help-28

[gaunt lynx]

that’s an

isosceles

right

what’s a property

for

isosceles

[little heron]

Ohh nevermind

I got it

[gaunt lynx]

aye aye

nice

let’s go

💥

[little heron]

yeee

I’m confused with this one tho

@gaunt lynx

[gaunt lynx]

yeye

alr

so

you know how

the sides

the 2 sides

length were equal

for isosceles

[little heron]

yeah

[gaunt lynx]

that

applies to

the angle as well

for the

2 side

so

u can use that

to find

JIH

[little heron]

oh ight

[gaunt lynx]

yeye

[little heron]

lemme try that

Is it 63

[gaunt lynx]

,w 180-58-58

[glossy valve]

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[gaunt lynx]

nope

[little heron]

dang

64

[gaunt lynx]

yeye

how’d u get

63

[little heron]

I think I subtracted wrong

[gaunt lynx]

alr

[little heron]

thank you tho

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[blazing quartz]

Did I choose the right sub ?

[kind jay]

u=sqrt(x-1) is better

[blazing quartz]

thank you! i worked that out, sqrt(x-1) was definitely the proper sub!

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[uncut vine]

Help

[torn jolt]

$\left( \dfrac{u}{v}\right) ^{'}=\dfrac{u'v+v'u}{v^{2}}$ with u=x²-9 & v=x-7

[glossy valve]

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

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[sharp shadow]

Isn’t it minus

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[slender tide]

do we only need to mines the elemnt from the set A when its in {} ?

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[balmy peak]

just wondering bec it takes a while to compute

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[charred storm]

A) The mean of 15,31,47,83,97,119 and p^2 is 63. Find the possible p.
B) The mean of 6,29,3,14,q,(q+8), q^2 and (10-q) is 20. FInd the possible value of q

[scenic wren]

for A, do you know how to calculate the mean?

@charred storm

[charred storm]

does this help?

[scenic wren]

i mean, i know how it works, but do you?

[charred storm]

yeah but im not sure how to solve that question

[scenic wren]

calculate the mean and set it equal to 63

then you get an equation

which you solve for p

[charred storm]

oh ok

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[grim kestrel]

Is my reasoning ok?

[fossil stump]

Looks good to me 🙂

[grim kestrel]

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[lunar loom]

<@&286206848099549185>

hello

haha

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[sterile holly]

The answer I attempted for sin(pi*x/3) was incorrect regarding my earlier question, is the following correct?

[sterile holly]

$\sum_{n=0}^{\infty }(-1)^{n}\frac{\pi^{2n+1}x^{2n+1}}{3(2n+1)!}$

[glossy valve]

Yelo

[sterile holly]

Trying to find the maclaurin series for sin(pi*x/3)

[fossil stump]

3^ 2n + 1

[sterile holly]

Ohhh, forgot that part. Ty

I'm likely to ask another question in a few minutes, should I just keep this channel until I'm otherwise timed out?

[fossil stump]

up to you - if you want, newer channels tend to be taken care of sooner in my experience lol

[sterile holly]

Makes sense, I'll close this one then

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[sterile holly]

$\frac{5}{(4+x)^{3}} = \frac{5}{64+48x+12x^{2}+x^{3}} = \frac{5}{1-(-\frac{3}{4}x-\frac{3}{16}x^{2}-\frac{1}{64}x^{3})} = \sum_{n=0}^{\infty }5(-\frac{3}{4}x-\frac{3}{16}x^{2}-\frac{1}{64}x^{3})^{n}$

[glossy valve]

Yelo

[sterile holly]

This is marked as incorrect but I can't figure out why

Finding the power series of the first expression

[fickle path]

this is just an example
If im given say x^4-3x^3-3x^2-ax+b and given zeros at -2,1 (order 2) how do i find a and b?

[sterile holly]

I'm not sure I understand your question

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[fossil stump]

adding 0?

Oh nope

[hot herald]

negation?

[fossil stump]

return a different number you started with,

[fossil stump]

This is a good one

[light sonnet]

2's compliment twice?

Or is that the same as negation?

[rare dock]

reciprocal too

[light sonnet]

I think this is the best because technically you'll get a different number

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[humble thunder]

How would I go about solving question 3?

[humble thunder]

do I just move the 5 to the right side and do the exact same thing?

Since there is a cos(z) do I differentiate with respect to z or do I just do x and y only

[crude relic]

Yeah. Just move everything to one side and use the general equation with
F(x,y,z) = xy^5 cos(z) - z - 5

[humble thunder]

oh I see thank you

[humble thunder]

Do I not add z_(0) at the beginning anymore?

[crude relic]

Naw, that's already taken care of when you move everything to one side. That's what the c is in the photo.

[humble thunder]

Ok gotcha thank you

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[tame lantern]

i was wondering on how to solve this question

i was not in class this day for school and i aws wondering how to go through with it

[deft zodiac]

whats with the 0s n 1s

[tame lantern]

no aidea i missed the entire day

[deft zodiac]

well just

[tame lantern]

i just understand theyre the zeroes of the equation so

(x-2)(x+4)

[deft zodiac]

a(x+2)(x+4)

[tame lantern]

is dat all?

[deft zodiac]

well

find that a in front

with

f(-8)=-1

[tame lantern]

so a is -1?

[deft zodiac]

err

no

mayb idk

[storm birch]

So it's asking to white a function ax²+bx+c, such that a(-4)²-4b+c=0, a(-2)²-2b+c=0, and (-8)²-8b+c=-1

[deft zodiac]

go work out f(-8) in terms of a

[deft zodiac]

oh my dont use the sum ver of poly

[storm birch]

So yeah, a(x+2)(x-4) gives us the formula

[tame lantern]

to be honest im a tad confused how do i solve for a in

a(x+2)(x-4)

[deft zodiac]

work it out normally

n thrs just an extra a outside

[storm birch]

Plug in -8 in place of x and equal the whole thing to -1

[deft zodiac]

a*(normally)

[tame lantern]

o so

-1 = -8(x+2)(x-4)

wait no im stupid

-1 = a(-8+2)(-8-4)

[storm birch]

Exactly

Solve and isolate a

[tame lantern]

-1/72 is wat ig ot

[storm birch]

Yeah

[tame lantern]

aight thanks man

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[opal elk]

Lowest degree polynomial from some of its zeros

zeros given are 2+i and 3. Coefficients must be rational.
I tried (x-(2+i))(x+(2+i))(x-3) but it doesn't foil out to be rational.

[smoky wing]

What did you get?

[opal elk]

x^3-3x^2-3x+9+(-4x+12)i

[smoky wing]

Ah wait it should be (x-(2+i))(x-(2-i))(x-3)

[opal elk]

oh fr? why is it (x-(2-i)) instead of what I had?

[smoky wing]

If you have a polynomial with real coefficients and you know a+bi is a root then its conjugate (a-bi) must also be a root

Then it’s just $(x-r_1)(x-r_2)(x-r_3)$ where $r_i$ is a root

[glossy valve]

Pure

[opal elk]

ohhhh tyty

[smoky wing]

[opal elk]

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[uncut scarab]

]

[uncut scarab]

ik this question is based in physics but my brain is dead and im confused on the algebra part

how do i go from the part where 240m is isolated to the one where aav is isolated

[silk obsidian]

Can you send the whole question

[uncut scarab]

im sorry i just solved it 😭

tysm anyways thoo

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[tough bolt]

is 1b asking for volume for solid of revolution?

<@&286206848099549185>

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@tough bolt Has your question been resolved?

[topaz valley]

no

surface area of revolution

[crude relic]

Nope, a surface area of revolution. Instead of integrating something like Pi (f(x))^2 where f(x) is the radius. You integrate a circumference, something like,
2Pi(f(x)) where f(x) is the radius about the x axis.

[topaz valley]

[tough bolt]

ah thanks

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[twin heron]

Could someone help me with b, say what exactly went wrong?

[short crest]

Ok so, first of all

what is the equation of the line

[twin heron]

Well i wrote d=10v+0.5?

[short crest]

the y is d/v and the x is v

[twin heron]

Y=10x+0.5

Or something

[short crest]

uhh... no

the gradient is wrong

[twin heron]

I see, i give up

[short crest]

or the slope

take 2 points from the line

[twin heron]

I took (0,0.5) and (10,1.5)

So (1.5-0.5)/(10-0)

1/10

[short crest]

yes

1/10

[twin heron]

The graident

I see

So y=1/10+0.5?

X/10+0.5

[short crest]

just write it as

y = 1/10x +0.5

since the standard from is y = mx + b

and then substitute the y and x with the d/V and V

y is d/v, x is v

[twin heron]

Yup

Or y is t

[short crest]

huh?

why t

oh

ye

[twin heron]

Speed = distance over time

[short crest]

yeah sure, but that won't help

d/V = 1/10 V + 0.5

ok so you have this now

just do some rearrangements

[twin heron]

For d in terms of v

[short crest]

multiply both sides by V

[twin heron]

Yup

[short crest]

yeah and you'll get it

[twin heron]

I see i see

Appreciate it

Also another question

Could you give me a similar problem to this

I couldn't quite get it, i asked for help

I got help but its the only such question

So i need the same question but Like a little different to make sure i got this

[short crest]

uhh

im bad at making questions

CYA

[twin heron]

Alright i hope someone else could help me here

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[jovial wind]

Hi

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[torn jolt]

can someone help me with this pls

[velvet spoke]

what does she earn per day?

[torn jolt]

14.50 multilpied by 24?

[velvet spoke]

why 24?

she only works 5.5 hrs per day

[torn jolt]

ohh

79.756

i meant

79.750

[velvet spoke]

yes

thats per 1 day, so per 5 days is then?

[torn jolt]

398.750

[velvet spoke]

👍

[torn jolt]

Thank you.

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[torn jolt]

.reopen

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✅

[torn jolt]

wait no

its 398.75

i think

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[fast peak]

what have you tried

[severe basin]

I computed the matrix A-(lambda)I

Equated it to zero

Got a quadratic with two unknowns

I know this is kinda related to eigenvalues from 3b1b videos

But, I don't have a formal introduction to the topic

[fast peak]

well it's a quadratic in lambda

solve for lambda in terms of a

[severe basin]

$(a-\lambda)^2=0 \implies (a=\lambda)$

[glossy valve]

QuantumBee

[severe basin]

Is that right?

Nvm. It should be correct.

If I plug in $a=\lambda$, $$\begin{bmatrix} \frac{a}{2}-a & \frac{-a}{2} \ \frac{a}{2} & \frac{a}{2}-a \end{bmatrix}$$

[glossy valve]

QuantumBee

[severe basin]

Determinant of this matrix can be zero iff a=lambda=0.

@fast peak

So, a+lambda=0

Con someone confirm?

@onyx glen

(Sorry for the ping if that disturbs you)

[fast peak]

lambda=0 is wrong

or lambda=a

[fast peak]

clearly this matrix is invertible for lambda=a, so the determinant is nonzero

[severe basin]

So, how do I go about it then?

[onyx glen]

,w det {{a/2 - λ, -a/2},{a/2, a/2 - λ}}

[glossy valve]

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Requested by Ann#0413

[onyx glen]

so this is... $\frac12 (a^2 - 2a\lambda + 2\lambda^2)$, or $\frac12 (a - \lambda)^2 + \frac12 \lambda^2$...

[glossy valve]

Ann

[severe basin]

Hahn, so that should be equal to zero

So, $$(a-\lambda)^2+(\lambda)^2=0$$

[glossy valve]

QuantumBee

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@severe basin Has your question been resolved?

[severe basin]

@onyx glen

How do I continue from here?

[onyx glen]

you have the sum of two squares of real numbers on the lefthand sidd

side*

they must both be zero

[severe basin]

Was my previous method wrong?

[severe basin]

@onyx glen

[fast peak]

the point of the question was more to determine lambda in terms of a

[onyx glen]

well denascite it turns out this shit only works if a itself is 0

[fast peak]

well I guess if we are assuming lambda has to exist

[severe basin]

It would be helpful if anybody of you can tell me if my approach was correct or wrong.

It can help me in doing similar kind of problems in future.

[fast peak]

yes it was fine. I overread that lambda had to be real. otherwise there are other solutions

[severe basin]

Ok

Thank you.

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[jolly tulip]

hii, could anyone help me with this?
-There are 8 red and 2 black balls in an urn. John takes n balls at once. What is the minimal number of balls that he should take so the probability that there is at least one black ball among those that he took, is greater than 2/3?
I'm really confused and idk how I should even start

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[elder oracle]

Hey, I've got a problem from the Cambridge 2018 entrance assessment. I've no idea where to start with the question but I know the answer is E

[clear lily]

well if a cube is twice as wide as another cube

how much greater will its volume be

[elder oracle]

It's volume goes up by 8

[clear lily]

exactly

because (2/1)^3 = 8

[cyan verge]

hi can someone help

[elder oracle]

So I'm meant to be cubing the expression for each dimension of the cup rather than just replacing one dimension?

[clear lily]

what no

just apply the same concept

the other cup is of equal shape

and is precisely 5/4 times as big

[elder oracle]

Right, I should be ok then

Thanks :)

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[whole inlet]

is this regex the same as 1*

i know anything concatenated with empty set is the empty set
but in 1*, is the set containing 0 1's empty string or empty set, cuz i think empty string has a cardinality of 1, while empty set has cardinality of 0
thats my main confusion

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[whole inlet]

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[foggy acorn]

A 3 dm long, 2 dm wide and 12 dm high glass vase in the shape of a brick body, open at the top, stands on the table. On the outside of the vase, on one of the 12 dm long edges, Hugo the Ant is standing 1 dm from the table, and on the opposite edge, inside the vase, 1 dm from the top of the vase, stands Margo the Ant. Hugo wants to get to Margo, who is standing still, by the shortest possible route, using only the surface of the vase the surface of the vase. How many decimetres must does Hugo have to go? (The thickness of the vase is negligible.)

[foggy acorn]

somehow i got a smaller number than all of the choice option

which is sqrt125

what did i do wrong?

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@foggy acorn Has your question been resolved?

[foggy acorn]

<@&286206848099549185>

I misunderstood the problem

let me try again

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[hot herald]

what have you tried

[gusty tinsel]

To be honest idk how to Solve it 😅 cause in class I would ask for help

[hot herald]

consider the trig function that can be used to relate the marked angles and sides

[gusty tinsel]

How do we solve it?

[hot herald]

did you think about what I said

[empty sapphire]

I would recommend using SOH, CAH, TOA:
$\sin(\theta) = \frac{\text{opp}}{\text{hyp}}\$
$cos(\theta) = \frac{\text{adj}}{\text{hyp}}\$
$tan(\theta) = \frac{\text{opp}}{\text{adj}}\$

[glossy valve]

MellowDramaLlama

[empty sapphire]

I see one trig value that fits the mould here. Do you see it?

[gusty tinsel]

I think

Do we have to multiply or do disvions ?

Near the certain angles?

[hot herald]

identify the positions of the given sides relative to your angle of interest

i.e. is the side with length n
adjacent, opposite to theta or is it the hypotenuse?

[gusty tinsel]

Hypo?

[hot herald]

no

the side with length n is not the hypotenuse of the triangle

[gusty tinsel]

It Is the opposite ?

[hot herald]

yes

now, is the side with length 2n
adjacent, opposite to theta or is it the hypotenuse?

[gusty tinsel]

Hypo

[hot herald]

yes

now considering soh cah toa
can you use that information to set up an equation

[gusty tinsel]

Uhh idk how

[hot herald]

read the soh cah toa summary above
to get a visual representation you could also google soh cah toa

you've identified you have
theta,
the opp
the hyp
which equation above uses those three things

[gusty tinsel]

You mean for like 2n?

[hot herald]

no

look at the soh cah toa image above

which of the three equations listed has
theta,
opp
hyp

[gusty tinsel]

SOH?

[hot herald]

soh would be applicable here

can you write the equation using that

$$\sin(\theta) = \frac{\text{opp}}{\text{hyp}}$$
earlier you identified your \verb|opp| as $n$ \and \verb|hyp| as $2n$,
substitute those expressions into the equation.

[glossy valve]

ℝamonov

[gusty tinsel]

Like that?

And what’s Thea?

I see that it says substitute

What’s that?

[hot herald]

theta is the Greek letter $\theta$ commonly used to mark angles

[glossy valve]

ℝamonov

[hot herald]

substitute is a very common term used in math

essentially meaning replace

since your opp is n, replace opp with n
since your hyp is 2n, replace hyp with 2n

[full forum]

@gusty tinsel Has your question been resolved?

[gusty tinsel]

Iam kinda lost 🥲

[hot herald]

which part of what I said do you still have an issue with

[gusty tinsel]

The part with the 2n thing

[hot herald]

what specifically about 2n

[gusty tinsel]

Like how you replace

[hot herald]

do you know what replace means?

[gusty tinsel]

I meant to like opp thingy

[hot herald]

doesnt answer my question

[gusty tinsel]

Oh sorry yes

[hot herald]

replace opp with n

do you know what that means

[gusty tinsel]

Like switch ?

[hot herald]

yes

[gusty tinsel]

N and opp ?

Like that

[hot herald]

what?

just swap out opp for n

you can pretty much just erase/rub out opp and write n in it's place

substitution is a very common mathematical concept

you might be overthinking

e.g.
y = 2x
substituting 2 for x
or x=2 into the equation results in
y = 2 * 2 = 4

[gusty tinsel]

So we have to multiply again?

Or divide

[hot herald]

your're skipping ahead

can you perform that simple action that I requested you do

[gusty tinsel]

I”ll try

So I have to solve for n right?

[hot herald]

stop skipping ahead

your going off on your own

don't overthink

[gusty tinsel]

Sorry

Also I have a learning disability

[hot herald]

starting with
$$\sin(\theta) = \frac{\text{opp}}{\text{hyp}}$$
all that I'm asking you to do is instead of \verb|opp|, write $n$, instead of \verb|hyp| write $2n$ and that's it. NOTHING ELSE.

[glossy valve]

ℝamonov

[gusty tinsel]

And I get nervous answering stuff cause Iam Scared of making the person angry

[hot herald]

demonstrate that you're reading, show a genuine attempt and people won't get angry

dodging questions, not listening, going off on your own to do stuff not being asked of you will annoy people

[gusty tinsel]

Oh

My bad

[hot herald]

if your doing this on paper, start with that equation
and you can literally cross out opp and write n in it's place
cross out hyp and write 2n in it's place
and you'll have what I want from you

[gusty tinsel]

Like this?

[hot herald]

yes

that was an overkill instruction btw

normally you'd just write
$$\sin(\theta) = \frac{\text{opp}}{\text{hyp}} = \frac{n}{2n}$$

[glossy valve]

ℝamonov

[hot herald]

can you simplify that fraction?

[gusty tinsel]

No

Can you teach me how?

[hot herald]

no

you have too many knowledge gaps for me to fill

at this point I'd recommend that you do a review on algebra

[gusty tinsel]

Oh alright

Well thanks for trying to help me

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[rancid notch]

How do i go about this quesiton

[full forum]

@rancid notch Has your question been resolved?

[velvet spoke]

look at the prime factorizations of the numbers and try to construct increasing sequences of factors, for example
$$144 = 2^4 \cdot 2^3 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = (2 \cdot 3 \cdot 4) \cdot (2 \cdot 3) = 4! \cdot 3!$$

[glossy valve]

nvx

[velvet spoke]

but $4! \cdot 3!$ obviously does not work as $c = 0$ or $c = 1$ in this case. so we can rewrite it to obtain
$$144 = 2 \cdot (2 \cdot 4) \cdot (3 \cdot 3) = 2 \cdot (8 \cdot 9) = \frac{2! \cdot 9!}{7!}$$

[glossy valve]

nvx

[rancid notch]

Hold on, ill review this later

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[rancid notch]

Would the answers not just be the same

[smoky wing]

Yeah I think so

[rancid notch]

But it aint though

A is 10 easy, b is somehow 50, c is like

[smoky wing]

Damn I hate combinatorics

[rancid notch]

1050

[smoky wing]

One sec

I guess it means you choose one of the vowels

So you times that by 5C1

And last one times it by 21C1 (and 5C1)

For choosing one consonant

[rancid notch]

Oh cuz liek the alphabet

Wait

[smoky wing]

Ye

[rancid notch]

Ok hold on

[rancid notch]

Yeah so 5C1 would be 5

Then what

Oh

Nah i dont get it

Two identical vowels

That would be 2 5C1’s

[smoky wing]

You’re choosing which vowel out of the 5

[rancid notch]

Any right

[smoky wing]

Ye

[rancid notch]

Two times

[smoky wing]

Because they are identical it’s only 5C1

[rancid notch]

Which is 10

Yeah

[smoky wing]

Not 2 times

[rancid notch]

But then we get 3 Bs

Oh

Hold on

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[mystic cedar]

Could someone help me here

with this equation

[tender sonnet]

Do you remember how to find the derivative of a log?

[mystic cedar]

no but ik how to find the derivative of ln

thats what im confused on

[tender sonnet]

Then maybe convert the equation to something like ln(x^2)/ln(10)

[mystic cedar]

this is the dervative of log?

[tender sonnet]

I belive so

[mystic cedar]

so how do we do this

[mystic cedar]

with this equationm

[tender sonnet]

Well start with what you do know

Convert the parts of the equation you understand

[tender sonnet]

Yup now it’s just the x^2 you need to worry about

The power rule doesn’t work here

[mystic cedar]

wym

[tender sonnet]

Well not in the way you think

Just remember when doing the power rule you are going to multiply this entire equation by 2 not just x

[mystic cedar]

what?

[tender sonnet]

Lemme try to explain

Consider that

d/dx(1/x^2)=-2/x^3

[mystic cedar]

?

how is that possible

[tender sonnet]

quotient rule

[mystic cedar]

oh yea

lol

[tender sonnet]

So now back to the original project

Try to use the quotient rule

Actually idk if quotient rule works here

[mystic cedar]

brugh

[tender sonnet]

But I do know that it’s basically the opposite of the power rule with this one

Kinda

You multiply the whole thing instead of just x then subtract 1 from the exponent

[mystic cedar]

chain rule?

can someone else help me

<@&286206848099549185>

[tender sonnet]

Nvm

Figured it out

No it makes sense

[mystic cedar]

these are the rules i leanred

for logs

[tender sonnet]

Well you can add this one to your list as well since it also works

Doesn’t hurt in know information outside of what’s taught

Another way to look at it is the 4th on down left side

[mystic cedar]

which rule from these

would work on this equation

[tender sonnet]

1/u*u’=u’/u

For this one

Top left however I’d like to make an addition to the top one

Makes things smoother

Now try

[mystic cedar]

wait

so we dont use log at all right:

[tender sonnet]

Nope

[mystic cedar]

\

oh thats what

i was

confused on

ok

[tender sonnet]

Yes

[mystic cedar]

so its just like this

[tender sonnet]

Derivative of x^2 on the right

Wait nvm

Yeah you got it just make sure to add the ln(a)

[mystic cedar]

i was using the 1/u

rule

1/u*u'

i did that correct right?

[tender sonnet]

That works but can be simplified a bit ^

[mystic cedar]

ye but i did this right?

answer would bne

2/x

[tender sonnet]

your still forgetting the ln(a)

But yes once you have that it’s correct

[tender sonnet]

So to make sure everything is correct show me your final answer

[mystic cedar]

I did this using the rule 1/u * u'

[tender sonnet]

I know you did but you still need to put the ln(10) in there otherwise it’s wrong I have to go to bed now gn

[mystic cedar]

but its nto in the answer

so how do u get rid of it

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[mortal forum]

Algebra word problems

How do I do these questions

[onyx glen]

do you know how percentages work?

[mortal forum]

sorta

im in gr9

[onyx glen]

...there is no sorta, you either do or you don't.

[mortal forum]

well no

[onyx glen]

the first question is "What is 80% of 20?"

are you able to answer questions like that?

[mortal forum]

yeah but not with algebra, and my teacher wants me to use algebra for these

[onyx glen]

...oh, so you have special instructions from your teacher? did they only say "use algebra" and nothing else

or was there more to it

[mortal forum]

use algebra

cause were doing algebra unit

[onyx glen]

so your teacher told all of you, "Use algebra" and gave no further instructions. do i understand correctly?

has your teacher already rejected a solution of yours because of you not "using algebra"?

[mortal forum]

yeah

[onyx glen]

these problems are not the kind that require algebra tbh

like sure you could like

let x be the number of questions answered correctly, then 0.80*20=x

what a deep and insightful equation...

[mortal forum]

what about the other one

[wide jasper]

they probably want it like 60x = 24 I cant read smh

[mortal forum]

60x/60 = 24/60

[onyx glen]

actually no

60x = 60-24, if we want x to be the percentage we are asked for

[mortal forum]

36%?

60%?

<@&286206848099549185>

im going to be afk so you can just paste how to do this problem #2

[slate zenith]

still on this?

So we lets figure out how many people didn't choose cycling, 60-24 and we get 36

so we got 36 out of 60

can be written as 36/60

lets solve 36/60 is .6

and .6 is the same thing as 0.60 which is 60%

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[stoic wedge]

i need help solving for P in this

[stoic wedge]

<@&286206848099549185>

[sharp shadow]

Vector TW is the average of YX and UV (vectors) this is seen from the equal angles leading to funny things

[stoic wedge]

huh

<@&286206848099549185>

man i am desperate

i am running on 2 hours of sleep

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[sterile swift]

v/

[sterile swift]

Monkey does not understand how he could plug this into wolfram alpha and still get it wrong

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@sterile swift Has your question been resolved?

[rocky vale]

Um

yeah

that's weird

As far as i can tell that's the right answer

At the top it says you entered the approximation 4.13643

You did use the exact form 79pi/60, right?

[sterile swift]

yes

[sterile swift]

I did

hmm

[rocky vale]

Oh

Wait

Your bounds are not correct

You integrated from 0 to 1 but that's not right

@sterile swift

[sterile swift]

oh

does it go into negatives?

[rocky vale]

It says the region is bounded by y=x^7, x=1, and y=-1

y=x^7 intersects y=-1 at (-1, -1)

[sterile swift]

oh shit

the function is odd

[rocky vale]

Yes

but the volume function isn't

So you can't just say it'll be 0

if that's where you were going with that lol

[sterile swift]

I see

[rocky vale]

But yeah you'll need to integrate from -1 to 1. Not 0 to 1

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[sterile swift]

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[little jay]

The function 𝑔 is given by: (see picture)
What is the definition domain of 𝑔?
Determine the points of intersection between the graph of 𝑔 and the two coordinate axes.
Determine 𝑔′(𝑥) and show that 𝑔 has no extreme point.

I was sick when we went through this and i have to do this task by today. I don't have anyone to ask, nor do i know where to even begin.
Can someone Help me?

[little jay]

Should also note we're not allowed to use programs like geogebra and have to do everything by note

[hot herald]

What is the definition area of 𝑔?
is this translated?

do you mean domain?

[little jay]

yeah domain

translated, sorry

[hot herald]

do you know the definition of domain,
and how to apply that here?

[little jay]

Isn't it basically the sum of all values you can put into the function and get a result out. But no, i don't really know how to apply that here.

We only went through this once in my lectures and i wasnt there when we did. I guess i can watch youtube videos etc if this task is a bit long to get help from

I dont want you spend a long time teaching me something i technically already should know 😅 . sorry for asking, i'll open the spot to someone else

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[valid kestrel]

What is the formula of this ?

[worthy ginkgo]

You're looking for $x \in [0,1]$ such that $9x + 14(1-x) = 11$

[glossy valve]

black_couscous

[valid kestrel]

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[fathom cairn]

Is the point on the parabola?

f(x)= (x-4)^2 Point P(1/9). Should I put 1 in x or what?

[fathom cairn]

So it looks lile 1= (1-4)^2
= 1 = 1 - 2 * 1 * (-4) + 4^2

[brave blaze]

point P of coordinate (1,9) you mean ?

[fathom cairn]

1= 9

[fathom cairn]

yea

[brave blaze]

????

[fathom cairn]

nvm

[brave blaze]

you found out ?

[fathom cairn]

Is that thought right?

It were 1 = 25

1=1 + 8 + 16

cause 1^2= 1

-2 * 1 * (-4) = 8

4^2= 16

1 + 8 + 16 = 25

[brave blaze]

how can 1 = 25 ?

[fathom cairn]

yea its wrong

[brave blaze]

plz write correct mathematical sentences

If P is the graph of f, then it verifies f(1) = 9

now you just need to prove that

[fathom cairn]

How? ://

[brave blaze]

by calculating f(1) bro

[fathom cairn]

ah

[brave blaze]

you want to prove f(1) = 9

just calculate f(1)

[fathom cairn]

lol ok

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[regal bloom]

hello can anyone help, where is the length or width here. I am solving for the area of corn and I need to find the length and width

[scenic wren]

2 areas

top area is 6x times xy+1

bottom area is x^2-9 times x+6

[regal bloom]

so what is length and width of corn

[scenic wren]

i just told you

[regal bloom]

i dont get it 😭

[safe trench]

Martin showed told you how to divide the corn into two rectangles

[regal bloom]

ohh

then the answer i get from that is the length and width?

[safe trench]

what is your original question?

[regal bloom]

.

[safe trench]

i am asking because there are two different lengths and widths for the irregular shape of the corn field

[regal bloom]

Wdym original questiob

[safe trench]

like the question written on the textbook or wherever you got it from

[regal bloom]

It's a group proj and I need to get the area of the corn field because that'a the one assifned to me

[safe trench]

so why do you need length and width?

[regal bloom]

Oh yeah because they told me to get length and width firat

First

[safe trench]

6x is the length xy+1 the width of the top area. Similar also for the bottom area if your are looking for that

[regal bloom]

Thank you

[full forum]

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[pallid sorrel]

G

[pallid sorrel]

to work out the directional derivative

do i take partial derivatives of the function at everywhere except (0,0)

or do i use the 1

and derive that to get 0

like

like can i sub (0,0) into the partial derivatives if the functions bounds dont include (0,0)

also this is a past exam question from 2018, so i cant check for a worked solution

[humble steppe]

https://tutorial.math.lamar.edu/classes/calciii/directionalderiv.aspx

There is a standard formula to compute direction derivative at a single point. Hope it can be helpful to you. 🙂

[pallid sorrel]

oh yea we have that

but

i dont get what i sub into

do i sub a + tu for both x nad y

@humble steppe

ohhh

wait

do i sub in (0 + t1, 0 + t1)

since a is (0, 0)

and u is (1,1)

so i use the x and y components of a and u

ok

[devout inlet]

I can help but I can only do it by a unusual definition of the directional derivative.

Set alpha = pi/4, then the answer comes quite easily.

[pallid sorrel]

wow

i have never seen this

is that the riemann equation or smth

that symbol

[devout inlet]

Xi I think.

[pallid sorrel]

ok well

i think i did it without ur definition hah

ahhha

but thats quite interesting

ill give it a try with urs

wait, this actually is the same as the other definition, but this one has the extra sin and cos

why is that

also, why set alpha to pi/4

[devout inlet]

Sorry, I should have included that information.

[pallid sorrel]

ohhh

bcoz thts to -1.-1

if its 1,1 u need to go 180 in other direction

which is 5pi/4 - pi

pi/4

interesting

but this only makes it easy when its going to either 1,1 or -1, -1

well

im guessing 1,-1 or -1, 1 is 3pi/4 or 7pi/4?

[devout inlet]

For any direction you could calculate the alpha value.

[pallid sorrel]

oh right i see

[devout inlet]

The direction u = <-1, -1> would be pi + pi/4 = 5pi/4.

$\pdv{f}{\xi_{\frac{\pi}{4}}} |{(0,0)} = \lim{\Delta s \to 0} \frac{f(\frac{1}{\sqrt{2}} \Delta s, \frac{1}{\sqrt{2}} \Delta s) - f(0, 0)}{\Delta s}$

[glossy valve]

stabulo

[pallid sorrel]

OHHHH

is that why its triple equal sign

bcoz its equivalent

but not equal

[devout inlet]

I don't know about that terminology. I think that's their definition.

[pallid sorrel]

am i stupid

or is it not the same with an extra cos and sin value

attached to the direction

WAIT

no

[devout inlet]

In the definition I provided?

[pallid sorrel]

yea

delta s is not the same as vector u

or is it

[devout inlet]

It comes from a line segment of length delta s at a angle of alpha. It's components are Delta s cos(alpha) and Delta s sin(alpha).

[pallid sorrel]

does delta s = (a times cos, b * sin)

oh there we go

line segments

interesting

i might ask my lecturer about that

[devout inlet]

The length of the hypotenuse is Δs.

[pallid sorrel]

ok thats interesting

i guess the other version incorporates the whole vector

instead of leaving it in its components

[devout inlet]

I believe this is more intuitive with the way my book presented things since it makes proving the dot product equivalent thing easy for me.

[full forum]

@pallid sorrel Has your question been resolved?

[pallid sorrel]

actually yea that makes alot of sense

actually very cool

thank you for sharing

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[next swift]

how am I supposed to do this?

[gilded quest]

Just assume Cameron is running at average human running speed which is 10km/hr.

Then calculate Alex and Sam's speed with the percentages.

[next swift]

so

[next swift]

using this, Alex is running at 11.2 km/h and Sam is running at 9.8 km/h?

from that find the time that Alex took to cross to the finishing line

[gilded quest]

What's 12% of 10?

[next swift]

1.2?

whoops

does that look good now

[next swift]

then multiply his time with Sam's speed

subtract from 400?

[gilded quest]

Figure out how long Alex would take to reach the finish line. Then figure out how much distance Sam would cover during that time.

[next swift]

Yeah

[gilded quest]

You got this. 👌

[next swift]

got the answer

that's epic

lol

thanks a lot

[gilded quest]

You're welcome.

[next swift]

it's 400 / 11.2 * 9.8 = 350
400 - 350 = 50

👍

.close

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[shy valley]

I'm having a slight issue with notation. I'm writing something where I have subgroups, subspaces and subalgebras, but i'm using the same symbol for all of them, is there a way to avoid this? Do any of these properties have a specific symbol? thanks

[onyx glen]

nop

youll have to make up your own

[shy valley]

Oh

is it an issue if I use the same symbol for all of them?

[onyx glen]

oh you mean like relation symbols?

like ≤ or something

i thought you were talking about letters to name those subobjects

i think you should not overload the symbol if the distinction between subgroup, subspace and subalgebra matters for you though

i can suggest $\leq$, $\preceq$ and $\trianglelefteq$ as three diff symbols

[glossy valve]

Ann

[shy valley]

Ahhhh amazing, thank you

.close

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[twin heron]

Is this correct

[smoky wing]

Yes

[twin heron]

Another question

[smoky wing]

Sure

[twin heron]

https://media.discordapp.net/attachments/978995705215606817/1031935283941359636/IMG_20221018_172214.jpg

What about this

I Dont think its correct

My answer feels wierd

Because it doesnt increase the time period

[smoky wing]

If T increases by 1.4 L needs to increase by (1.4)^2

[twin heron]

What obviously doesnt make sense

[smoky wing]

To make the equality hold

[twin heron]

Oh i see

Yea i get the 1.4^2 part

[smoky wing]

Ah wait L increases by 1.4 here

So T must increase by sqrt(1.4)

[twin heron]

Yea, that

[smoky wing]

,w sqrt(1.4)

[glossy valve]

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[twin heron]

Proof I under

[smoky wing]

So like 18.3%

[smoky wing]

Correct

[twin heron]

Ok and heres a question i dont know the answer to

No idea, absolutely

[smoky wing]

[twin heron]

First mistake is : wrong values in the frequency density

[smoky wing]

Oh you better ask someone else

[twin heron]

But like second is that the hologram is wrong anyway?

[smoky wing]

I hate this topic and still don’t understand it till these days

[twin heron]

Oki doki

Big help, big thanks

Ill ask someone else

[smoky wing]

[twin heron]

Is there a way to repin a message?

[smoky wing]

Okay it’s actually not that ba

Bhavna plots frequency instead of freq density

[twin heron]

Yes

Whats the second one