help-10

[whole forum]

Something useful is one revolution takes 60 seconds and the wheel is split into 12 even sections

[obtuse pebble]

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[severe sand]

I can’t seem to figure out how to do my first problem. I am given the answer (mean = 90.5) but i’m not sure how my instructor got that.
I was able to do question 2 correctly on my own, but i can’t seem to apply that to the first one. Things aren’t connecting in my noggin :/

[obtuse pebble]

@severe sand Has your question been resolved?

[severe sand]

<@&286206848099549185> does anyone know anything abt weighted means v__v

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[timid silo]

Hihi

[timid silo]

Did you figure it out?

[severe sand]

haiiiii I FIGURED IT OUT!!!

mhm mhm

[timid silo]

Ok great lol

[severe sand]

ty for getting back to it tho ^-^

[timid silo]

Ofc, Have a good night/day!

[severe sand]

You as well :)

[obtuse pebble]

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[shadow cipher]

while differentiating in calculus,

suppose we have

log (a²y) = log (sin[x - 2x⁴])

how do we find derivate of y?

[shadow cipher]

cuz lhs is filled with stuff apart from y

[river lily]

u can get derivative of y in terms of y

and x

or you can write y in terms of x rn

and then plug in for y

when u take the derivative

[shadow cipher]

can you explain it w.r.t the question 🥲sorry

im having a hard time understanding

[river lily]

like

so solve for y first

and then take the derivative of y

and the isolate the derivative

y' = smth

in that smth

has a y term

so plug in ur solved y

for that y term

[severe reef]

I believe that 'stuff' is just constant

So why worry

[river lily]

I don't think so

log is ln right?

for both sides?

[severe reef]

You mean a is not a constant?

[lapis charm]

ln(ay) = lna + lny and lna is constant

[river lily]

is log ln?

[lapis charm]

Just to clear stuff up

Yes log is ln

[river lily]

ok

then take power to e

on both sides

then take derivative

[severe reef]

I can let it stay like that as well and go 1/(ay) * a

[lapis charm]

Ofc

[obtuse pebble]

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[regal sequoia]

i need help setting up this problem

[tepid yoke]

What is the 140 degrees

[regal sequoia]

this im p sure

[obtuse pebble]

@regal sequoia Has your question been resolved?

[regal sequoia]

<@&286206848099549185>

[grand marten]

What to find

[regal sequoia]

x

on the answer key x = 72

[grand marten]

Where x touches?

Is it inside circle?

[regal sequoia]

ig but whatever makes sense

[grand marten]

Or it's near tangent

[regal sequoia]

im pretty sure its the arc

[grand marten]

Is it a point of cords?

[grand marten]

I am still unable to understand your question 😅

[regal sequoia]

i just started the unit sorry i dont really know the vocab and terms well

but im pretty sure its refering to this

the highlighted part

[grand marten]

X is a point?

[regal sequoia]

no its a measure

degree

nvm i solved it

the major arc would be (220-x) and the minor arc would be just (x)

so the equation would be 1/2 (220-x - x) = 38

or 1/2 (220 - 2x) = 38

[grand marten]

Yea I was trying to do same

Taking 220 and reverse it

[regal sequoia]

ya

thank u

have a good night

[grand marten]

Lol I didn't do anything

[regal sequoia]

emotional support

[grand marten]

Have a sweet dream

[regal sequoia]

u too bro

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[strong moss]

<@&286206848099549185>

[pulsar quarry]

pls do not ping helpers until your question hasnt been answered for 15 min

[strong moss]

ok ty bro

cant tell how much i appreciate you

rather than helping tteaching me rules

love ya

keep grinding and teaching rules

<3

[pulsar quarry]

love you too blud

<3

[sage dagger]

lmfaoo

[strong moss]

your fucking cool

[pulsar quarry]

ikr

[strong moss]

yh ofc

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[stable wharf]

heyo. can someone check my work? i need to know if this set of vectors T is linearly independent. each of them are in R3.
when solving [T | 0], i have more equations than i do variables. i think i can simply say that they are linearly dependent, but i went ahead and reduced it to row echelon form. column 4 seems to be "free". is it always true that if a system has a free variable, its linearly dependent?

[stable wharf]

i was able to write the fourth column in terms of the others as well when i did put it back into a system form

[analog python]

well you have four vectors in R3

so yes you know they can't be linearly independent

at most there can be 3

[pure tusk]

you can row reduce it

if you have one free variable

then its LI

[stable wharf]

ic ic

thanks for the help y'all. im just double checking even if it seems obvious

[pure tusk]

but if you have more than 1 its LD

[analog python]

no free variables = linearly independent

[stable wharf]

wait 🤔

[pure tusk]

ok but he has 4 columns and 3 row

so wouldnt it have 1 free variable

[stable wharf]

yeah, i believe that if theres even 1 free variable, ie. it can be written in terms of others, its linearly dependent.

[pure tusk]

if it had 3 pivots

[analog python]

there's 4 vectors, so its not possible to have linear independence no matter what

[stable wharf]

i reduced it (maybe incorrectly) and got

1 0 3 0 
0 1 5 2
0 0 1 1/2

column 4 is a free column

[pure tusk]

thats crazy i love spreading misinformation on the internet

mbmb

[stable wharf]

yea its fine

[analog python]

yes 4th column is free

[kind hawk]

for linearly independent you need exactly one solution to the linear system. so as soon as you have at least one free variable they are not independent

[analog python]

so yes it is linearly dependent

[stable wharf]

and that solution has to be zero right?

[kind hawk]

yes

[stable wharf]

ah okay

linear algebra is weird because theres like a dozen ways to say the same thing or show the same properties

[pure tusk]

i was thinking if one column became all 0, then it wouldnt matter but forgot you can multiply that column by any number and you get infinite solutions

mb

[stable wharf]

so im just now getting this "obvious" stuff because each thing i read online will show a different way/form for the same property

oh yeah , what about a case where i have columns that become 0?

[analog python]

but yeah u dont need to row reduce it since you have 4 columns, its not like you can have no free variables

[stable wharf]

actually nvm

[analog python]

0 is automatically linearly dependent

[stable wharf]

solving [T | 0] just makes 0 vector redundant anyway

and yeah, then everything else in the system has to be linearly independent because no other nonzero C can get a nonzero answer

hmm thx !

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[stable wharf]

and ye i was just making sure that i understood the math

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[rose ferry]

hey how do i do a.

[obtuse pebble]

@rose ferry Has your question been resolved?

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[shell moth]

I calculated these limits and got this

But this is how the graph looks

What did i do wrong?

[runic void]

[shell moth]

Heh?

[runic void]

These are not numbers as you expect, 1/0+ and 1/0-.

you can write lim x to 0-, meaning you approach 0 from the left

what does 1/2- and 1/2+ means?

[shell moth]

Yeh it's just different notation

So how would you solve this then?

[shell moth]

Well, for numbers slightly bigger than 2 (the first example) it won't be exactly 1/0, but 1/ an ever so slightly positive number

Thus the 0+

It's the way I was taught

[runic void]

Notice, $\lim _{x\to 2+} \frac{x-1}{x^2-6x+8}$

put slightly bigger values than 2

like 2.00001, or 2.000001ish

[shell moth]

Aren't you approaching form the left here though?

So shouldn't it be slightly smaller?

[warm shale]

.doc

[runic void]

mb

[shell moth]

Ah ok

[runic void]

i really mean 2+

[shell moth]

And you basically get this

No?

[runic void]

aren’t you getting closer to +infy

[shell moth]

Well yeh

[runic void]

as x approaches to 2 from right

[shell moth]

Cause 1/0+ = +infinity

Which is also what I wrote down

[runic void]

I mean that notation is not correct

[shell moth]

Why not?

[runic void]

$\lim _{x\to 2+} \frac{x-1}{x^2-6x+8}= \infty$

[warm shale]

.doc

[shell moth]

It's the same thing, just the notation differs bro

It's the way all the teachers in romania do it

[runic void]

1/0 is not equals to +infty or -infty

it just not defined

[shell moth]

Yes

Because it diverges

[runic void]

we really mean $\lim_{x \to 0+} 1/x = \infty$

[shell moth]

Yes

[warm shale]

.doc

[runic void]

this notation is correct

1/0= infty isn’t really correct

Essentially your answer is limit doesn’t exist

[shell moth]

I didnt write that anywhere

0 != 0+

Anyway

We both agree that approaching 2 from the right

The limit is infinity

[shell moth]

Why does the graph show otherwise then?

[runic void]

graph shows what you expect

get closer to 2 from right, you bounces off to +infty

[shell moth]

Approaching from the right of 2, it goes to - infinity

No?

[runic void]

lim x to 2- is ?

how much you got?

[shell moth]

2- you mean?

Negative infinity

Online calc agrees with the graph

I don't get why though

[runic void]

to find lim 2- you try f(1.9999) right?

[shell moth]

Yes

This is the explanation it gives

But I'm having trouble understanding it

[runic void]

I’m getting a positive value

[shell moth]

Ok that makes sense

Because it agrees with the graph then

[runic void]

1.9999999 ish makes it more closer

[shell moth]

But what did I mess up in my calculation then?

[runic void]

maybe you calculated them wrong

[shell moth]

Idk

I'll just ask my teacher next time I see her ig

Thanks

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[pliant elbow]

could someone walk me through this problem? i dont know how to set up the stars and bars stuff

[ember frost]

what have you tried

[pliant elbow]

for a since all the quantities are greater than 15, i think it should just be (17 | 15)

for b im not sure

i mean it guarantees two things of each so maybe it would be like taking out possibilities

in fact it would mean you only have 9 slots really

so i think that one would be (11 | 9)

c is where im stumped because it has at most

idk how to do at most

i can trim it down to 100 slots because at least 10 cherries

the at most is what im stuck on and im not sure what to do

does it have to do with taht stuff about uh the not in group

like

complements

so maybe i subtract for when its not the 19 orange candies?

am i getting hotter or colder

can someone help me?

[shell moth]

I got 360 for the first one

But i'm not 100% tbh

https://math.stackexchange.com/questions/1368230/bowl-containing-candy-how-many-handfuls-of-15-are-possible-with-extra-conditio

Heres a link that could help you

[pliant elbow]

the math exchange link doesnt seem to cover stuff with at most, only at least

culd you walk me through how you got 360

[shell moth]

I thought of it like this

For 15 candies, you can have 3 sets

(15 cherry, 15 orange, 15 pineapple)

For 14 candies, you can have, for example, 14 cherry and one orange, or 14 cherry and one pineapple. So 2 ways, and since you can do this for each of them, you get 2 × 3 = 6 sets

For 13 candies, you can have 13 cherry and 2 orange, 13c and 2p, 13c, 1o, 1p

So 3 × 3 = 9 sets

This pattern continues

[pliant elbow]

do you know if you can help me with 3

[shell moth]

So I just found the sum of of the sequence 3n where n is 15

Tbf idek if my idea for the first is correct, so I don't think so sorry

[obtuse pebble]

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[rocky dove]

Number or triples (a,b,c) of positive integers
such that 2^a−5^b ∗7^c =

[obtuse pebble]

Please don't occupy multiple help channels.

[ember frost]

!1c

[obtuse pebble]

Please stick to your channel.

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[rocky dove]

Number or triples (a,b,c) of positive integers
such that 2^a−5^b ∗7^c = 1

[gilded topaz]

perhaps you meant for the equation to have something on the right-hand side?

[rocky dove]

yeah it,s 1

2^a−5^b ∗7^c =1
i missed it while copy pasting

[rocky dove]

i corrected it

[gilded topaz]

i would first take the diophantine equation modulo some small numbers

[rocky dove]

i tried but couldn't go any further. Tried modulo 5

[gilded topaz]

i have found this problem in a couple of different places

https://artofproblemsolving.com/community/c4h2493803p21007402

https://math.stackexchange.com/questions/1181946/find-number-of-positive-integer-solution?noredirect=1

https://math.stackexchange.com/questions/3948580/if-2a-5b7c-1?noredirect=1

https://artofproblemsolving.com/community/c4h1230802p6217475

https://math.stackexchange.com/questions/1827071/number-theory-problem-finding-triplets?noredirect=1

lol many more

seems to be a well-known problem

[rocky dove]

The issue is I'm not really familiar with these kind of problems, I was looking for some help, Thanks a lot

I saw this on one of the sites you mentioned

5|2a−1⟹4|a⟹3|2a−1

I understood till 5|2a−1⟹4|a
butr how did he arrived at the conclusion 3|2a-1

[gilded topaz]

which of those sites is that on

[rocky dove]

https://math.stackexchange.com/a/1182110/1312771

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[tender tusk]

do u know how negative exponents work?

[pale haven]

man i js want the answers

my teacher aint know how to teach

how do i do it

[pale haven]

?

[timid silo]

thats how the negative exponent work

work for answer

[pale haven]

how

[timid silo]

😭

[warm shale]

Project_Nova

[timid silo]

in your question

[rocky dove]

2^-4

[pale haven]

thats all

[timid silo]

no obviously

[pale haven]

Hey I did what u said

is this rght??

@timid silo

[timid silo]

got two wrong

[pale haven]

Which ones?

@timid silo

[obtuse pebble]

@pale haven Has your question been resolved?

[rocky dove]

c is also equivalent

d is not equivalent @pale haven

[obtuse pebble]

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[brave moon]

Do you need to find the characteristic polynomial in order to find the algebraic multiplicity

[brave moon]

Their was a question on my exam that asked to find the eigan space of a 3x3 it gave you both Igan values

And then part b was to diagonalize the matrix

But it didn’t say the algebraic multiplicity of ither eigan value

Is their a way to tell without solving for eigan values

I just solved it in a scrap peice of paper

But the question said specifically not to cheak if those where the eigan values as to not waist time

[kind hawk]

well while solving for the eigenvectors you will see how many solutions you have

[obtuse pebble]

@brave moon Has your question been resolved?

[brave moon]

Oh ok thank you thank you

[obtuse pebble]

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[trail tundra]

hey! very dumb question here: how do i determine the formula for the sequence for:

[trail tundra]

i know the bottom is 3^n

[molten grove]

numerator is alternating between (denom + 1) and (denom - 1)

so 3^n + (-1)^ n

[trail tundra]

oh i just did not catch that at all

lmao

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[vivid creek]

Can someone help me with this question please

[obtuse pebble]

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[outer geyser]

how do i find the coefficient of x² in the binomial expansion of (x² + 3/x)¹⁰

im stuck with multiplying out the powers for example (10C2)(x²)⁸(3/x)²

[tropic sand]

Write the formula again, but replace 2 with a variable r

Then simplify

You'll get x^20-3r

You want the coefficient of x^2, meaning you need to find a value of 'r' which simplifies to give x^2

So set 2 = 20-3r

r = 6

Now plug 6 into the formula

10C6 (x^2)^4 (3/x)^6

This does indeed simplify to x^2

So the coefficient is 10c6 * 3^6

@outer geyser

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[fluid oar]

can someone help me pinpoint my mistake here?

[placid charm]

Have you tried taking the integral more explicitly? You might've forgotten to account for something

@fluid oar - so you know I am trying to help you

[fluid oar]

i dont know intergreals

bc we havent gotten to that part

😭 we only know them as aanti derivitives

[placid charm]

Well darn. That makes it a little more difficult, doesn't it

[tropic sand]

I guys have done derivatives right?

Specifically chain rule

[fluid oar]

yeah

[tropic sand]

So differentiate that bottom function

And compare to the original one

[fluid oar]

i thought it was ln(3x-5)

cos d/dx lnx is 1/x

but idk where i went wrong

[tropic sand]

No, that's not what I mean

[fluid oar]

?

[tropic sand]

You see the function f = a ln(bx + c) + d?

[fluid oar]

yes

[tropic sand]

Differentiate this

And compare it to 7/3x-5

[fluid oar]

a 1/bx+c * b ?

[tropic sand]

Yes

So now compare

b = 3

c = -5

ab=7

If b = 3 and ab = 7, then a=7/3

[fluid oar]

ohhh

thanks for helping me understand

.close

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[timid silo]

https://media.discordapp.net/attachments/1230158901555757149/1230177725772206214/remix-802b7270-c6e7-42b5-8d08-91dc671c8ca7.png?ex=66325f49&is=661fea49&hm=2b45f8c019aa865282dbcc754060a638d2dbee42290044ba602f0bdf8121fe26&=&format=webp&quality=lossless&width=554&height=415

AD= BC
BD =CD
Angle DBC = ANGLE DCB = 20°
find x

[timid silo]

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[molten grove]

consider the ways you can rewrite 8^2

for example 64^1 is one way

[obtuse pebble]

@unborn stream Has your question been resolved?

[unborn stream]

yeah but then after that what do i do

[molten grove]

equate (x-1)^(x+y) to each of those cases

and try solving for x-1 = base, x+y = exponent

[obtuse pebble]

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[wide oracle]

So i m trying to solve this question but im a bit stuck

[wide oracle]

i think i did something wrong

[obtuse pebble]

@wide oracle Has your question been resolved?

[obtuse pebble]

@wide oracle Has your question been resolved?

[obtuse pebble]

@wide oracle Has your question been resolved?

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@wide oracle Has your question been resolved?

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[hoary rain]

any help here?

[vast bridge]

i think you could try $dS=\sqrt{1+f_{x}^2+f_{y}^2}dA$

[warm shale]

Jaxx

[vast bridge]

with dA = dxdy or dydx since x and y bounds are already given

alternatively maybe parametrization but idk if that would be easier/harder

[obtuse pebble]

@hoary rain Has your question been resolved?

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[drowsy drum]

I tried to take moments but I don't think im doing it right

can someone walk me through it?

<@&286206848099549185>

[tawny copper]

What have u tried?

@drowsy drum

[drowsy drum]

Taking moments from the left gets me really close

but shouldnt it be equal to the right?

seeing as it says the forces due to both supports

[tawny copper]

Assume the shelf doesnt collapse

You need to make a system of 2 equations

[drowsy drum]

i did 3 x 100 x 9.8 + 7 x 150 x 9.8 + 8.5 x 9.8 x 200 = F x 10

= 2989

the answer is 2990 so I think thats basically it but it should be equal to the right hand side right?

[tawny copper]

.

[drowsy drum]

?

[drowsy drum]

i dont understand

[tawny copper]

Hmm

Can u VC?

Its much faster to explain over VC

[drowsy drum]

not right now

i think im just confused bc i have calculated the force on both sides but the answers only give the LHS force

so i assumed that the force on both sides would be the same if it only gives one answer

which is why i thought i was doing it wronh

[tawny copper]

This doesnt make sense

[drowsy drum]

this got the answer

by taking the moments from A

that got 2989 and the answer is 2990N

[tawny copper]

Answer:
||F_reaction at E = 305 (upward)
F_reaction at A = 145 (upward)||

[drowsy drum]

no

the answer was 2990N in the textbook

which i got by using the method above

[tawny copper]

Yeah forgot the multiply by g

305 * g = 305 * 9.8 =2992.05 (N)

145 * g = 145 * 9.8 = 1421 (N)

@drowsy drum

[drowsy drum]

yes

but the answers only showed 2990 N so thats why im confused

[tawny copper]

They round it up

[drowsy drum]

no but it doesn't give me an answer for the right side support which is why im confused

I understand the rounding

[tawny copper]

Cause u only consider the moment on 1 side (A)

Consider the moment at E

[drowsy drum]

it says forces for each support?

[tawny copper]

There's 2 supports

A and E

[drowsy drum]

yes i know

which is why the other one is 1421 N

but the answers dont show that

so i thought i was doing something wrong

[tawny copper]

.

Calculate the other force

Do u know how?

[drowsy drum]

yes i know

i calculated that force

I was just wondering why the answers didnt show both answers but its just the textbook that is wrong

[tawny copper]

wdym

[drowsy drum]

the answers only show 2990 N when its actually 2990 and 1421N

so i thought i was doing it wrong because i wasn't getting the right answer, i was getting two

[tawny copper]

Probably cause they're lazy

LMAO

[tawny copper]

You should get 2

[drowsy drum]

yeah i think the answers are just wrong

thank you anyway

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[exotic latch]

hi

[exotic latch]

can someone check if i’m right

[torn citrus]

do you have solutions

[exotic latch]

mope

[vast bridge]

this is a calc ab sheet

[exotic latch]

yes

[vast bridge]

are you sure the answers arent uploaded somewhere

this looks awfully familiar

[exotic latch]

oh let me check

i didn’t even think abt that

[torn citrus]

imagine even doing questions without solutions 😔

[exotic latch]

🙁

omg i goin fit

FOUND

THE ANDEERS

answers

OK THX

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[torn citrus]

very nice

[exotic latch]

wait i’m not understanding c

[obtuse pebble]

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[exotic latch]

c

[exotic latch]

are we finding maximum and minimum values?

[torn citrus]

bro works under ultraviolet light

[exotic latch]

it’s LED 😭 SORRY

so there will be two?

where h’(t) is 0?

[exotic marsh]

there is another

[exotic latch]

oh right

(0, 3)?

and

(6,10)

wait

and (2,5)

three

[exotic marsh]

t=3, t=5, t=9

[exotic latch]

ok got it

thanks

wait

Oh yeah

cuz min counts too

thanks

.close

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[exotic latch]

WAITWAIT

CANT t= 9 be another

@exotic marsh

oh

u said

nvm

[exotic marsh]

…

[exotic latch]

.close

[exotic marsh]

lol

[obtuse pebble]

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[oblique pebble]

Task 10. (3 points) Let ( f: \mathbf{R}^2 \rightarrow \mathbf{R} ) be defined by ( f(x, y) = (\sin x) e^y ). Which of the following statements is true: \
A) For all ( \epsilon > 0 ), there exists ( \delta > 0 ) such that ( |x+y| < \delta ) implies ( |f(x, y)| < \epsilon ). \
B) For all ( \epsilon > 0 ), there exists ( \delta > 0 ) such that ( x^2+y^2 < \delta ) implies ( |f(x, y)| < \epsilon ). \
C) For all ( \epsilon > 0 ), there exists ( \delta > 0 ) such that ( |x| < \delta ) implies ( |f(x, y)| < \epsilon ). \
D) For all ( \epsilon > 0 ), there exists ( \delta > 0 ) such that ( |y| < \delta ) implies ( |f(x, y)| < \epsilon ). \
E) There exists ( \epsilon > 0 ) such that ( |f(x, y)| > 0 ) for all ( (x, y) ) such that ( x^2+y^2 < \epsilon ).

[warm shale]

Michael

[oblique pebble]

B) is correct here, but why is it $x^2+y^2 < \delta$ and not $\sqrt{x^2+y^2} < \delta$?

[warm shale]

Michael

[kind hawk]

well if x^2+y^2 < delta, then sqrt(x^2+y^2) < sqrt(delta) which is just another delta. so you could rename it

and same vice versa

[oblique pebble]

Ah

That's true

Ok so it was that simple. Thanks!

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[river falcon]

lets say i have a quadratic ax^2 + bx + c = 0 and its roots are p and q, now how do i find the equation whose roots are (1+p)/q and (1+q)/p

[ember frost]

!xy

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[river falcon]

i tried making a quadratic with sum of roots as coeff of x and product of roots as constant

[river falcon]

its literally what the problem says

[ember frost]

i highly doubt the problem starts with "lets say i have"

im asking you to send the problem verbatim

[river falcon]

The equation ax^2 + bx + c = 0 has roots p and q. What equation will have roots as (1+p)/q and (1+q)/p?

[errant lark]

Given the sum of roots and product of roots, can you find the quadratic satisfying those roots?
If yes, you have everything.

[river falcon]

the sum of roots and product of roots are variables too

like -b/a and c/a

so i just use this?

[errant lark]

Yes.

Of course, the obtained quadratic will have expressions of a and b as coefficients.

[river falcon]

yeah

lemme try

ee

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[dapper river]

Hey guys

[dapper river]

I neeed help

How do i make something the subject

The one on electronically is the correct answer but the one on paper is mine and it is wrong. I understand how to solve it but why is my method incorrect?

[safe haven]

its not wrong

[crude coral]

both are same

$$\frac{x^2-75}{-4x} = \frac{x^2 - 75}{-1(4x)} = \frac{-1(x^2-75}{4x} = \frac{75-x^2}{4x}$$

[warm shale]

JustToPro

[dapper river]

Ohhh okay thanks

[obtuse pebble]

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[distant solar]

In (b)

I'm quite confused of the question

Do I just solve the equation and get the answer?

[marsh geyser]

Which one?

[ember frost]

you are essentially asked to prove this

,tex .butterfly

[warm shale]

فطر

[marsh geyser]

But he is asked to prove that

[ember frost]

yeah i meant prove, idk why i said solve

[distant solar]

You mean solve the equation?

[graceful rapids]

they're asking why ad = bc
which usually means something like a verbal explanation

[distant solar]

How to prove it?

[marsh geyser]

Use the part a

To make a general proof

Or if you want, to prove the second

[distant solar]

Ok

. Close

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[distant solar]

.reopen

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✅

[distant solar]

.close

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[mellow jewel]

for this problem shouldnt the variance only be 3*3^2

in the ans key they did 3^2 * 3^2

but doesnt that assume that each runner has the exact same weight

it says 3 runners are chosen

so shouldnt it just be 3 * 3^2

[warm shale]

y0shi

[alpine verge]

what they have there is right

the a+bX just signifies a linear transformation

[mellow jewel]

but that doesnt apply to all cases right?

like this one for example

it would not be 4x+2y because that would assume all the four males weight the same and the two females weigh the same

so instead of multiply the variance by 4^2 or 2^2 u would just multiply by 4 and 2

right?

[alpine verge]

it’s not necessarily assuming that they have the same weight, but it’s rather just shifting the distribution up so that the expected weight would line up

[alpine verge]

this is the general rule, if you are scaling the variance by 2 then you are multiplying it by 2^2

[mellow jewel]

why in some examples they dont square the scale factor

[mellow jewel]

like for this example

this one did not square the scale factor

what makes this different to the original problem

[obtuse pebble]

@mellow jewel Has your question been resolved?

[alpine verge]

i can’t tell if that problem is trying to find the new mean or variance

it just simply labeled x and y without any indication

i would assume it’s the mean since that’ll be correct

[mellow jewel]

it's finding both

and they found the variance by simply multiplying it by 4

not 4^2

[obtuse pebble]

@mellow jewel Has your question been resolved?

[obtuse pebble]

@mellow jewel Has your question been resolved?

[obtuse pebble]

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[white trout]

helpp

[obtuse pebble]

@white trout Has your question been resolved?

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@white trout Has your question been resolved?

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[runic swallow]

If a, b, c, d are integers such that a+b+c+d=0, show that the number (image attached) is natural.

[runic swallow]

what i've tried so far:

[marsh geyser]

You mean nothing?

[runic swallow]

wait

no idea what to do after

[warm canopy]

square root of something squared does not in general return that thing

[runic swallow]

you mean that the answer in the end is not (b+c)(c+d)(b+d)?

[warm canopy]

Indeed it is not

Try squaring -1 and then square rooting

You don't get -1 back

[runic swallow]

i'm not sure where should i square -1?

[warm canopy]

I'm using it as an example

As to why $\sqrt{x^2} \neq x$ in general

[warm shale]

ΣAC

[warm canopy]

Your final result is clearly an integer, but your issue is it might not be positive

And that's bc you did sqrt(x²) = x

[runic swallow]

oh ok

so

should I take the absolute value of every parenthesis?

like so

but still don't know what to do next

[warm canopy]

Yes

Well, is your result a natural number?

[runic swallow]

oh damn

i am blind

ueah

TY

[obtuse pebble]

@runic swallow Has your question been resolved?

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[peak mirage]

How to do this question

I don't have any idea to start, I can only think of using coding (That's surely impossible)

Now I am determining the approximate range of the answer (between 1000 and 1500)

[peak mirage]

however, this should not work well

I am stuck because some of the multiples of 9 are actually containing 9

<@&286206848099549185>

Ok I am finished

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[surreal pebble]

For some reason, I cannot figure out how to properly draw this.

I've tried this but I don't think it makes sense

[torn citrus]

put down the points and connect the dots

[torn citrus]

thats not quite right

the angle of elevation/depression is the angle between the line that connects two horizontal lines

so you should really swap the place of A and E

B and D should swap as well

btw yuo didnt have to draw this out

[surreal pebble]

Would this express it properly?

[torn citrus]

for the purposes of the question that works

it should look something more like this

but either way the angles are the same hence why i said it doesnt really matter

all you need to know is the relation between angle of elevation and angle of depression

[obtuse pebble]

@surreal pebble Has your question been resolved?

[surreal pebble]

Ah, I see. Thank you!

So I set them equal to each other for x since alternate interior angles should be congruent and got 22° but that's not an answer choice so I'm not sure where I fucked up... : /

[surreal pebble]

<@&286206848099549185> : )

[small rover]

Problem?

[tribal citrus]

@small rover

[small rover]

Bro what's wrong with this problem's language 💀

[tribal citrus]

ikr

[small rover]

I didn't get it at all

[tribal citrus]

proffessor had a bad day 🙏

[humble wave]

the angle of depression is 2(x+8)

[tribal citrus]

i can rephrase it for you

or at least what i understood

[humble wave]

so 2x + 16

[small rover]

Yes pl

[tribal citrus]

We have two angles:

1. Angle E: This is the angle of elevation, observed when looking from point A up to point B. Its measure is given by 3x+13x+1 degrees.
2. Angle D: This is the angle of depression, observed when looking from point B down to point A. Its measure is given by 2(x+8)2(x+8) degrees.

We need to find the measure of each angle.

[small rover]

Then can't we just put them equal to each other because the horizontal is parallel

[tribal citrus]

i used that

[small rover]

That should give us the answer?

It didn't?

[tribal citrus]

Yeah

[surreal pebble]

I solved for x wrong

[small rover]

Umm but if what you've said is correct then it should.. i think there no other way than that.. and btw in the problem the angles re different i think its just a typo right?

[surreal pebble]

I didn't use the distributive property even though it says to

Because 2(x+8)

3x+1 = 2(x+8)
3x+1 = 2x + 16
3x = 2x + 15
x = 15

[tribal citrus]

i got the same

[small rover]

2x+16=3x+1=>x=15°?

[small rover]

Yeah same

[surreal pebble]

Plug in x for both angles and they equal 46°

[tribal citrus]

i got the same answer\

[small rover]

So its correct right?

[surreal pebble]

oh thank god im not the only one haha

[surreal pebble]

yep

thank you guys so much!

[small rover]

😅

[surreal pebble]

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[obtuse pebble]

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[ripe grove]

yo

[ripe grove]

an easy one but idk why im getting it wrong

[daring ravine]

AE || BC?

the arrows tell you

if no arrows you can still tell because of the 2 right angles

ED ≈ CD because of the little tick in the middle

AE perp AB and BC perp AB because of the right angles

is this just asking what the diagram symbols mean

[ripe grove]

so ae,bc are parallel ed,cd eqyal

[daring ravine]

yea

[ripe grove]

and whats the perp is

[daring ravine]

perpendicular

[ripe grove]

yeah

how do i find those ones

[daring ravine]

right angle

[ripe grove]

ab,ae,bc

not the other right angle cos its not deinfed as one

[daring ravine]

ok

[ripe grove]

is that right?

[daring ravine]

yeah but you need to say what is perpendicular with what

[ripe grove]

the answer is in these form

[daring ravine]

$\overline{\rm AB} \perp \overline{\rm AE}$

[warm shale]

mochaccino

[daring ravine]

oh ok then just do ae ab bc

but when u notate it write it like the bot

[daring ravine]

read as AB is perpendicular to AE

[ripe grove]

agh ok

cheers boss

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[solemn flax]

I'm not really sure what to do here, I'll translate the text top to bottom:

Task 5

What is the maximum size of the product of the positive numbers a and b if their sum is 3?
a) Find a possible solution by systematic trial and error.

possible solution: a*b = 2,25

b) Find the solution using a quadratic function. Complete the given solution steps and draw the graph of the appropriate function.

[solemn flax]

The following applies for a = x:

The vertex of f(x) = _ _ _ _ is S (_ _ _ | _ _ ), so the product of a and b can be at most _ _ _ _ _.

[obtuse pebble]

@solemn flax Has your question been resolved?

[solemn flax]

<@&286206848099549185>

If anyone is reading and doesn't understand, please tell me and I will try to simplify it more

Sigh.

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[mint oak]

wjat does this mean?

[zenith raft]

what is unclear about it?

[mint oak]

I dont understand what it wants me to do?

[zenith raft]

it wants you to draw a graph

with the properties it specifies

maybe what i'm saying sounds stupid since i'm just repeating the question

but do you understand it wants you to draw a graph that satisfies some conditions?

[obtuse pebble]

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[timid silo]

I did this without completing the square.

A/(s+3) + (Bx+c)/(s^2+8s+25)

Got to:

20 = A(s^2+8s+25) + (Bs+C)(s+3)

Thus:
s^2: 0 = A + B
s: 0 = 8A + 3B + C
cons: 20 = 25A + 3C

matrix calculator gave me A = 2, B = -2, C = -10. C should be -2/3 according to my professors notes.

What did I do wrong? Did I setup the PFD wrong somehow?

anyone?

[obtuse pebble]

@timid silo Has your question been resolved?

[prime reef]

what have you done exactly?

s^2+8s+25 doesnt have a solution

[timid silo]

that is my professors work (the screenshot)

i explain my work in the text after i sent the screenshot

our A & B values were the same, but not C.

[prime reef]

let me take a look at wiki then i might be wrong

cause i think when a polynomial doesnt have a solution you just place it the way it is

[timid silo]

hes a bit of an idiot

but i still think he got it right

okay nope

he got it wrong lmfao

i plugged it into a PFD calculator.

[prime reef]

yeah i see it

when you reach something without a solution you put cx+d on top and the full poly on bottom

i m not sure what he did there i cant understand his writing too well

[timid silo]

I think he tried completing the square.

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[prime reef]

he factored the polynomial into wrong solutions unlucky

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[formal turtle]

Could I walk through these notes with someone

I am so confused on what φ is

[obtuse pebble]

@formal turtle Has your question been resolved?

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[vital skiff]

why is this answer correct? shouldn't the area just be a single number?

[obtuse pebble]

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[mortal lotus]

How this shows it cannot be?

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[solid hound]

Is every odd number equal to (p-1)*n - 1 greater then 5, where p can be any odd prime?

[high lily]

no

[solid hound]

Why's that?

[high lily]

fails for the first odd prime

[drifting sandal]

5

[solid hound]

3n - (n - 1) = 2n +1

So idk how you got that

[high lily]

wheres
3n- (n-1) coming from

[obtuse pebble]

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[rich ermine]

.reopen

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[errant scarab]

struggling with this question, could someone please show the steps for the tangent line?

i tried doing this, but it feels like its getting too complicated so i think im doing something wrong

[graceful rapids]

the tangent line at p is $y = f'(p)x + f(p)$

[warm shale]

b

[graceful rapids]

is that your derivative^?

[errant scarab]

i dont think so?

[errant scarab]

is the x here intentional?

[graceful rapids]

think about y = mx + b
our m, or slope, is whatever the derivative is at the tangent point
which is f'(x)
our b is simply f(x)

[errant scarab]

so the +f(p) is just so we can move the slope up and down so that it will just touch the part of the function where we want x=p?

am i understanding this right?

[graceful rapids]

yup

exactly

[errant scarab]

ok

so then

so for getting the derivative of the funcion,

can you explain the steps?

i tried to use the quotient rule

[errant scarab]

this is where im at currently, but it looks nothing llike the answers lol

[graceful rapids]

umm you're definitely on the right track, the deriv is just ugly lol

math mistake i assume?

[errant scarab]

and for the f(p) part, ln(0^3)/(3-0) = undefined/ 3?

oh wait

its 1 not o

0

so 0/2?

ln(1^3)/3-1

so how do i get this to the derivative?

[graceful rapids]

quotient rule is the right method

again i'm not sure what exactly you did, but i suggest photomath or something for the actual steps

[obtuse pebble]

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[viral tree]

I got to 0.0011 mols of NaOH

but then in the answer it says that its 1.1 M

I dont understand this process

[graceful rapids]

is that per mL or

[viral tree]

this is the original question

[polar fossil]

1g of water = 1 mL

[viral tree]

the way I see it I have 0.0011 mols in 100 mL

and I need it to be in 1000mL

so I multiply it by 10

[polar fossil]

where did you get 100mL from

[viral tree]

0.011/1000

it said w/w here and w/w is x gram / 100 grams

[polar fossil]

no, it's gram for gram

0.05g NaOH / gram of solution

[viral tree]

because 1 = 100%?

[polar fossil]

yes

[viral tree]

so 5/100 = 0.05g

[polar fossil]

yes

[viral tree]

ok so I multiply the 0.05 grams with the density which is 0.88 g/mL = 0.044

[polar fossil]

you now have units of g²/mL. is that what you want?

[viral tree]

I dont understand this part here

[polar fossil]

M is the same as mol/L

[viral tree]

can you explain this to me?

[paper surge]

moles = mass over mr

moles = mass over mr moles = mass over mr moles = mass over mr

[polar fossil]

I'm not sure what's to explain

[viral tree]

so both answers are correct?

[polar fossil]

M is a unit that means mol/L