x in to f(x) = x²

So to cancel cosu with an inverse f^-1 (x) = arccosx, what should we do?

[maiden musk]

plug cosx into f^-1(x)

[cedar lichen]

Exactly

And we would do that to both sides

[maiden musk]

so would you put f^-1(x/2)?

[cedar lichen]

Yes, but what's f^-1?

[maiden musk]

cos^-1

[cedar lichen]

So your final answer is?

[maiden musk]

u=cos^-1(x/2)

[cedar lichen]

Bada bing bada boom

[maiden musk]

ahhh thank you

thats fine now :)

.close

[obtuse pebble]

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[light geyser]

Does this look right?

[obtuse pebble]

@light geyser Has your question been resolved?

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[timid silo]

hi i dont understand this

[timid silo]

im leaving

[sage geode]

What's confusing you here

[topaz bridge]

he left

...

[obtuse pebble]

@shrewd mantle Has your question been resolved?

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[cerulean pine]

Let P € R[X].
It is assumed that the remainder of the Euclidean division
of P by X²+4 is X+1 and that its remainder by
X-3 is 14. Determine the remainder of the division
of P by (X²+4)(X-3)

that's what i have for now :
let R be the remainder. There exists Q such that P = (X²+4)(X-3)Q + R
we have degR < 3 so R = aX²+bX+c
we have P(3) = 9a+3b+c = 14
idk what to do next
because (X²+4) doesnt have any root

[sweet plaza]

x = 1? like 9+x = 9+1?

nvm

[royal basin]

it does though

X^2 + 4 has two roots

2i and -2i

[cerulean pine]

we are in R[X]

[royal basin]

does your teacher threaten you with the guillotine if you so much as mention complex numbers

or maybe a gentler punishment like zero on all your assignments for the year

[cerulean pine]

loll it's not a homework i just want to know how to do it

[royal basin]

hm

feels like there should be a way to do this without complex numbers but for some reason im blanking rn

[obtuse pebble]

@cerulean pine Has your question been resolved?

[obtuse pebble]

@cerulean pine Has your question been resolved?

[high lily]

i think you should be able to sub x^2 = -4 to get
-4a +bx + c = x + 1

[obtuse pebble]

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[balmy mortar]

.reopen

P = (X²+4)(X-3)Q + (aX²+bX+c)
P = (X²+4)R + (X+1)
P = (X-3)S + 14

Can't you figure out a, b, c from equations?

[obtuse pebble]

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[frozen willow]

According to the fundamental theorem of calculus:

[frozen willow]

But shouldn't the left side of that equation be F(x) - F(a)?

[spiral maple]

no, FTC is that $f(x)=\dv{x}\int_a^xf(t)\dd{t}$

[warm shale]

Mosh

[long peak]

Is this defining what F(x) is or has it already said F(x) is the antiderivative?

[frozen willow]

I'm not sure

Here is where I got this from
https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#First_part

[spiral maple]

yeah, that's true.

F(x) is that function

F'(x)=f(x)

[frozen willow]

What’s the problem with this?

[long peak]

When you differentiate you lose any constant terms

so they can ignore the F(a)

and still have F'(x) = f(x)

[frozen willow]

So, F(a) is a constant?

Actually, yeah that makes sense

[long peak]

yeah, you could similarly have [F(x)-F(a)]' = f(x)

[frozen willow]

Yes, I was able to get there

[frozen willow]

Thank you

.close

[obtuse pebble]

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[obtuse pebble]

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[sterile kernel]

idk how to solve for x and h

*y

for the top triangle

[obtuse pebble]

@sterile kernel Has your question been resolved?

[sterile kernel]

<@&286206848099549185>

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[distant plinth]

help me

I got $101_{b-1}$

[warm shale]

BigNose99

[distant plinth]

but I want to verify

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[sleek sinew]

Can some explain why this is wrong for #61? Ans = 220

[twilit loom]

be careful with your units

[sleek sinew]

I think i messed up velocity but not sure what im supposed to do

Is a(t) right?