help-26

[neon iron]

I think I do tho

Bc, i dont understand in the first place how do I know if it makes a concave

or a convex

Bc I usually get = 0

and it always turns out to be somehow concave / convex or a stationary point

[azure panther]

you just dont know the theorems that are used

[neon iron]

perhaps ig idk

[azure panther]

imma go

gl

[neon iron]

lol

Ty

[neon iron]

have gun

FUN*

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[vocal escarp]

isnt cos(-180) just cos180?

[lime pond]

yep

[vocal escarp]

so would it be 1?

[lime pond]

-1

look at the graph

[vocal escarp]

oh yes

mb

wait that solved everything

[lime pond]

mfw

[vocal escarp]

goddamn

sometimes u just dumb

-mistav

[lime pond]

im just teh greatest

[vocal escarp]

u truly are my specialz

anyways im closing this before it gets awkward

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[weak orchid]

hello i'm new

[weak orchid]

is there a simpler way to get the answer

[dusky harbor]

Try doing log of that num

[weak orchid]

log (6/35)⁴⁰?

[dusky harbor]

Yeah

[weak orchid]

ohhh thanks

[dusky harbor]

It's like driving a number by 10

[weak orchid]

yeah

[dusky harbor]

Dividing*

[weak orchid]

thanks for mentioning th way

[dusky harbor]

Np ..just finding log might be lil time consuming

[weak orchid]

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[river arch]

Can you guys help me with grade 8 math I'm writing a test tomorrow

[sleek gate]

what topic?

this channel is for specific questions

start doing exercises for the test and if youre stuck on something ask a question

and if you dont understand some concepts you can ask on #prealg-and-algebra or other channel with specific topic

[neon iron]

grade 8 math is very broad, could u be a little more specific

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[lusty yoke]

i am supposed to find a formula for the n summs and then prove its correct with induction.

[lusty yoke]

is s_n=2^n-1 a correct formula for n sum?

because when i try to prove it with induction i get that it is not correct.

[remote agate]

Try the summation with more small values of n and see what kind of pattern you get, you're fairly close

[topaz sinew]

@lusty yoke Has your question been resolved?

[lusty yoke]

i dont see any other pattern?

[remote agate]

If you add 1 to S_n you can notice that the sequence is powers of 2

[lusty yoke]

oh i am dumb

it doesnt start at 1

it start at 0

so its 2^(n+1)-1?

[remote agate]

Yes

[lusty yoke]

thank you

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[dull ravine]

i tried finding the parallelogram but all answer ive got is 0

x+10+5x-4=180 right?

6x+6=180

subtract both sides by 6 so 6x=174

and then 174/6 am i correct?

x=29?

oh it is 29

oh i solved it

then moving on to 2

Rhombis

Rhombus

<A°+<B°=180°

so <180-<68=<B

<B=112

but im finding x and y

[remote agate]

A rhombus has 4 sides equal, so AD=AB

You can then proceed using the fact that ABD is isosceles

[dull ravine]

ic then is <DBC= half of 112?= 56?

and DAB is also 56

[remote agate]

Should be

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[dull ravine]

ic ty

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[dull ravine]

.close

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[ornate topaz]

can some1 teach me the basics of vectors, with small assignments?

[icy sky]

https://www.khanacademy.org

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[flat juniper]

how to solve these type of problems?

[calm prawn]

Note for the future: If you see someone typing, please use another channel

[flat juniper]

i only saw you typing after i started typing

[topaz sinew]

@flat juniper Has your question been resolved?

[crystal goblet]

Solve for 1/a , 1/b and 1/c from ax=by=cz=30

you have 3 relations, ax=30, by=30 and cz=30

[flat juniper]

so like 1/a = x/30

let me try

[crystal goblet]

Right

Similarly 1/b=?

[flat juniper]

ah much easier this way

thanks a lot

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[cinder oxide]

what formula am I using to solve these?

do I just plug in approximate values and do dot product on them?

[radiant marlin]

a.b=|a||b|cos(theta), and with unit vectors those lengths are 1

like the calculation definition of dot product is a1b1+a2b2 but the geometric definition is the one with cosine

[cinder oxide]

https://tenor.com/view/sinewave-sineline-sine-gif-22707024

trig always messes me up

too much to think about

[cinder oxide]

i mean, i could memorize this, but maybe it would help to really understand it too?

using visualization perhaps, to understand why we are using this formula to begin with

it's a lot to ask, I know..

making a graph like this with motion is not easy, but it helps to visualize

[tawdry comet]

Guys

can someone help me with this question

i am missing a key step which is resulting in an incoorect answer

[cinder oxide]

https://tenor.com/view/disappointed-hercules-disappointment-shouting-kevin-sorbo-gif-14893643

[tawdry comet]

i forgot the thing

what was the darn thing

[cinder oxide]

https://tenor.com/view/the-offer-matthew-goode-gtfo-the-offer-gif-the-offer-tv-series-gif-25872057

[radiant marlin]

here's how it looks with unit vectors, the dot product is the shadow of one vector onto another

and cos() just comes from doing trig to get the shadow

[cinder oxide]

hmmmm...

[radiant marlin]

so like if the vectors vaguely point in the same direction, you get a positive shadow

[cinder oxide]

but you don't always use cos right, for all of these angles on the question

[radiant marlin]

of A stuck up perpendicular to B its shadow would be a point, 0

and if the vectors are vaguely going in opposite directions it's negative, shadow in other direction of B

shadows/dot product is always cosine

[cinder oxide]

i thought it depends if angle is greater than 180, or something along those lines

i dunno, maybe these both do the same thing

cos uses dot product

sin uses cross product?

the big difference is that cross product is a new vector

dot product is a scalar

so i guess they are both good to know, depending on the question

but anyways, these would require entries, which we don't have

that's why I was thinking I could "guess" the entries, to get an approximation and good idea

[cinder oxide]

wait but doesn't the geometric formula also require entries for a and b?

we don't have them based on the graph

[radiant marlin]

when you have cos^-1 and sin^1 there's sometimes issues with the range of the angles yea, but we're going in the safe other direction

by entries you mean x and y coordinates? with the geometric definition you just look at the angles between the vectors and plug into cos()

to save yourself from guessing, theta<90 is positive, theta>90 is negative

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[thorny flame]

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

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[steady pulsar]

oh what the heck

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[sonic bone]

need help with f,g,I,J will upload work in a sec

[sonic bone]

<@&286206848099549185>

these 2

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[manic vapor]

sin37 = 37/x

[manic vapor]

how do i some

[spare monolith]

Three terms, two are known, isolate the unknown one.

[manic vapor]

ok ill try

[tall knot]

Me when i replace values

Me when i cross multiply

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[tight zenith]

solving this with characteristic equation makes no sense for me:

[tight zenith]

Solution is but im not sure how i would get that by using the constant coefficient method

[keen venture]

I'm sure you've found the characteristic equation is -x² = 0

[tight zenith]

yup

[keen venture]

So it's a double root at x = 0

First solution is a constant, C2 in your case

Second solution can't also be a constant, because that's already taken. When this happens, you multiply the solution by t.

So the second solution is the C1t

[tight zenith]

Ohh yeah, true for n repeated roots its C1e^at + tC2e^at + ... + t^(n-1)Cne^at right, where a is our root (repeated)

mixed it up for two distinct real roots, wasnt sure if +-0 counts as two roots or repeated root

[keen venture]

And hopefully this makes sense. We're looking for the space of functions, that when differentiated twice, give 0. Even without doing math, this is clearly just any line

[tight zenith]

yup, i just was a bit fuzzy on the rules since ive only had 2-3 questions on them

thanks!

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[heavy cove]

In this picture:

[heavy cove]

What does the UPSIDE DOWN V in the RHS mean / equal?

OMG

WAIt

[heavy cove]

GUYS I FIGURED IT OUt

it repreesnts the matrix on the left

🤩

ily kookiemon

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[spare cliff]

For letter a, i just plugged in values
Letting X be the brain weights of swedish men, since X follows a normal distribution

X bar also follows a normal distribution, so X bar ~ (mu, variance/n)

So for letter a, X bar (n = 3) ~ (pop. mean = 1.40 kg, variance/n = 4.033x10^-3)

and X bar (n = 12) ~ (1.40, 1.0083 x 10^-3)

I dont know for letter b

I think it says find the probability that the population standard deviation is <= 0.1

I used chi squared distribution but the values are off from the distribution table

Im stuck

[verbal crater]

could it be |x̄ - μ| < 0.1...?

[spare cliff]

Oh shit

Wait can u explain why

[verbal crater]

it says the sample mean is within 0.1 kg of the population mean

so the difference between the sample mean and population mean is at most 0.1

[spare cliff]

damn

thank you

Lemme just solve it

[spare cliff]

Is it okay to just round it off?

The result would be P[-0.1/(0.11/sqrt of 3) < Z < -0.1/(0.11/sqrt of 3)]

So P ( -1.57459 < Z < 1.57459)

Can i just find the p values for -1.57 and 1.57?

[verbal crater]

yeah

[spare cliff]

Oh okay

Okay i know what to do for c now

Thanks so much @verbal crater

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[regal horizon]

Is this function continious or not? The ‘als’ means ‘if’.. I tried to work with limits but I just cant figure it out

[keen venture]

Let's look at the limit as x approaches 1

What's the limit from the left?

[regal horizon]

1?

[keen venture]

Nice. What's the limit from the right?

[regal horizon]

0

[keen venture]

Bingo. Limit doesn't exist, function isn't continuous

[regal horizon]

Ah, I see. thanks!

[regal horizon]

But then how do I know if there is a minimum value in this function? I can't use the method that requires that the function is continious, the domain closed and 'bound/restricted' (I don't know the right term, sorry)? What else am I supposed to use to figure it out?

[keen venture]

Are you looking to find the minimum?

[regal horizon]

Yeah that is the end goal

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@regal horizon Has your question been resolved?

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@regal horizon Has your question been resolved?

[regal horizon]

Maybe I could take the derivative of each section? Although I don’t think that helps because
f’(x) = 1 and
g’(x) = 0..

Mhh, I’m out of ideas to be honest. Because although its convenient to just look at the picture I dont know what I would do if It was a function I couldnt draw

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[hollow kite]

i get how you do this

but

dont answer this

its done

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[narrow chasm]

Is the answer to this .0179?

[balmy crescent]

I desperately need help with this, it keeps saying my answer is wrong

[crystal goblet]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[crystal goblet]

how did you get 0.0179?

[narrow chasm]

1-P(0)-P(1)-P(2)

0=4.984
1=.3724
2=.1113

1-.9821

[thorny flame]

Result:

0.3939040643

[crystal goblet]

,calc (0.87)^5

[thorny flame]

Result:

0.4984209207

Result:

0.323973598455

[crystal goblet]

,calc (5*(0.87)^4(0.13))

[thorny flame]

Result:

0.3723834465

[crystal goblet]

,calc (10(0.87)^3(0.13)^2)

[thorny flame]

Result:

0.111287007

[crystal goblet]

This is correct

@narrow chasm

[narrow chasm]

sorry i had my discord shut off

[narrow chasm]

thanks for clarifying, i was doing the calculations again when i read this

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[obtuse olive]

@topaz sinew i need class 11 math formula

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[clear sedge]

x^2+y^2=1

@obtuse olive Does this clear your doubt?

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[frank brook]

Two candidates were standing in an election. Of the total number of people in the electoral roll in that election, 10% did not use their votes and 60 votes were declared invalid. The winning candidate secured 47% of the total votes of the voter list and he won the election by 308 votes. How many votes were cast in that election and how many votes did the losing candidate got?

[frank brook]

as 10% did not use their votes and 90% did that mean loser got 90 - 47 = 43 % votes

47 - 43 = 4% that mean (4% = 308 - 60)
4%=248
1%=62
100%= 6200

total votes are 6200
is this correct ?

[sonic dawn]

first sentence already seems incorrect
loser got 90% -60 - 47% votes

[fair thorn]

^^

[honest leaf]

lmao

[honest leaf]

(total_voters, votes_cast, losing_candidate_votes)=(6200, 5520., 2606)

[frank brook]

how did you calculate losing candidate votes

I am getting answer in decimals

[honest leaf]

Through code programming. have you written down the formula? Can you take a look at it?

[frank brook]

what formula?

there is nothing in chat

[frank brook]

even Gemini advance could not solve it

[honest leaf]

This is what I wrote, the total number of people on the electoral roll as T.

[frank brook]

I still don't understand how do you get losing candidate votes

[honest leaf]

losing_candidate_votes = 0.47 * total_voters - 308.

[frank brook]

.close

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[potent venture]

.close

[mental surge]

just not sure how to do it

[mental surge]

i tried 214x=95(35/60 -x) but still nothing

[woeful stone]

So total_time = d/214 + d/95

Because speed = distance/time

multiplying both sides by time we get

speed*time = distance

Divide both sides by speed

time = distance/speed

[mental surge]

and then try to find d? right?

would that be 35/60 = d/214+d/95 ?

[woeful stone]

correct

[mental surge]

i got something like 38.379

thats the total distance i think

[woeful stone]

Then that is the answer assuming you made no algebraic mistakes

[mental surge]

then do i divide that by 95 cause i am trynna find the time from the pond to the fire?

[woeful stone]

Yep, distance/speed = time

[mental surge]

i got like 0.40 something, i think thats in hours so i times that by 60 and i should get the final answer

thanks big bruh @woeful stone .close

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[vocal nova]

pls give tips on how to solve assertion and reason questions

[fair thorn]

if you have a specific question, ask here

[shrewd lance]

uhh... there are many ways depends on the type of question
if it's a question which need solving then yeah u need to solve
and if it's theoritical then u should know the concept

[fair thorn]

otherwise, go to #prealg-and-algebra or #geometry-and-trigonometry or the topic of your choosing

[shrewd lance]

yea .btw

[fair thorn]

also, A and R questions aren't very common in maths im not sure what you mean

[ivory sorrel]

depending on the exam authority, they are these day IMO

[vocal nova]

i know the concept and ace the calculation but fail in assertion and reason i simply dont know why

[fair thorn]

nahi he's indian so probably CBSE

[vocal nova]

how did u know ?

[fair thorn]

example de de, tab samaj mein aayega

[fair thorn]

ur name ofc

im indian too xD

[vocal nova]

damn

[shrewd lance]

bruh

[vocal nova]

thanks y'all

[fair thorn]

!done

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[fair thorn]

i don't think you're done but ok

[vocal nova]

.close

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[static raven]

This is a quick but also very dumb question I feel

[static raven]

If $A \subseteq B$

[thorny flame]

Curry

[static raven]

does this also mean the converse is true

[empty breach]

no

[static raven]

oh right?

[remote agate]

maybe try thinking of very simple examples

A:{1}, B:{1,2}

[bitter hemlock]

{1} subset {1, 2} but

lol i was literally typing same thing

[static raven]

ah right

[remote agate]

lol

[static raven]

so what about a proper subset?

[bitter hemlock]

the above example is a proper subset also

[static raven]

ah okay

I just got confused since I learned this today and thought aren't they the same thing

[bitter hemlock]

well $A\subseteq A$ is true but $A\subset A$ isn't

[thorny flame]

Soosh

[static raven]

yeah since they share the same elements

[bitter hemlock]

it's just similar with $\geq$ with numbers though with $\subset$ you have to be careful because it is used differently by different authors, some might use it for proper subset and some might use as the first one i believe

[thorny flame]

Soosh

[static raven]

ah I will defintely take note of that when looking at some set theory books

I'm not too good with this stuff sorry and also thank you for your time 😭

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[thick hound]

Converges or diverges?

[worthy storm]

it's an $\infty - \infty$ form

[thorny flame]

Bungo

[cursive patrol]

hmm if they aren’t allowed knowledge that the sum of reciprocal primes diverges…

[worthy storm]

i'm not sure it even makes sense to ask if this converges or diverges, it's not a sequence

but rather the difference of two limits

which exists if and only if those limits exist

i don't know how you avoid determining whether they exist

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[limpid gate]

Hello, I'm definitely being dumb - but if I have a bearing of wind coming from one direction, and a building with a bearing to a road. How do I determine if the building is between the road and the incoming wind, or the other side of the road. Bearings are in 360 degree compass directions, so 0 degrees the wind is coming from the north, 180 degrees etc.

[limpid gate]

For instance here - the building is the other side of the road to the incoming wind, so would be classified as leeward.

whereas this example its on the same side as the incoming wind, so windward.

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@limpid gate Has your question been resolved?

[long stirrup]

@limpid gatewhat would a bearing of a building to a road mean

[limpid gate]

I mean I've made this complex, but essentially the angle from a point to the green line.

[long stirrup]

ok so there's a point

[limpid gate]

The essential problem is one point on a certain angle away from the line, in the same 180 arc as another point.

i.e. in the picture above, how do I algorithmically show that a point at 330 degrees is on the same side as a point at 30 degrees

and the green line may change orientation

[long stirrup]

i would make sure both angles are in −180 to 180 range

then the sign should determine where that is

[limpid gate]

my issue has been the compass bearing is 0 - 360 so a point at 30 degrees compass bearing and 330 degrees compass bearing are both on the same side of the green line.

so would I be working it out as:
((green_line_angle - point_bearing) + ((green_line_angle + 180)-point_bearing))

[long stirrup]

that shouldn,t happen: 30 = −330 not 30= 330

[limpid gate]

sorry, I'm confused.

do you mean the absolute values of those?

then if abs(((green_line_angle - point_bearing) + ((green_line_angle + 180)-point_bearing))) > 180 then it's on one side of the line, and < 180 its on the other.

[long stirrup]

@limpid gate
find wind − road and building − road
for example you get 30 and 330

now 330 is more than 180, we subtract 360

so we get −30, different signs means different sides

you said it's not like that, that they are on the same side actually

i don't get it

[limpid gate]

yeah the green line is oriented at 90 degrees right.

So I think my math above makes sense.

[long stirrup]

ok ok that's cuz you mean before subtracting road

yeah if you subtract 90, you get 240 and −60, which is −120 and −60, same side

[limpid gate]

in this example it's abs(((90-30) + ((90 +180) - 30))) = 300 which is greater than 180 so it's on one side, and if we repeat for abs(((90-330) + ((90 +180) - 330))) = 300

so they're on the same side

but if I put a point on the other side of the line abs(((90-170) + ((90 +180) - 170))) = 20 so it's on the other side of the line

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[open breach]

is there a really easy short anf fast way to do this question

[upper bone]

explain why it is (1 - dy/dx) and not (-1 multiply dy/dx)

[upper bone]

oh sorry i got the channel first

[open breach]

my fualy

ut good

[upper bone]

explain why it is (1 - dy/dx) and not (-1 multiply dy/dx)

[noble laurel]

rewrite the left hand side as e^(x)e^(-y)

and then differentiate with respect to x

remember to use the product and chain rules

and then simplify

[upper bone]

why would i do that

[noble laurel]

because you are confused about how it was differentiated

that makes it easier

[upper bone]

is that just something ur supposed to do

oh

[noble laurel]

It isn't necessary, but if you're getting confused it might help to break it up like that

[upper bone]

ok thank you

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[wary tulip]

hmmm

[noble laurel]

yeah it also shows them as that to me too

idk why

[cold sigil]

not for me

[analog light]

Normally sending an above average amount of API requests but not enough for them to take further action

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[versed trail]

Need help with this

[versed trail]

Only with 12 b i need help

[topaz sinew]

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@versed trail Has your question been resolved?

[versed trail]

1

[mint crescent]

What is $-t(-x)$?

[thorny flame]

Civil Service Pigeon

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[versed trail]

bro thats what i am asking

[versed trail]

how is it implements

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[trail goblet]

electric flux

why did he use 60° instead of 30°

[radiant marlin]

the equation just uses the normal vector to the area instead of the area itself

I remember it from the most flux happening when the field goes straight through the area

[trail goblet]

it's 30° because it's from the surface to the electric field line?

instead of from the normal line to the electric field line

[radiant marlin]

30° to the surface but 60° to the surface vector

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[trail goblet]

what's a vector in this case again?

forgot

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[patent light]

.

hello

[patent light]

$\lim_{x \to -5^+} \frac{x^2-3x}{x^2+4x-5} = \frac{25 + 15}{25 - 20 -5} = \frac{40}{0^+} \to \infty$

[thorny flame]

alee

[patent light]

i dont get why the solution is $-\infty$

[thorny flame]

alee

[patent light]

can someone ping me if answer 🙂

<@&286206848099549185>

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[patent light]

<@&286206848099549185>

[fluid token]

doesn't the solution say positive infinity in the first image?

[patent light]

its my solution

on wolfram is $-\infty$

[thorny flame]

alee

[tidal hollow]

yeah it should be 0- down there

[patent light]

why

[tidal hollow]

when x is approaching -5 from the right

[patent light]

isnt like $25,001 - 20,001 - 5$ ?

[thorny flame]

alee

[tidal hollow]

more like 24.99-19.99-5

since its coming from the right

it's like (-4.999)²

a good way to find this instead of plugging is to check the sign of the polynomial

you find that it's negative between -5 and 1

and since -5+ is bigger than -5 then the polynomial would be approaching 0-

[patent light]

why??

😦

why not 0+

[tidal hollow]

hold on gimme a sec

[patent light]

ok

[tidal hollow]

do you see how when x approaches -5 from the right

x²+4x-5 is negative

[patent light]

i cant see very well the photo

[tidal hollow]

it's okay it's not that important

if you look at the graph of the polynomial

you'll find that when approaching -5 from the right, the polynomial is negative

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[brittle void]

how does one find said holes?

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[brittle void]

<@&286206848099549185>

.close

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[ivory sorrel]

A small ball is suspended over an infinite horizontal conducting plate, by a string of stiffness k, as soon as the ball is charged, it decends by a distance of x cm, and the seperation becomes l , find the charge of the ball

[ivory sorrel]

how do I even find the charge induced on the plate here?

The flux is one 12th of the total flux

that's q/12\epsillon

but I doubt that will help

hmm

I draw a guassian surface enclosing the sheet

hmm

I'm getting teh charge induced is q/12

does that sound right?

[rapid pagoda]

https://en.wikipedia.org/wiki/Method_of_image_charges

This might help

[ivory sorrel]

hmm, did try that, but that gives a wrong answer

[rapid pagoda]

Can you show what you did?

[ivory sorrel]

yeah

will do

so the charge induced is

q

thus the force between the plate and charge is kq^2/l^2

oh

right

[rapid pagoda]

2l

[ivory sorrel]

that;s the net charge

why 2l

[rapid pagoda]

By method of image charges, 2l

[ivory sorrel]

actually, now that I think about it, why isn't it q/6

one sixth of the total flux passes via this plate

[fleet maple]

you can start by putting electric Force = spring Force[cos it'll always counter balance]

so, F(el) = F(spr)
=> q^2/4 pi epsilon (2l)^2 = Kx
thrfor, q = 4l sqrt(pi epsilon K x)

[ivory sorrel]

2l is because of the method of image charges?

[fleet maple]

yep

[rapid pagoda]

How 1/6th

The solid angle subtended by the infinite plate is 2pi, while 4pi is the total solid angle around a point

[ivory sorrel]

ah

oh

wait what

I can have 6 plates around it

right?

forming a cube

[rapid pagoda]

Sure but they’re infinite

[rapid pagoda]

You are neglecting flux contributions to the region outside the cube (which exists as the plates are infinitely large)

[ivory sorrel]

hmm

[ivory sorrel]

thanks

[ivory sorrel]

got it

is there any way to do this without this method?

from first principals

[rapid pagoda]

Technically yes

This is a part of conductors

[ivory sorrel]

I am familiar with the properties of conductors

so could I just have a hint

[rapid pagoda]

The condition that must be satisfied is that the electric field outside of the conductor is perpendicular to it

[rapid pagoda]

Well, the hint was method of image. The problem is, figuring out a charge distribution function is kind of tricky, the best method I know is guessing

It’s not that hard to realize two opposing charges create a perpendicular field at their perpendicular bisector line

[ivory sorrel]

got it

thanks!

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[balmy roost]

any Idea how to solve part b?

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[balmy roost]

<@&286206848099549185>

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[warm monolith]

I need confirmation for a question
If I choose 3 random numbers from 1-1000, what is the probability of their product being an odd number?

[warm monolith]

I got 1/8, is that right?

[snow nimbus]

Yes

[warm monolith]

Thanks

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[hidden spear]

I need help with 23 to figure out how I'm doing it wrong. 27 because I can't find it on the mixed answers chart and I erased the work and tried to redo it but got to the same steps. Then 21 to help with figuring out the other half of the answer.

[fluid token]

okay with 27 – i'm assuming you squared both sides

that's the correct first step

then you solve the resulting equation which is just 2x - 10 = 5x - 15

and you get x = 5/3

but you have to check for extraneous solutions! when you plug 5/3 back into the equation, it doesn't work

so i'm rpetty sure the answer is no solutions (in set notation that would simply be the empty set or { } )

[sterile finch]

23. 81 = 3 * 27, not 3 *4.

[fluid token]

21. there is a mistake in the third step – you split sqrt(18) into sqrt(9) and sqrt(2) in the previous step but lost the sqrt(9)

so it should end up being 2sqrt(6) - 5sqrt(2) - 12sqrt(2) + 20 sqrt(6)

i hope this has been helpful!

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[hidden spear]

27 can't be extraneous because 29 is and some other thing.

[fluid token]

Do you have the answerrs with you?

[hidden spear]

I think I messed up on 26. Cab I have help figuring out what?

[fluid token]

honestly 26 looks right to me

[hidden spear]

26 I put as extraneous.

[fluid token]

you can graph it on desmos if you want to check

[hidden spear]

I have to use my calculator.

Only.

I think I put it in wrong in the calculator.

So. After plugging 5/3 in it didn't show extraneous.

[hidden spear]

I do have it as that also can you write it out possibly because Idk if I'm visualizing right what you typed please?

I tried changing 23 up as well but I think I messed up.

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@hidden spear Has your question been resolved?

[hidden spear]

<@&286206848099549185> .

[hot anchor]

i got u

so

start by finding out their common multiples or whatever

in this case it would be 2

then i would simplify each one individually before combining

for 5 (4throot) 32 i would split it into

5 (4throot) 2^4 * 2

[hidden spear]

I prefer if it's written out then typed tbh.

[hot anchor]

ah ok

gimme a few minutes and ill send a picture

[hidden spear]

Thank you, also is there a way to explain certain steps?

Why the steps were done.

And how it was done.

[hot anchor]

sure ill write it at the bottom

@hidden spear

[hidden spear]

Thank you!

[hot anchor]

no problem

if u cant read something just tell me

ik its quite small

[hidden spear]

It's fine, I understand.

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[round delta]

{2,3x,4x^2+1} is this vector is orthogonal?

[wary tulip]

do you mean is the set of vectors orthogonal?

[round delta]

yeah

[noble laurel]

With respect to what inner product?

[round delta]

standard

inner product

[wary tulip]

backing up a step from there... do you know what this means?

[round delta]

yeah i know

damn sure about abt that

[noble laurel]

Then what is confusing you?

[round delta]

is that orthogonal?

[noble laurel]

You tell me

[round delta]

idk

[noble laurel]

You just said you knew what it meant for them to be orthogonal?

[round delta]

orthogonal is mean to be perpendicular right?

[noble laurel]

In some contexts you can think of it like that but that isn’t what it means here

Not precisely

[round delta]

......

[noble laurel]

There’s a definition of what it means for vectors to be orthogonal with respect to an inner product

Find it

[round delta]

Ok got it

.close

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[untold birch]

Why does this

[untold birch]

imply this

i memorized how to get between the x <=> dx and how to invert but

WHY IS IT SO

<@&286206848099549185>

no it didn't help

😂

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[neon iron]

i got 6.25J

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[north canyon]

Need help with 47.(b)

[north canyon]

I guess we are removing the 'bad' cases from all cases but still why the 'bad' cases equals c(n-1,k)?

[azure panther]

lemme think

O_O

[north canyon]

Wait let me think more

[azure panther]

i dont even know why its written in reccursive form

like why

it can be directly calculated

if im not wrong 🤔

[sonic dawn]

it’s almost like that’d make for a good extension

[azure panther]

idk

and even when i calculate it directly

its not the same with part c

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[nocturne osprey]

I was thinking of a range tree storing a extra field in the subtrees containing the y-coordinates. This extra field stores the amount of nodes in that subtree. Is this a good idea?

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<@&286206848099549185>

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[neon iron]

lower bound of 38.5 to 1 decimal place and
lower bound of 5.0 to 2 significant figures

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[twin heath]

uhhh
how

[twin heath]

i understand the first step (taking out a0 because its a constant) but what does changing the dt to d(t/t0) and then multiplying by t0 mean??

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<@&286206848099549185>

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[neon iron]

Giving the second soln as well wait a bit

[neon iron]

After the final step u can take e to the power 1/To commen as well to make it more simplified

I would suggest dude to go through ur basics once more and then proceed to these questions

[twin heath]

.close

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[quartz portal]

Hello! I am struggling here with this equation:

The answer is $943.05 but for the life of me cannot get this answer, I've tried so many ways:

1. I've put the whole equation into a TI-84 and it couldn't solve it
2. Multiplied the numerator all together, then the denominator whole. It ended up being .093333333 divided by 0
3. Then I .112/12 and then mulitpled by 990000. Next did the bottom parentheses. The result was 11088/it gave me a syntax in my calculator

[restive inlet]

show what you're entering into the calc

oh,and you can't cancel those 12 like that

[quartz portal]

yeah I didnt think so, I just wanted to try it lol

1sec

[vernal vale]

you may want to use something more sophisticated than a ti 84

unless you have mathprint working alright on it

i mean, something that has better formatting so you can be sure that all the parentheses are where they should be

[quartz portal]

What's mathprint?

[vernal vale]

mathprint is TI's formatting thing on their calculator

so that like, fractions show up as fractions

exponents go up to the corner

all that stuff

you might have it on and not know its called that just worth asking

but, for example, symbolabs calculator is nice for problems like this

[quartz portal]

yoo that is nice

[vernal vale]

calculator is worth figuring out if youre going run into issues like this on an exam

but handheld calculators are a bit of a relic at this point

[quartz portal]

yeah agreed

[vernal vale]

theres that button on the ti 84

up near the 2nd button

lemme see here

[vernal vale]

you know it also defpends on what version you have

[quartz portal]

It sucks cause I can’t get the whole equation on the calculator

[vernal vale]

yea so, try hitting mode

can you show what comes up

[quartz portal]

I see math print

[vernal vale]

mathprint is on

[quartz portal]

Turn it off?

[vernal vale]

i know on some calcs you have to like

upgrade the OS

[quartz portal]

Damn I can do that to a ti 84?

[vernal vale]

yea if you can hook it to a pc

but, you know

being careful about parens is just part of the game, too

try uhh

[vernal vale]

try hitting alpha and then hitting the y= key above the second key

can you enter in a FRAC

[quartz portal]

So much better

[vernal vale]

hit the green button then the y= button

[vernal vale]

yea

hit 1

it will crreate a fraction

if you enter parens it should scale them too i think

[quartz portal]

So I’m putting this frac when I’m about to divide the numerator by the denominator?

[vernal vale]

i mean if you see what you should be seeing

this actually puts the numerator visually above the denominator

things arent grouped by parens anymore

this prevents you from making a stupid order of operations mistake and messing up your fraction

[quartz portal]

i'm confused on what I'

m supposed to be doing with that input

[vernal vale]

enter in your problem correctly formatted

so you get the right answer

[quartz portal]

thats what I'm trying to do

[vernal vale]

i guess im not sure what else to tell you

you can either use the nicer formatting on your calc

or use desmos or something

[quartz portal]

hm okay so based on this: you can't tell what I'm doing wrong?

[vernal vale]

youre certainly missign parens

you havent wrapped your denom

but, you also arent using mathprint

so this error is common

[quartz portal]

.close

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[swift slate]

hey fellers, im confused of my teachers answer to this question

[proven grove]

what’s the part cut out at the top of the picture

[swift slate]

why is there a 14? and why are there two (-6)^k?

a different question

all the writing in blue is the solution to this question

[proven grove]

there’s a 14 becuase 8+6 = 14

[swift slate]

but where'd he get the 8 from?

[proven grove]

the question

[swift slate]

okay but isnt it being used at the front of 8(8^k-(-6)^k)?

how did it also get added with 6

[wary tulip]

the algebra is a little tricky there

[wary tulip]

take this and multiply it out

to see that it’s the same as the previous line

the important thing is 14(-6)^k - 8(-6)^k = 6(-6)^k

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[swift slate]

im still confused D:

why not keep it as -(-6)^k?

<@&286206848099549185> hi sorry can you please help?

why is there a +14?

i understand u need 8^k-(-6)^k for substitution but like. whered the 14 come from

[swift slate]

zSo

is it something to do with the difference between 8 and -6?

[vernal matrix]

Yep, as per...

[vernal matrix]

...here you have +6 but you ideally want a -8, so that you can factor and find your 8(8^k - (-6)^k)

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[neon iron]

Naba and Iji along with 10 other volleyball players with the same abilities will take part in the selection to form a volleyball team to take part in a championship. If one team is allowed to include 4 reserve players, many teams can be created if Naba and Iji are always included in the volleyball team formed.

[neon iron]

This means that in total there were 12 people who wanted it, then 10 were taken. (12C10)

become one team (Team=players[6]+reserves[4]).

But Naba and Iji (these two people) must play, does that mean the formula is become 10C8? 45 ways?

is it correct?

[exotic carbon]

Naba and Iji must play.. so those 2 are sorted.. but your other players can either be the actual players or reserves, so you have to check individually for that

as in 4 players into the player squad multiplied by 4 into the reserve squad

[neon iron]

hmm

but we don't know whether naba and iji will play as players or reserves? What is certain is that they have to play as a team

If you break it down into players and reserves, it means we have to create possibilities

both in players, 0 in reserves

naba player, iji reserve

iji player, reserve naba,

0 players, both reserves

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[sonic escarp]

!15min

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[restive inlet]

especially not before posting an actual question
and ensure that when posting, that the question is clear and legible

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[balmy roost]

here the prof was calculating the moment of inertia of a sphere

which led to this result $I_{cm}$ = $\frac{2}{3}$ $\int dmr^2$

[thorny flame]

Hamdy Hisham

[balmy roost]

why can't I just say by definition that $I_{cm}$ =$\int dmr^2$

[thorny flame]

Hamdy Hisham

[balmy roost]

here is the full video https://youtu.be/QmCQUBSsKwQ?si=-ejbTfvPNCGkd-RE

[coarse tusk]

That’s not the result.

The result is 2/3 MR^2

Where M and R are the mass and radius of the whole sphere respectively

[coarse tusk]

You can

The problem is that r depends on what part of the mass you’re talking about

[balmy roost]

why is this solution wrong

[coarse tusk]

The 2/3 MR^2 formula is for a hollow sphere, it is 2/5 MR^2 for a solid sphere

[coarse tusk]

You can’t write dm like that

Well you can but then you have to take the moment of inertia of that piece into account

You can write $$dI=\frac{2}{3} dm r^2=\frac{2}{3}\cdot 3\frac{M}{R^3} r^4 dr$$ and then integrate dI from r=0 to r=R

[thorny flame]

kheerii

[coarse tusk]

The first step comes from the result about the hollow sphere

[coarse tusk]

The problem with this is that you’re considering your element to be a point mass

dI = dm* r^2 is only valid for a point mass, otherwise you have to do it like I said above

[balmy roost]

ok so this chunk of the sphere (sphere of radius (r+dr)-sphere of radius(r)) is not considered a point mass

why?

@coarse tusk

[coarse tusk]

Because it’s not a point..

It has its own unique moment of inertia which probably will not equal to dm r^2

[balmy roost]

but when you calculate the moment of inertia of a disk

you also take a chunk of the circle

[coarse tusk]

Ah that’s because of a different reason

It just happens to be that the moment of inertia of a ring is dm r^2

If it were something else then yeah the result would be different

[balmy roost]

aha

[coarse tusk]

It infact doesn’t “happen to be” that that’s true

There’s a sound reason why

Do you wanna hear itv

V

[balmy roost]

so in the sphere why is $dI=\frac{2}{3} dm r^2$

[thorny flame]

Hamdy Hisham

[balmy roost]

sure

[coarse tusk]

Because the element you’re considering is a hollow sphere, which has that moment of inertia

[coarse tusk]

Basically you can rotate any point about the axis and also move it up and down along the axis without changing the moment of inertia

Since it doesn’t change the distance

So just rotate all points of the disk such that they lie on one point

You can also prove other results, like how the moment of inertia of a cylinder is the same as that of a disk

[balmy roost]

ok why is that

[coarse tusk]

What do you mean why?

That’s the element you chose to use

You can prove the result with a different choice of element as well

[balmy roost]

I mean why is the moment of inertia of a hollow sphere this formula

what is the proof

[coarse tusk]

The video you sent is a proof of precisely this

[balmy roost]

I don't understand it actually

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[raw horizon]

ive gotten it down to x^4+6x^2+9x=f(x)

[ivory sorrel]

now sub $x^2=y$

[thorny flame]

Why am. I here

[gusty bane]

substitute x^2 - 3x for f(x) on the RHS

[gusty bane]

this doesn't quite help because of the single x

[raw horizon]

thats what i had but i just dont know what to do with that

[gusty bane]

its an equation for x

start by dividing everything by x

(and in doing so noting that x = 0 is one solution)

from there you'll have a cubic

[raw horizon]

yeah x^3+6x+12=x

[gusty bane]

you ucan probably find one of the roots by guessing

well not for this polynomial

[gusty bane]

the exponents here are incorrect

[raw horizon]

yeah it should be x^4-6x^3+6x^2+9x correct

x^3-6x^2+6x+12=x

[gusty bane]

yes

[raw horizon]

i dont see how i could find possible values of x besides guess and check unless maybe i could substitute x back into f(x)=x^2-3x?

[gusty bane]

you should guess and check

that'll give you one root

then just divide
x^3 - 6x^2 + 5x + 12
by
(x - that root)

and you'll get a quadratic you can solve

[raw horizon]

okay

-1 is a root

so -1 and 0 are roots so far

[gusty bane]

yes

[raw horizon]

$\frac{x^3-6x^2+6x+12}{x+1}$?

[thorny flame]

gof

[gusty bane]

why +6x

[raw horizon]

from here?

[gusty bane]

that equals x though

we want
f(x) = 0