help-0

[ruby plover]

If Big Square A equals 5

Then what does Big Square B equal?

I think I got it

It's 14

[woeful pulsar]

it doesn't say much though

[upbeat gorge]

it is 14, yes

[woeful pulsar]

you have to infer what it's asking which is urgh

[ruby plover]

(3*3)+1

[upbeat gorge]

there's a formula for this btw

[ruby plover]

please show me

[ruby plover]

It really doesn't have any text

But the correct solution was 14 indeed

[woeful pulsar]

*answer

solution is when it's explained

[ruby plover]

Answer :) ty for correcting me

[upbeat gorge]

if you have an $n\times n$ grid of squares, then there are $$n^2+(n-1)^2+...+2^2+1^2=\frac{(n)(n+1)(2n+1)}{6}$$ squares in the grid

[ocean seal]

CST

[ruby plover]

what are the dollar signs for

[upbeat gorge]

it's a signal for texit to format it

[ruby plover]

Thank you for the formula, sir. Did you whip it up on the spot?

[upbeat gorge]

no, I've seen it done before

[ruby plover]

I've seen people who can make formulas of their own to make their maths life easier and for others as well

one day i will be like that

[modern tree]

is there such thing as amgm for real numbers

[charred flint]

uh what part being real numbers

[modern tree]

n

[charred flint]

so like the average of 5.4 numbers?

[modern tree]

mhm

[charred flint]

yea but no one uses it https://math.stackexchange.com/questions/2247940/is-this-continuous-analogue-to-the-am-gm-inequality-true

it's a special case of jensen's inequality which is super important though

[split summit]

anyone good at stats?

[modern tree]

@charred flint so is this a valid proof of holders

[charred flint]

[modern tree]

[charred flint]

oh you mean just the set of numbers in AM-GM can be real lol

yea sure, the mean of 2.4 and 2.8 follows amgm

[modern tree]

no

i mean the index

because i want this to be true for all real pq

so a+b/a should be real

its like my index

[charred flint]

I'm not completely following, maybe you mean weighted am-gm

[modern tree]

no the stackexchange you linked is what im talking about

[foggy crypt]

Is virtually worth doing something that can give you from 5 to 5000 earnings but it has a 35% chance to fail and lost you from 2000 to 5000?

[charred flint]

I'm pretty sure you don't mean the stackexchange

you can prove holders with weighted amgm like the proof here https://artofproblemsolving.com/wiki/index.php/Hölder's_Inequality

[modern tree]

cause if i dont have continuous AMGM

then my proof only works for rational p q

[charred flint]

if rational works then real will work

since they're infinitely close

[modern tree]

ye but i didnt write that

part

[tight locust]

rational will work. think about it

if you terminate the decimal expansion of any real number at any finite number of digits you get a rational number

also infinite number of digits if it's a repeating sequence

like 1/7 = 0.142857...

[hardy patrol]

I'm studying for a placement test and a question of this nature is given. I know e has something to do with ln/natural log, but I'm not sure what type of question this is or how to solve it. can anyone point me to the right direction?

[alpine sable]

hmm this is a quadratic in e^x

so you'll have e^x = something by quadratic formula

and then you can carry on with ln

[hardy patrol]

is there a khan academy video on this? I'm having trouble visualizing the process

[grave matrix]

Try substituting y = e^x into this

[alpine sable]

substitute e^x=u if you have trouble visualizing it

yea that might help

[grave matrix]

(Further, note that e^(2x) = (e^x)²)

[hardy patrol]

ok I see

ty ty!

[grave matrix]

nps

[golden sluice]

Guys is this correct?

Im not sure how to count it

[alpine sable]

so we have 8 ways to pick the breads

and after you pick your bread you can pick the cheeses in 5 ways

you can make a table to visualise

[golden sluice]

Table?

[alpine sable]

will look something like this

sorry for the crude drawing

but do you know what i mean?

hopefully this makes it clear that there are 8*5=40 ways to pick the bread and the cheese

does that make sense?

[golden sluice]

Oooohhh

Yeahh i understand

So its 40 ways?

Because 8*5

Okiee thank you

[alpine sable]

yeah but we're not done yet

[golden sluice]

Do we need to count each?

[alpine sable]

because then we want to pick the topping and sauce

you just need to multiply 8*5*3*4

hopefully that seems intuitive

[golden sluice]

OH WAIT

120

[alpine sable]

multiplication mistake

[golden sluice]

480

LMAO IM SORRY :')

[unique kiln]

why is f(x,y,z) = z^(x+y) defined at z=0 but the equivalent f(x,y,z) = exp((x+y)ln(z)) is not defined there?

for x+y>0

[silent path]

Anyone know what to do in this problem?

[raven mica]

Guys, i need to find the nuclear charge of an element which doesn't exist, how do i do that?

[vale wigeon]

what's that 121 there?

is that its atomic number?

element 121?

how many protons do you think it has in its nucleus?

[raven mica]

121

[vale wigeon]

so

[wild needle]

Can someone help me with this

[vale wigeon]

@wild needle channel busy

[raven mica]

go to a different channel

[wild needle]

Oh ok

[raven mica]

ok so?

[vale wigeon]

so what exactly is the issue, zenia

you know this element has 121 protons in its nucleus

the only other thing in the nucleus is neutrons, which have no charge

[raven mica]

i need to find the nuclear charge but i know that u need to substract electrons from protons but they're equal?

[vale wigeon]

the NUCLEAR charge doesnt include electrons

electrons arent IN the nucleus

[raven mica]

oh

so what do i do?

[vale wigeon]

stop overthinking

the answer is +121 elementary charges

[raven mica]

why is it so high lol

[vale wigeon]

because 121 protons?

[raven mica]

so that makes the nuclear charge 121?

[vale wigeon]

the nuclear charge of gold is +79

yes

[raven mica]

may u explain how?

how do i calculate that

i have this done already

[raven mica]

that cant be correct

[vale wigeon]

why not

what do you think the charge of a gold nucleus is

[raven mica]

cuz nuclear charge isnt literally just thte atomic number

[vale wigeon]

then what is the nuclear charge according to you

[raven mica]

i watched multiple videos on youtube it says u have to subtract the electrons from protons and that gives u the answer

[vale wigeon]

are you sure you didn't mishear anything

[raven mica]

but that gives u the effective nuclear charge

no

[vale wigeon]

"the answer" is vague

Nuclear charge is the electric charge of a nucleus of an atom, equal to the number of protons in the nucleus times the elementary charge.

from wikipedia

[vale wigeon]

atom ≠ nucleus

[vale wigeon]

an atom isnt the same thing as a nucleus

an atom isnt the same thing as a nucleus

[raven mica]

wdym

[vale wigeon]

an atom isnt the same thing as a nucleus

i mean exactly what i said

the nucleus does not include electrons

the electrons are AROUND the nucleus not IN the nucleus

[raven mica]

but thats how u find the nuclear charge

I know that lol

[vale wigeon]

no it isnt!

[raven mica]

i know how a nucleus looks like

so ur telling me the video isnt correct

[vale wigeon]

no

i'm not saying that

i'm saying that the video is irrelevant

because you're not finding the total charge of an atom

but only of its nucleus

which doesnt have any electrons

[raven mica]

b) Write down the charge of each atomic nucleus.

this is the question i have to do

[vale wigeon]

yes

the charge of the NUCLEUS

the nucleus doesnt include the electrons

am i not getting through to you w/ that ????

[raven mica]

ok sure, so how do i find the answer now?

[vale wigeon]

the charge of a nucleus is LITERALLY just the number of protons in it

that's it

[raven mica]

so i just write down the atomic number for example k=19?

or +19

[vale wigeon]

yes

[raven mica]

wtf is this task lol

is this correct? @vale wigeon

[vale wigeon]

yes

[raven mica]

thats so odd

usually our tasks are way more complicated

[pulsar pollen]

can anyone help me w this problem 🙂

someone give me a hint or clue what to do, my mind is lagging rn

<@&286206848099549185>

what formula should i use?
principal(1+rate)^years or (p)(rate)(time)

[vale wigeon]

you've got compound interest going on here

but also you don't have a single investment but an annuity

[austere thorn]

Anyone help me with this

I’m lost

[pulsar pollen]

meaning i have to add up the money per year to make it an investment? or principal?

[vale wigeon]

...per month.

you should try to avoid using formulas

[pulsar pollen]

oh i see

wdym avoid formulas?

[vale wigeon]

i mean exactly what i said

[alpine sable]

ask in an unoccupied channel please

[vale wigeon]

try to think about whats really going on instead of just applying formulas blindly

brb class

[pulsar pollen]

ahhhh yes okay

[grand jolt]

if cos(x) = -1/2 how do i find x?

[night blade]

you can draw the unit circle

[mossy oracle]

...

I know the answer is 264 cans

[alpine sable]

before the restock, there were 200-68=132 cans

before the restock, half the canned drinks in stock were sold out, and the other half remained

the other half (132 cans) remained

132 is half of the total cans before any cans were sold

multiply by 2 to get the whole, 132*2=264

[mossy oracle]

Ohhh, thank you! You've taught me more than my teacher could in 2 weeks xd

[south stream]

Is factorial of 5: 5*4*3*2*1?

[alpine sable]

correct

5!

[south stream]

The syntax for it is !

[echo spire]

Okay so there is a triangle ABC, with C1 the middle of AB, B1 the middle of AC and A1 the middle of BC.

I need to find where the point O is located to get this equation valid
OA + OB + OC=OA1 + OB1 + OC1

I have been thinking about placing O as the center of gravity

Like OA = 2/3 AA1

And OA1 = 1/3 AA1

[alpine sable]

intersection of the 3 medians is the centroid, which is also the center of mass of the triangle

[echo spire]

Thanks, I didn't know how to translate that. I am now stuck on what to do next

[alpine sable]

Like OA = 2/3 AA1
And OA1 = 1/3 AA1
these are also correct

what do you want to do next?

[echo spire]

Prove that this
OA + OB + OC=OA1 + OB1 + OC1
Is valid ((p.s they are vectors))

I got stuck here

[alpine sable]

umm

coordinate bash?

not the best solution

but should work

[echo spire]

Well, yeah but we are supposed to don't do coordinate bashing.

[alpine sable]

ok i think i've got an idea

we wanna prove the sum of the circle vectors = the sum of the square vectors

lets consider adding the two bottom circle vectors

this is going to be double the bottom square vector

[echo spire]

Well, I got an idea as well?

From yours

We could try and write them until we get AB + CB like substitute them

[alpine sable]

oh, does this work out to prove OA + OB + OC=OA1 + OB1 + OC1?

[echo spire]

Let's hope? So far it's going okay

[alpine sable]

well my idea was to take this and apply it to all 3 pairs of circle vectors and the square vector between them

[echo spire]

The circle inside triangle theory?

[alpine sable]

B+C=2E
A+C=2F
A+B=2D

add them all up

2(A+B+C)=2E+2F+2D

A+B+C=E+F+D which was what we wanted

[short turtle]

how to find the vector

[golden arch]

Is there a formula to calculate the distance between a Point and they yz plane?

[vale wigeon]

yes, it's the absolute value of the point's x coordinate.

[short turtle]

nvm i got it

[golden arch]

@vale wigeon can you elaborate?

or do you mean its 4

[vale wigeon]

the distance from the point (x,y,z) to the yz plane is |x|

[golden arch]

Ah okay thanks!

[vale wigeon]

idk what else there is to elaborate on

[sharp anchor]

Hey im not really sure where to go from here

[left spear]

Behold, my amazing art skills

[left spear]

Me neither, that's the full solution is it not

[sharp anchor]

Perhaps i just wanted to try it and it looks like it could be simplified, guess not

[swift chasm]

how do i start :/

[alpine sable]

the picture doesn't look like it's to scale

draw in the radii

[austere thorn]

Anyone help me on this one

@alpine sable

[alpine sable]

ask in an unoccupied channel

[alpine sable]

from here use special right triangles to solve for x

so start with the area of the whole sector CAD (r*theta) then subtract off the right triangle and the circular sector with central angle 150 deg
@swift chasm

[alpine sable]

are you having trouble setting up the integral?

[short turtle]

how to find area? by using intergral or finding the area of trapezium?

[short turtle]

yea the intergrall

[alpine sable]

trapeziums won't help here

you need to use an integral

all these blue lines are just the height of the line - the height of the parabola

[short turtle]

so use intergral to find the area

[alpine sable]

yes, but the integral of what?

[short turtle]

this?

3 2 12 5 xx x − += +

wait i cant pres

3x^2-2x+1 = 2x +5

then use the values of x ?

[alpine sable]

the area we want is the difference in height

height of the line - height of the parabola

does that make sense?

then we need to find the lower and upper bounds

[short turtle]

Yeah got it thanks

[swift chasm]

got it now thanks c;;;

[crystal cape]

How do I solve this

[alpine sable]

area of shaded = area of isosceles triangle - area of white circular sector

[crystal cape]

But i dont know height of the triangle

How do I calculate the area?

Cause I don't have either base or height

[crystal cape]

Right yeah

[alpine sable]

you can find base as well similarly

[crystal cape]

R^2= b^2 + (r sin theta) ^2

Or simply r cos theta

Right?

[alpine sable]

the base is 2*rcos(theta)

[lethal lichen]

how to do part b?

[alpine sable]

did you do part a? it should help with part b

[lethal lichen]

yeah i did

i got log_3(x^2 a)

[alpine sable]

correct

now we can set that equal to 2

then from there we can solve for x in terms of a

[lethal lichen]

ok

so log_3(x^2 a) = 2

how to re-arrange?

[alpine sable]

are you familiar with converting log notation to exponential notation?

[lethal lichen]

i think so

[lethal lichen]

ahh i see thanks

[alpine sable]

you can also think about it as going from
log_3(x^2 a) = 2
to
3^ [log_3(x^2 a) ] = 3^2

and on the left you end up with x^2 *a

[lethal lichen]

ok

i got 3^2 = x^2 a

[alpine sable]

correct, now solve for x

[lethal lichen]

so x = sqrt (9/a)

[alpine sable]

yup

[lethal lichen]

thank you for your help

how do i simplify

(3-sqrt(3)) / 6

[glass lichen]

that's pretty much simplified unless you mean rationalize the numerator

[lethal lichen]

yeah rationalise

do i multiply it by:

(3+sqrt(3)) / 6

?

@glass lichen

[glass lichen]

multiply by $\frac{3+\sqrt{3}}{3+\sqrt{3}}$

[ocean seal]

moshill1

[lethal lichen]

ok

how would i do part b?

i was trying 1 - (0.49^2 + 0.38^2 + 0.10^2 + 0.03^2)

but do i need to account for getting the same blood group twice, twice for each goroup

like 1 - (2 * 0.49^2 + 2 * 0.38^2 + 2 * 0.10^2 + 2 * 0.03^2)

i hope that makes sense

[alpine sable]

1 - (0.49^2 + 0.38^2 + 0.10^2 + 0.03^2)
yes this is exactly correct

p(different)=1-p(same)

well you don't have to ping me specifically

how would I proceed here

also you're kind of interrupting the conversation

you can post your question in an unoccupied channel

[alpine sable]

so the probability that both people have the same blood type = P(both have O)+P(both have A)+P(both have B)+P(both have AB)

but do i need to account for getting the same blood group twice, twice for each goroup
no, you can label the two people person 1 and person 2 , and we just need the probability that both of them have the same blood type

P(both have O) = p(1st has O AND 2nd has O)

=p(1st has O) * p(2nd has O)

=(0.49)^2

[lethal lichen]

Ok thanks

[copper thicket]

This might be (definitely is lol) a stupid question but can someone explain how one read this kind of notation

[sly mantle]

the notation reads as "function name:domain->codomain"

so this states a function f with R\{0} as its domain & R as its codomain

[copper thicket]

oh ok and what exactly does it mean by R/{0}

is it just that the domain does not include 0 ?

[sly mantle]

R\{0} is the set of real numbers excluding 0

[copper thicket]

yeah perfect. Thanks 🙂

[lethal lichen]

OK, so i have the equations

y=3sin^2(&)

y=2cos(&)

where & = theta

how would i find the points where they intersect

i tried simultaneous equations but struggling to solve them

[vale wigeon]

$3\sin^2(\theta) = 2\cos(\theta)$ is the equation you're interested in here

[ionic jewel]

2 cos theta ^

[lethal lichen]

ok

im trying to solve it but i just can't

[ocean seal]

Ann

[vale wigeon]

can you show an attempt you made?

[lethal lichen]

ok

i want to make it into 2 brackets

and then solve from there

sorry if its messy

[vale wigeon]

so you got to 3cos^2(θ) + 2cos(θ) - 3 = 0?

and then you tried to factor manually without success

[lethal lichen]

yeah

i would know how to solve via quadratic formula

[vale wigeon]

so why not do that

[lethal lichen]

because it seems to me that i would just run into roots

it seems unpractical to do like that since i never have done this question without being able to solve manually

[vale wigeon]

you would run into roots yes

[quick talon]

is y= 3x -2 and** 9x -3y =6** equivilant???

[vale wigeon]

this channel is occupied. please don't intrude on ongoing convos in questions channels in the future.
but yes, y=3x-2 is equivalent to 9x-3y=6.

[quick talon]

can u explain why and im sorry

[vale wigeon]

go to another unoccupied channel

@lethal lichen and i are not done.

[lethal lichen]

so i will try quadratic formula i guess

and see what happens

[barren sinew]

https://i.redd.it/jq9q3qnknrr61.jpg

somebody tell me if there is any maths from calculus 3 in this question paper

[lethal lichen]

-_-

@hollow oyster @barren sinew please go to another question channel

and delete your messages

np

[wary harness]

A river in normal condition is 28 cm deep. After a rainstorm, its level increased by 3 1 / 2m. At 3.89 m, he is in danger of getting out of bed.
a) How much more can the water level rise before it gets out of bed?
b) The record height is 5.18 m. How much higher than the normal river level is this height?

Can some1 pls help me with this ASAP?

[lethal lichen]

anyways, Ann i found the solution to the question

so no longer need help for now

thank you

[hollow oyster]

If i could get some assistance for this question that would be greatly appreciated

[ionic jewel]

doesnt look like it

[barren sinew]

so its only calculus 1 and 2 right?

[ionic jewel]

I learned everything I would need in calc 1 and 2 from that, the educational cutoffs may vary

[ionic jewel]

set up an equation

[alpine sable]

Can somebody simplify this to the equation

I don’t understand how to

[ionic jewel]

f = 69
f = 4s-3

[barren sinew]

This is a final term question for my upcoming semester. So I am assuming that learning up to calculus 2 is enough for the semester

[ionic jewel]

wait i lied no its not

the first problem is calc 3

it was crossed off so I skipped over it before

partial derivatives & 3 dimensional stuff is all calc 3

[barren sinew]

except the first one, all are calculus 2?

[ionic jewel]

yes

[barren sinew]

god damn. I have a long way to go then. haven't even started with calculus 1 yet

[ionic jewel]

good luck w that

[barren sinew]

thank you so much for the help

[hollow oyster]

@ionic jewel any chance you can help me out?

[ionic jewel]

[ionic jewel]

dont ping me specifically who knows if i could answer

[frail viper]

i know all the answers in the world

so ping me anytime

my daddy actually invented maf

jk

[sacred otter]

Hey

Im new here

[frail viper]

hello!!!

[sacred otter]

What to do xD?

[frail viper]

do fun!

be happy!!!!

[sacred otter]

Wru from?

[frail viper]

my mom?

u mean where im born?

canada

[sacred otter]

Where u live

[frail viper]

cana

da

[sacred otter]

Oh

Nicee

[frail viper]

u?

[sacred otter]

Pakistan

[frail viper]

nice!

u speak hindi?

or punjabi?

[sacred otter]

Urdu

Yea i understand punjabi a lil bit

And hindi too

[frail viper]

nice!

[alpine sable]

The total area of ​​the yellow rectangle and the blue triangle is

[limpid spade]

You can already find the area of the rectangle

[alpine sable]

2a * b + 2b * 2a * 0,5

but i need to reduce and idk how

[lost steeple]

What do you mean by reduce

[ionic jewel]

$2a\times b + 2b\times 2a \times 0.5$

[ocean seal]

bunny

[lost steeple]

Do you mean simplify?

[ionic jewel]

$= 2ab + (0.5)(4ab) = 2ab + 2ab = 4ab$

[ocean seal]

bunny

[alpine sable]

yes

how's 2a * b = 2ab

[lost steeple]

How isn't it

4 * 6 * 3 = 4 * 6 * 3

[ionic jewel]

pushing two variables together implies multiplication

[alpine sable]

2a * b = 2ab
2a * 2b = 2ab

[lost steeple]

2 * a * b = 2 * a * b

[alpine sable]

brug

what

[ionic jewel]

NO

2a*2b is NOT 2ab

[lost steeple]

2 * a * b = 2ab

[ionic jewel]

its 2*a*2*b = 4ab

[alpine sable]

4b

4ab

[ionic jewel]

yes

[lost steeple]

when they are next to each other it implies multiplication

[alpine sable]

wait

so bunny

and mystifine

when you have like 2a * 2b
u do 2 * 2 and a * b
4ab

same with 2a * b
you do 2 * nothing
and a * b
2ab

[lost steeple]

When you have 2a another way to represent it is 2 * a

when you have 2a * 2b
you can do
2 * a * 2 * b

[ionic jewel]

that is not the right intuition but you get them right so

[alpine sable]

How's it wrong

[lost steeple]

and in terms of multiplication it doesn't matter what order you multiply

so you can group like constants

2 * 2

and the rest just comes along

[ionic jewel]

you dont think of it as "2 * nothing"

[alpine sable]

2a * 2b = 2 * 2 and a * b = 4ab
2a * b = 2 * 1 and a * b = 2ab

Prove me wrong

[lost steeple]

2a * b is not 2 * 1

[ionic jewel]

that is correct

hes doing it a weird way but it works

its fine

[alpine sable]

how would you do it then

[ionic jewel]

2ab = 2 * a * b = 2ab = 2ab

[alpine sable]

It's the same

[ionic jewel]

yes but theres no "1" coming in anywhere

it gets the same answer but thinking about it is different

you are just doing extra thinking for no reason

[alpine sable]

2a*b = 2 * a * b = moved space = logic confirmed

Lmao

2a * 2b = 2 * a * 2 * b /// 2 * 2 * a * b
2a * b = 2 * a * b /// 2 * a * b

@ionic jewel

[ionic jewel]

yea

[alpine sable]

ok

wait

isn't it

2a * b + 2b * 2a * 0,5
2ab + 4ba * 0,5
6ab * 0,5
3ab

[ionic jewel]

no

remember PEMDAS

[lost steeple]

Bedmas

[ionic jewel]

always do multiplication before addition

ok british guy

[lost steeple]

I'm canadian 😦

[ionic jewel]

okay budget british guy

[lost steeple]

What does P stand for

[ionic jewel]

parenthesis

[lost steeple]

oh

[ionic jewel]

brackets are [] to me

[lost steeple]

Brackets 💀

[ionic jewel]

not ()

[lost steeple]

I call those square brackets

lmao

[alpine sable]

i did

okay say if this is wrong or right

2a * b + 2b * 2a * 0,5

[lost steeple]

Bunny could u help me with a question in #help-1

[alpine sable]

2ab + 4ba * 0,5

2ab + 2ba

4ab

[lost steeple]

yes

[alpine sable]

of yeah i just overlooked it before

circumference and area

Is the answer the third one

[drowsy scroll]

Programmers

[alpine sable]

circumference: a + a + b + a + b + a = 4a + 2b
area: a^2 + ab

[ionic jewel]

looks like it

[alpine sable]

bunny

is this correct

[ionic jewel]

yes

its right

[alpine sable]

is 1ab the same as ab

[ionic jewel]

yes

[lost steeple]

yes

[alpine sable]

ok

lol

Thanks for helping me

can anyone help me with this have no clue

<@&286206848099549185>

simplify

[amber marsh]

a^4?

[alpine sable]

how

😔

[amber marsh]

cos u add the powers then take them away?

[alpine sable]

are you familiar with the exponent multiplication/division rules?

[amber marsh]

laws of indeces

[alpine sable]

no

[amber marsh]

ye u should learn them first

[alpine sable]

^

[amber marsh]

then u will be able to do them, it’s called laws of indices

[alpine sable]

ok

[amber marsh]

i am confused

how is this the case

[alpine sable]

also called exponent properties

[amber marsh]

why is the last line like that

[alpine sable]

both sides were divided by cos(theta)

sin/cos=tan

[amber marsh]

omggggg

[alpine sable]

-cos/cos=-1

[amber marsh]

ur a life saver, lmao i am slacking

alr thx

[junior warren]

how would i solve this?

im also confused because there is a negative side length i think

[alpine sable]

(sintheta)^2+(costheta)^2=1

tan =sin/cos

[junior warren]

thats the trig identity right?

so i take that identity

solve for sin

and then solve for thetea

theta

[alpine sable]

(sintheta)^2+(costheta)^2=1
pythagorean identity
tan =sin/cos
definition of tangent

[junior warren]

ok

so i need sin first

[alpine sable]

they don't ask for theta

[junior warren]

which i get from the first identity

oh right

[viral owl]

hey guys

[alpine sable]

find sin, then divide that by cos

[junior warren]

ok thx

[viral owl]

im 13 years old so please dont laugh if this is "easy" for you, im doing a kangaroo test and i really need help

geometry test

[lost steeple]

I think it's against the rules

[viral owl]

oh

let me check them

[lost steeple]

#rules

[alpine sable]

if it's a test then we can't help you there

[lost steeple]

oh #❓how-to-get-help 6

[alpine sable]

but if its a practice test/worksheet/hw then it is perfectly fine

[junior warren]

wait dan one thing

[lost steeple]

dansman help me

[junior warren]

with the sin and cos idenity

[viral owl]

its not an test, i just dont understand it because the test is in english

and im spanish

[junior warren]

does the fact that its squared matter at all?

[viral owl]

LIKE

im saying its not a test

[alpine sable]

yeah, you will get 2 possible values for sin(theta)

[viral owl]

its a quiz

[alpine sable]

so 2 different values for tan(theta)

[junior warren]

so will i have to square -3/8 when subbing in?

[lost steeple]

@viral owl If it's for marks we simply can't help

[alpine sable]

don't expect help with quizzes/tests

[viral owl]

ok

[alpine sable]

hello

need some help over here

[alpine sable]

post in unoccupied channel please

oops

sorry

[alpine sable]

(sintheta)^2+(-3/8)^2=1

[junior warren]

yeah

so i have sintheta^2=55/64

now just sub both for sin/cos

i think

[alpine sable]

square root both sides, the pos and negative solution for sin are both valid

[junior warren]

so i dont have to square root the 55/64 before plugging into sin/cos?

[alpine sable]

sintheta^2=55/64
first you need to square root both sides to get sintheta

then plug into tantheta=sintheta/costheta

[junior warren]

oh ok

so its sqrt55/64 divided by -3/8

[wary harness]

<@&286206848099549185> can some1 help me with this pls?

[junior warren]

@alpine sable im stuck now lol, so i just multiply the fractions sqrt55/64 and 8/-3?

[alpine sable]

sintheta^2=55/64
first you need to square root both sides to get sintheta

so sintheta=+-sqrt(55/64)

[junior warren]

yes

i got that

[alpine sable]

sintheta=(sqrt55)/8 or -(sqrt55)/8

[junior warren]

oh right

you sqrt the denominator too

rigt

[alpine sable]

so now, [(sqrt55)/8] / [-3/8] and [-(sqrt55)/8] / [-3/8]

[junior warren]

right

so then just solve?

[alpine sable]

then you just simplify

[junior warren]

yeah its +-sqrt55/3

[alpine sable]

correct

[junior warren]

thx

[cold roost]

In the future, go to a channel that isn’t in use when you present your question. As well as pinging helpers while people are still working on a question. It’s viewed as rude / interrupting and you’re less likely to be helped. Try posting in #calculus

[wary harness]

I said please and Its not that I interrupted anyone

I didnt say

Oh leave him

Dont help him

Help me

I said please and I respected the 15 minutes rule

So Im not being rude

[cold roost]

The rules says to not ask a question in a channel that’s in use as well as what you just mentioned.

[wild shard]

[viral crag]

i have a question that goes like this if a-b=b-c=7 then what is the value of c^2-2b^2+a^2 ?

[tulip bear]

how do i find this

[wild shard]

use subsitution

[viral crag]

but there is 3 variables

and i only have 2 equations

[strong smelt]

Ruffini

I don't think thats resolved through inequations

[wild shard]

no u have 3

[viral crag]

how ?

[wild shard]

a-b=7

b-c=7

a-b=b-c

[strong smelt]

tru

[viral crag]

wait yea thats true

[strong smelt]

a=2b-c?

yeah yeah

right

lol

[viral crag]

so there is no clever way

just solve the 3 equations right ?

[wild shard]

the easiest way is often the most clever

but besides

there is no other way

in your case

[steady frost]

can y'all explain how can i find the area of a isosceles triangle with just knowing that the hypotenuse is 25, and the altitude's bigger than the base by 10 cm?

just a hint would do cause i've been struggling

[viral crag]

when i try it just return to the same equations

[wild shard]

ill try rq

[wild shard]

pythag, 25 = (10+x)^2 + (x/2)^2

where x is the base of triangle

[steady frost]

lemme tryyy

when using pythag staring with the hypotenuse does the hypotenuse not get squared?

[unreal forum]

‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎

[viral crag]

how to solve these 3 equations

[loud kayak]

😐

[wild shard]

im lost now lol

[wild shard]

it doea mb

[steady frost]

dude

im gonna do pythag and send it here u'll see it just doesn't wanna like work

[wild shard]

x should be equal to 14 or -30 @steady frost

[woven shoal]

hey guys, i need help for some homework

i dont even understand it, if someone can explain?

[wild shard]

just post someone may or may not help

[manic quail]

Sure, it would be better if you posted in another channel though, @woven shoal

[woven shoal]

oh

which one'

?

[manic quail]

Let's go #help-3 .

[alpine sable]

i need help badly i have no clue

[steady frost]

@wild shard this is what i got out of pythag

a is base

help 😢

[wild shard]

yep thats corrext

[steady frost]

what's nextttttttttttTT

[wild shard]

solving for x gets you 14 or -30

[steady frost]

quadratic?

[wild shard]

ofc

[steady frost]

sheesh this teacher dude

[wild shard]

but use 14 as -30 will get you complex numbers

[steady frost]

u got it

thanks dude : p

[dapper patio]

Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of the top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?

[ionic jewel]

draw it and use trig

[spare hill]

i think you use the sum of two tangents for that problem

[dapper patio]

aight ill have a look ty :)

[spare hill]

so i did this in class

teacher was watching over and didn't disprove it

but

the last two equalities now look sus to me'

<u,u> + <u,v> + <v,u> + <v,v> = <u,u> + 2<u,v> + <v,v>

is this actually true?

it would mean that <v,u> = <u,v> but i dont think that's the case

[charred flint]

yea inner products are commutative

[spare hill]

oh?

https://math.stackexchange.com/questions/1311394/why-conjugate-when-switching-order-of-inner-product

i saw this earlier

so i'm overthinking it?

i'm not sure what conjugation does for inner product :/

[charred flint]

oh I mean specifically dot products sorry

[obsidian laurel]

Plur

[charred flint]

if you're using real numbers it's fine

[spare hill]

so in my case, it's still commutative?

[charred flint]

I'm assuming you're doing real vectors so yea

conjugation just changes complex numbers

[spare hill]

ok thanks

[obsidian laurel]

You know how to do Law of Sines? Plur

[charred flint]

I know there's a formula for it

[obsidian laurel]

Lmao

I needed help on this

Ggwp

[alpine sable]

@tough tangle

[tough tangle]

uhm

[hexed glacier]

sine rule?

[tough tangle]

no

[hexed glacier]

can't remember

[tough tangle]

cos 30 = x/7

[hexed glacier]

$z^2 - z +1 = 0$

[ocean seal]

zyzt

[hexed glacier]

how do i factorize this?

i tried quadratic formula

[charred flint]

you can't

it has no zeroes, so you can't factor it further

,w plot x^2-x+1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Plurmorant#1811

[charred flint]

since it doesn't touch the x-axis

[alpine sable]

well you could always factor it over the complex numbers

[hexed glacier]

yeah, that's what i am trying to do

quadratic formula is only for real(side question)?

[crude nacelle]

no, you'd just get a negative discriminate and you can get an imaginary solution (2)

[alpine sable]

you can use quadratic formula to find complex zeroes as well

[hexed glacier]

yeah, i thought it works for complex too
this is what i get(next post)

[ocean seal]

zyzt

[hexed glacier]

which is not the answer i believe, which is cube root of -1

(editing the post above)

$\frac{-(-1) +- \sqrt{(-1)^2 - 4(1)(1)}}{2} = \frac{-(-1) +- i *\sqrt{3}}{2}$

[ocean seal]

zyzt

[ionic jewel]

you are looking for $\pm$

[ocean seal]

bunny

[smoky skiff]

Can someone help me with this integral?

$\int e^x\cdot cos^2x$

[ocean seal]

Bardak

[limpid spade]

Integral by parts

f(x)=cos^2x and g'(x)=e^x

Formule is f(x)*g'(x)-integral((f'(x) *g(x))

@smoky skiff

[smoky skiff]

Ok I tried that what then?

[limpid spade]

Show me

[hexed glacier]

yeah, thank you. i think my mistake is not checking if their absolute value equals to 1

and then factorizing them, and then using euler formula...etc etc...

and get my anwer

[smoky skiff]

$\int e^x\cdot cos^2x = e^x\cdot cos^2x + \int e^x\cdot 2cos(x)sin(x)$

[ocean seal]

Bardak

[limpid spade]

Wait

It's Formule is f(x)*g(x)-integral((f'(x) *g(x))

But here it doesn't matter

[unreal forum]

Hello my dear friends
Well, here I am on record at last
And it feels so wonderful to be here with you on my first album
I'm so happy
Aha! Happy go lucky me
I just go my way
Living everyday
I don't worry
Worrying don't agree
Things that bother you
Never bother me
Things that bother you
Never bother me
I feel happy and fine
Aha
Living in the sunlight
Loving in the moonlight
Having a wonderful time

[smoky skiff]

so what's the problem?

[limpid spade]

2cosxsinx is sin2x try to redo per partes with f(x)=sin2x and g'(x) =e^x

[smoky skiff]

alright I will try

give me 2 min

[limpid spade]

So e^xcos^2x-new per partes

[smoky skiff]

and what then?

it is like a circle isn't it?

[limpid spade]

Show me what u get

[alpine sable]

any ideas

[limpid spade]

It's occupied

[alpine sable]

my bad

[limpid spade]

Occupied

[smoky skiff]

$e^x\cdot cos^2x + \int e^x\cdot sin(2x) = e^x\cdot cos^2x + e^x\cdot sin(2x) - \int e^x\cdot 2cos(2x)$

[ocean seal]

Bardak

[limpid spade]

Mhhh

I see

cos^2x is the same as (1+cos2x)/2

Write as (1/2)+(cos2x/2) integral will be 1/2integral((e^x(cos2x+1))

Then u choose f(x) as 1+cos2x and g(x) as e^x

U would apply per partes 2 times

And u will see at 2nd time that the integral will be the same as the original integral

I'll explain what to do next when u do per partes 2 times first

cos^2x=(1+cos2x)/2 because of product to addition Sampson formula. It's an identity

[smoky skiff]

yeah the identity is fine

I will try per partes twice now

[limpid spade]

Okie

[tacit breach]

does this mean ur done? @smoky skiff

[limpid spade]

No

It's occupied

Other channel pls

[smoky skiff]

$\frac{1}{2}e^x\cdot (1+cos(2x)) + e^x\cdot 2sin(2x) - \int e^x\cdot 4cos(2x)$

[ocean seal]

Bardak

[old quarry]

Oh sorry, there was a gap with 5 mins

[limpid spade]

U should become this

[final acorn]

idk what im doing, can someone tell me what ones go where?

[limpid spade]

$=\mathrm{e}^x\sin\left(2x\right)-\left(2\mathrm{e}^x\cos\left(2x\right)+\class{steps-node}{\cssId{steps-node-10}{4}}{\displaystyle\int}\mathrm{e}^x\sin\left(2x\right)$

[ocean seal]

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

[limpid spade]

I don't understand how e^x sin2x is the same as e^xcos^2x

[smoky skiff]

I don't understand u

[manic quail]

,w e^x sin(2x)=e^x cos^2(x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[manic quail]

you mean this, @limpid spade ?

[limpid spade]

Yeah

[manic quail]

Wolfram doesn't think it is true.

[limpid spade]

Veryhappyperson how would u solve integral of cos^2xe^x

[manic quail]

Maybe by parts?

[smoky skiff]

lol

[manic quail]

Sorry, I was never good at solving integrals xD

[limpid spade]

Doing it 2nd time u get e^xsin2x

Which is not equal to e^xcos^2x or integrable (without per partes)

Weirds

[pallid horizon]

Is anyone good with finding perimeters using angles?

[alpine sable]

of a circle?

[pallid horizon]

Triangles

[alpine sable]

send ur problem rq

[pallid horizon]

I have to find the perimeter

But i don’t know what to do with the angles

[daring violet]

aight so yeah you could see that they're both right triangles

and the left triangle is 45 45 90 and the right one is 30 60 90

[pallid horizon]

Right

[terse iron]

do you know any methods ?

[alpine sable]

do you know the ratios for special right triangles

[daring violet]

there's certain ratios

[pallid horizon]

I missed class so no

Not really

[alpine sable]

45 45 90 would be A A Asrqt2

in this case Asqrt2 being 8

u could get A from that

[pallid horizon]

I’m confused

I’m sorry

Not good at math

[alpine sable]

what grade r u in

or what math class

[pallid horizon]

9th

Geometry

[daring violet]

yeah i'm also in geometry

i learned this last semester

[pallid horizon]

Really?

[daring violet]

for 30 60 90 triangles the ratios for them are

[terse iron]

i used pythagorean theorem

[daring violet]

short leg: x
long leg: x*sqrt3
hypotenuse: 2x

[pallid horizon]

That sounds familiar the short leg

[daring violet]

legs are the two sides that aren't the hypotenuse

[pallid horizon]

Yup

That makes sense

[terse iron]

dont

[polar gull]

???

[terse iron]

this chat is being used

thats why there is 10 of them

[daring violet]

JEEZ what kind of math is that? i'm in geometry

[pallid horizon]

@daring violet so what do I do with that knowledge of the legs and hypotenuse

[polar gull]

which channel is available?

@daring violet graph

[terse iron]

5

[daring violet]

so from the 45 45 90 triangle (the left one) there are also ratios for that which someone had said but in case you forgot they're
legs: x
hypotenuse: x*sqrt2

[terse iron]

https://www.youtube.com/watch?v=OE2g2SgPC6s&t=36s

watch this

[daring violet]

nice vid

[pallid horizon]

Ok give me a second to watch

The video doesn’t show how to do it with only 1 side and the rest angles

So what do I do with the legs

[alpine sable]

@pallid horizon

[pallid horizon]

Is there an equation I have to use

[tender glacier]

yo can someone help me with a few problems

[woven shoal]

HI

open channel¿

[woven shoal]

yes i can

[primal tiger]

Hi. If I have the equations of a line (a) x=2, y =3z and a line (b) x=2z, y=3 and I want to find the angle θ. between them using the formula a*b=|a| |b| cos θ.

Is it correct to say that the direction vector of the first line (a) is (0,3,1) and the direction vector of the second (b) line is (2,0,1).

So a*b=1

And |a| =sqrt(10), |b|=sqrt(5)

so cos θ = 1/5sqrt(2) ?

[tender glacier]

can i dm

[woven shoal]

sure

[pallid horizon]

So the perimeter is 34.76 @alpine sable

?

[alpine sable]

8+4sqrt2+4sqrt6+8sqrt2 would be the perimiter idk what that is

[pallid horizon]

K

[alpine sable]

Hey, let's say 42 = 100, what is 13 out of the 42 in percentage then? Can you show me the calculations?

[alpine sable]

13/42 x 100

Is it seriously that fucking simple

https://tenor.com/view/sad-boy-crying-gif-12465917

yes

I did this shit and I was struggling with that

You know you hit rock bottom when you're that fucked.

😂

[alpine sable]

when u overwork ur brain and have to put 1+1 in the calculator during a test

[pallid horizon]

May I have help with a couple of other questions?

I have to find x

[alpine sable]

x is the short line segment on the bottom or the whole thing

[pallid horizon]

Short line

[daring violet]

30 60 90 triangles

[pallid horizon]

Both are?

[daring violet]

not both

there's two i see

the one that's very large and the little one

[pallid horizon]

Yea

[alpine sable]

i would say use x to get the length of the line in the middle in terms of x

then use that to get the line on the very right

[pallid horizon]

How would I go about that

[daring violet]

use the triangle ratios

you could see that the short leg is 18/2 since the hypotenuse is 2*short leg

oh yeah and it's similar triangles

[pallid horizon]

For the overrall triangle?

[alpine sable]

Haha! Exactly

[daring violet]

the overall triangle and the little one

[daring violet]

heh that's what i'm doing rn

[alpine sable]

shi hold on

[terse iron]

lol

[alpine sable]

nvm it was right

[daring violet]

yeah i forgot

[terse iron]

same

[alpine sable]

do u know the radius or is it just r

[terse iron]

just r

[alpine sable]

if the radius is just r it would be pi*r^2(110/360)

for PQ

[pallid horizon]

Just two more and then tell me if I did another one the right way

[daring violet]

isn't arcPQ just 110?

if O is the center?

[alpine sable]

no thats for radians

[terse iron]

no

[pallid horizon]

If you don’t mind

You guys are a huge help

[alpine sable]

arc length is only the same as the angle when it's radian