help-36

[tranquil pine]

Yeah bro, sorry

I got it now

Done

Sorry for understanding so hard bro.
Thanks for help

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[teal loom]

A component has an impedance of jΩ.

a) Is this component a coil or a capacitor?
b) What is the value of the inductance or capacitance of this component at an angular frequency of 10^6 rad/s?

[teal loom]

I don't understand how to find the answers to these questions

its apparently a coil but idk why

I also dont answer these calculations

we only have omega, but for some reason we make Z equal to j??

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<@&286206848099549185>

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: (

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[vale reef]

Where should i start with this

[terse dagger]

think about what happens to the basis vectors

(1, 0) and (0, 1)

maybe basis vectors isn't the right words but those two vectors is what i mean

[rain star]

do you know the values of sin and cos at 45 deg?

[vale reef]

Root 2 over 2

I’m aware there’s a formula but i think they want us to understand how to derive it

[vale reef]

Are you saying what happens if you go from (1,0) to (0,1)

[rain star]

this is your matrix

[terse dagger]

no i'm saying what happens to (1, 0) if you rotate everything by 45 degrees anti clockwise

and to (0, 1)

if you know what they become

you can set up the equation

equations

and use them to find the matrix

[rain star]

the new x-coord. of a point after rot. can be found if you multiply the original x-coord. by cos and the y-coord. by sin

[vale reef]

Yeah this is what I don’t get

[terse dagger]

Think of a 45-45-90 degree triangle

where the long side has length 1

and the other sides are the x and y axis

the goal is to find those sides

by using the cos and sin of 45

[vale reef]

Oh ok

Yeah got it

Not sure how you’d apply that reasoning to the matrix formula tho

[distant ridge]

I'll send the derivation of rotation matrix ok

[vale reef]

Thankyou

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[distant ridge]

sorry I forgot

ok btw

from youtube

[vale reef]

Thanks

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[acoustic flax]

Why doesn't this converge? Isn't it equvialent to the integral of 6/x^2, which converges?

[zenith pollen]

yea but the 0 part makes it infinity

if it's 1 to infinity you're right

[acoustic flax]

ohhh

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[drifting burrow]

I am not even sure how to set this up. I know it's a momentum problem but I don't get it

[drifting burrow]

Would I take the initial angular momentum of the rotating rod and set that equal to the angular momentum due to rotation of the second rod + the angular momentum from translational momentum of the first rod? That was my idea but it doesn't really make sense to me

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[ivory vessel]

$x^3-6x^2+3(m+2)x-m-6=0$

[soft zealot]

Fungus 34A05

[ivory vessel]

Find m such that this equation has 2 real roots

so first i derive this and i found the roots of the derivative to be:

$1 \pm\frac{\sqrt{2-m}}2$

[soft zealot]

Fungus 34A05

[ivory vessel]

but this is the extrema only

from here im stumped

[warm python]

if this equation has two reals roots, it has two turning points , one is a repeated root

I think

and one turning point is for y>0

and the other is at y=0

maybe use that

[versed shuttle]

that's what i was going to suggest too... one of them would have to be at a local extremum

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[ivory vessel]

hm

[ivory vessel]

so sub this to the original equation and solve for m?

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[wise crescent]

Net work done = change in kinetic energy

[iron spindle]

Thanks

How to calculate(formula)

[vast summit]

gravitational potential energy is mgh

[iron spindle]

How to find the time

[vast summit]

find the vertical speed of the ball after leaving the track and use constant acceleration formulae

[wise crescent]

After you get the velocity at C, use s = ut + 1/2 at² along the y axis

[iron spindle]

Thanks!

how to get the velocity at C

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[vast summit]

the lost gravitational potential energy is the gain in kinetic energy

use that to find the speed and trigonometry to find the vertical speed

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[timid plank]

Hello! Im doing a maths psmt and i am trying to find a way to get a hyperbola to go between two points, the points i have are (10,-30cos(pi/6)+30) and (20,15). Is there anyway to do this and if so can someone walk me through a tiny bit of it, thanks!

[gritty solar]

Can't you just assume

[soft zealot]

NEON

[gritty solar]

Chuck in the points and solve for 1/a^2 and 1/b^2

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[timid plank]

I might have done something wrong but i couldn't get a answer via that method

one moment ill send photo of my working

Very messy but was just experimenting

hang on

i forgot to times 1 by a^2 and b^2

let me do that

[timid plank]

Im probably doing something wrong but i still cant solve for those points

<@&286206848099549185>

[timid plank]

<@&286206848099549185>

<@&286206848099549185>

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<@&286206848099549185>

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[rich rapids]

I don't understand this step

[desert mantle]

binomial theorem backwards

[rich rapids]

okay

thats easy then

thanks!

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[coral idol]

How to find C?

[gloomy kelp]

there are some sin or cosine rules u could use

[static galleon]

You can use distance formula which will give one equation

[coral idol]

havent learn that yet

well I found it by finding x of c, then using the triangle formula and solving for y

[static galleon]

And second equation with formula of area

[coral idol]

another thing I have to ask is when using the shoelace method for finding area, do I take the absolute value before or after all the calculation is done?

[neat wolf]

i tried to use vector formula but finally come out with 2 positive values of y

[coral idol]

I got -1 for y

[tranquil pine]

after

[coral idol]

thanks

[tranquil pine]

ye

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[ancient monolith]

on the second line

shouldnt it be -3log

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[ancient monolith]

how did they do taht

[fathom walrus]

$\log_a{\frac bc} = \log_a {b} - \log_a{c}$

[soft zealot]

Stephen

[ancient monolith]

ohjhhhh

cause log2 (8) = 3

okay that make snese

thanks

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[cinder roost]

Whats the way to find out (3x-5)(2x+3)

from the =0 on top of it

[crude wagon]

Are you asking how to get to step 2 from step 1?

[cinder roost]

yes

[crude wagon]

The idea is to split the middle term

find two numbers a,b such that product is -(6*15) and sum is -1

[brazen plume]

3x-5=0
With that you can find x

[crude wagon]

he is asking ahout the factoring

[brazen plume]

Ohh

My bad

[cinder roost]

im still a little bit confused sorry

could i do the factors of 6 that add up to -1?

[final tangle]

no

[brazen plume]

For middle term splitting, find two numbers such that, their product is equal to -90 (6x-15) and their sum would equal to -1 (coefficient of x)

[final tangle]

missing - sign ner

[cinder roost]

10 and 9?

[brazen plume]

Yep

[crude wagon]

sign

[cinder roost]

-10 and +9?

[crude wagon]

product must be -90 and sum -1

It will make sense why after you split the middle term

[cinder roost]

but the answer isnt -10 and +9 though?

[crude wagon]

yes, those are the numbers use them to express -x

rewrite -x using these

[cinder roost]

so what 6x squared -90x-15?

[crude wagon]

$6x^2-10x+9x-15=0$

[soft zealot]

Dubs

[crude wagon]

now see if you can factor

you picked a,b to be multiple of those first and last coefficient , so guaranteed to factor

[cinder roost]

ohh

i get it

so you get a common bracket 2x+3

then you take the left out numbers 3x and -5 and form a new bracket

[brazen plume]

Yes

[cinder roost]

ok thank you

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[quartz jackal]

How can i solve this math'

[quartz jackal]

I know its exponent math but how do i approach it

[fallen vigil]

convert everything to base 3

[quartz jackal]

How can i do for 9^(m+1)

[fallen vigil]

9^a=3^{2a}

[quartz jackal]

so it will be 3^2(m+1) right?

[fallen vigil]

yes, 3^{2(m+1)}

[quartz jackal]

ok then how would i approach

[fallen vigil]

a^b * a^c=a^{b+c}

division is multiplying with negative power

[quartz jackal]

i quite didnt understand in which line it can be applied

[fallen vigil]

(a^b)^c=a^bc

[quartz jackal]

um..

[fallen vigil]

1/(3^a)=3^-a

[quartz jackal]

oh yeah got it

ty

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[vast stump]

is my

work here

correct?

😔

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[vast stump]

unfotunately

no

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@vast stump Has your question been resolved?

[vast stump]

😔

[zenith pollen]

your P(B) is wrong, they'll turn out to be independent (the intuition is there's always exactly 1 second dice outcome that gets you 5)

[vast stump]

how would i correctly determine P(B) then?

i thought i had it right

😭

[zenith pollen]

find numbers that add up to 5, order matters

and total possibilities is 4*4=16

[vast stump]

(1,4) , (2,3) , (4,1) , (3,2)

i think

[zenith pollen]

yea

so 4/16=1/4

also for the RHS, having the first dice be 1 and the sum being 5 only happens with even {1,4}, so RHS=1/16

[vast stump]

Yeah
but then RHS =/= LHS still, since 1/32 = LHS .
the question asked if them not being independent is true or false, since there not equal to each other, shouldnt it be true that they arent independent?

[zenith pollen]

LHS is 1/16 too with 1/4 and 1/4

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[primal hemlock]

hello

I'm stuck on this question

I'm not sure which are the solutions for this

cz first you move the k^6i to the other side, and then idk what to do from here

nvm

after you convert to polar form

and idk which are the solutions for the question

so z^3 = k^6 cis (pi/2 + 2kpi)

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[eager stirrup]

for part b, what do they mean by h_8?

[eager stirrup]

anyone???!?!

bruh

<@&286206848099549185>

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[eager stirrup]

yooooooooooooo

anyonee??

please

[keen thicket]

use integrals

[eager stirrup]

in what way?

[keen thicket]

wdym what way

[eager stirrup]

how would i use integrals

im super confused

[keen thicket]

to calculate the volume

[eager stirrup]

of the slice?

[keen thicket]

yes

[eager stirrup]

cant we just use the cylinder formula

find the radius in terms of h

[keen thicket]

but u got a problem with it

thats why you are here

[eager stirrup]

well i was confused about what they meant by starting at h_8

[keen thicket]

i need to understand that question a bit

[eager stirrup]

wdym?

[keen thicket]

i didnt understand that exercise

its a bit complexe

[eager stirrup]

hm

im also confused

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[eager stirrup]

anyone>

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@eager stirrup Has your question been resolved?

[eager stirrup]

pls

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[eager stirrup]

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[ivory vessel]

asking this again

[ivory vessel]

because i still dont get how to do this

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@ivory vessel Has your question been resolved?

[vital surge]

as stated earlier i think this problem would be very simple to see if u consider parameterization of circle

with the setup u used z = x + yi

do u agree this becomes w = (2y + 5) + (2x - 6)i

[ivory vessel]

yeah

[vital surge]

right and the problem tells u w is a circle

so the properties of the circle in the first equation u have has center (2, -3) and has radius 4

[ivory vessel]

yes, 2i should only expands the circle by a factor of 2 right?

or would it also rotate it around the origin by 90deg?

[vital surge]

u don't have to think about it in terms of rotation

[vital surge]

x and y are both being multiplied by 2 so yes the circle is dilated by a stretch factor of 2

what does this tell u abt the radius of w ?

[ivory vessel]

if the circle originally has the radius of 4

[ivory vessel]

so 8?

[vital surge]

ye

[vital surge]

and we know the center is (2, -3)

[vital surge]

using our equation of w, can u find the center of the new circle

[ivory vessel]

so +5-6i

hm, (7, -9)?

[vital surge]

check work

i think

[ivory vessel]

oh wait

[ivory vessel]

sub (2, -3) in this

i get (-2, -1)

that should be the new center right?

so a+b+R is 5

seems to check out with the answer key

holy shit

@vital surge thanks for the help!

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[vital surge]

welcome 🙂

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[solid tendon]

idek what im doing it says to use thickness

but i cant use thickness

theres no thickness

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[solid tendon]

<@&286206848099549185>

please

anyone

please.

[misty wadi]

Can you draw the image?

[misty wadi]

You can't solve it without the thickness

[solid tendon]

i did but how do i figure out the thickness

[misty wadi]

Solve it for a thickness of r

[solid tendon]

i know the first one is something pi over 3

[misty wadi]

Send the picture here

[solid tendon]

kk

[misty wadi]

So that's equivalent to push the mass of that water in the tank by 21m

[solid tendon]

1000⋅9.8⋅π⋅(5^2−x ^2)⋅(5−x)dx

is that wrong

[misty wadi]

I don't think you need to use an integral If you push everything up they will move equally (ideally)

[solid tendon]

i did that with the integral of 0 to 5

[misty wadi]

You still need to know the radius of the cone

The work would be

W = m * g * h

Where

m is the mass of the object you're moving
g is gravity acceleration
h is the height you are moving the object

[misty wadi]

Sp you just need to find the mass in this case

[solid tendon]

do i rearrange

[misty wadi]

No you just use the volume of the half sphere with radius 5 and multiply by water's density

[solid tendon]

let me try again

the volu,e is 250/3 pi right

[misty wadi]

For that one

[solid tendon]

which?

[misty wadi]

Yip

Yup*

[misty wadi]

The sphere one

[solid tendon]

idk

[misty wadi]

What you put in there is the mass

[solid tendon]

i thogutht thats what i needed

[misty wadi]

To calculate the work you need to use that formula

Using g, m (the mass) and h(the height you move the water)

[solid tendon]

wait do i do 9.8 x 250000/3 pi ?

x 5?

[misty wadi]

Yup

[solid tendon]

i still got it wrong

[misty wadi]

It should be a fraction I guess

[solid tendon]

how else could i write this?

[misty wadi]

Nvm

[solid tendon]

?

[misty wadi]

That's more complicated because the water Will fall once its out of the bowl 🤡, I'll sleep If no one answered you I Will hel you tomorrow

[solid tendon]

Tysm

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[high meteor]

Question : A cyclist rides north at 15 km/h and observes that the
wind appears to come to her from the north-east. On the
return journey she rides at the same speed in the opposite
direction. Now the wind appears to be coming from the
south-east. Calculate the true speed and direction of
the wind.

I dont understand how to draw the daigram to solve this probelm

[high meteor]

So I understand the first step is to draw a diagram but the diagram i drew is completely different to one shown in the teachers solution. Teachers solution is below:

I don't understand why the actual velocity of the wind would labbled be after the influence of the the bike, and the wind the biker feels is before the influence

@spring depot

[trim crown]

Cause it's not

The relative wind speed is after the influence and the actual wind speed is before

[high meteor]

ohh but when i try to draw a diagram where the actual wind speed is before i get kind of confused

like when i draw it it seems like the actual wind speed is caused by the speed of the biker

[trim crown]

Why do you think that?

[high meteor]

because like the actual wind speed is between the vector of the speed of the bike and wind speed biker feels

like it seems like going 15km/hr upwards makes wind speed the biker feel into the vector of the actual wind speed when i draw it out

but when i think aboutt it without looking at the picture i drew it seems to be the other wayy

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[plucky obsidian]

n=?

[tranquil pine]

what

[plucky obsidian]

how to find n?

[tranquil pine]

that's 0 for any n

no n exists

[plucky obsidian]

how

ok

can u help me with thias

[rain compass]

@plucky obsidian

[plucky obsidian]

?

[rain compass]

you said in the other channel you had no channel open

it's this one

[plucky obsidian]

it said it was closed

so i made new one

[rain compass]

that was another one

ye i'll close the other one you're good

[plucky obsidian]

can u hjelp me with this problem

no one is answwering

[rain compass]

give it some time

[vital surge]

to start, u suppose that cbrt(2 + sqrt5) is of form a + sqrtb

[plucky obsidian]

ok

nvm i found ans

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[crude wagon]

How many boxes are crossed by a diagonal in a rectangle table formed by 199 x 991 small squares?

[crude wagon]

This question is from mathematical circles ( A Russian experience)

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[crude wagon]

<@&286206848099549185>

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[stone plover]

just calculating the expectation for the poisson distribution and I was wonderign why doesnt the (k-1)! shift when the index of the sigma increases?

[stone plover]

maybe Im just misunderstanding how changing indecies with sigma works?

[neon pendant]

You're not allowed to index from 0 when your expression is (k-1)! . -1 factorial isn't defined.

What you'll see is that you can just ignore the series element where k=0. Since k is a term in the series, that particular element will multiply out to be 0

So you're not shifting the whole index, you're just ignoring the element where k=0

[stone plover]

damn that really cool

is that also the case if I had k! and I wanted to shift from 0 to 1

since 0! is just 1 can I ignore adn leave it as k!

[neon pendant]

Not entirely sure about your setup. Ask youself, does k=0 imply that the element of the series = ZERO? If so, then you know that the sum from 0 to infinity = the sum from 1 to infinity.

If k=0 implies that the elemnt of the series = 1, then you can't ignore the k=0 term.

If you can't ignore the term, then yeah, you gotta shift all the indices. You're doing that part right.

[stone plover]

yep thats what I was talking about

thanks for the clarification 🫡

appreciate the help, have a good day/night!

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[soft zealot]

Jasonnn

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[pliant saffron]

question about integrals

[pliant saffron]

if i get integral of 1/sqrt(1+(2x)^2) [bounds 0 to 1]

and say tan(theta) = 2x

if i wanted to change the bounds

would i be doing 1 = tan(theta) find theta OR 2 = tan(theta) find theta?

2 since 2x = tan and 2(1) = 2

[ornate knot]

2 = tan theta

[pliant saffron]

if tan(theta) = 2x, then what is sec(theta) = ? lets say we cant use any theta on the right hand side

[ornate knot]

why finding sec(theta)?

u changed bounds from variable x to variable theta and u found the bounds of theta using tan theta

[pliant saffron]

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[outer lintel]

Hi, the question is to find the area

and by that

do i just integrate x^3 - x from -1 to 0

or do i have to do it this way?

or should there be "+" signs between integrals?

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[tranquil pine]

Am i solving this correctly?

[modest hornet]

nope

[tranquil pine]

Where am i committing a mistake?

[modest hornet]

second step to third

[tranquil pine]

What can I do different?

[modest hornet]

1/a^2 + 1/b^2 = (a^2 + b^2)/(a^2 * b^2)

its not 1/(a^2 + b^2)

[tranquil pine]

Where did you find (a^2*b^2)

[modest hornet]

do you know whas is 1/x + 1/y ?

[tranquil pine]

Is a sum fraction

[modest hornet]

so what is 1/a^2 + 1/b^2

[tranquil pine]

A sum fraction too?

[modest hornet]

so ....

[tranquil pine]

Can you explain It another way? Starting with the (a^-2+b^-2)?

[modest hornet]

you cant just inverse a sum of fractions

[modest hornet]

its just this one

[tranquil pine]

Their expoent is negative so in theory It should be done?

[modest hornet]

(a+b)^n is not equal to a^n +b^n

if this helps

[brazen plume]

The last step is wrong

[tranquil pine]

What can I do different?

[leaden flax]

you have to add the fractions

1/a²+1/b² = (a²+b²)/a²b²

[tranquil pine]

1/a+B?

[brazen plume]

Try adding them

[leaden flax]

thats not how is done

[tranquil pine]

Okay, wait I'm gonna do It on my notebook

This ? 😅

I took the denominator a and b

Put It on the denominator as If an mmc

And then i did the process that happens with + fractions

Example: ab/a, a disappear and then multiply b for the numerator 1

And then put the expoent that It was on the fraction on the result

[brazen plume]

The denominators are a² and b²

a^-2 = 1/(a²)

Same for b

[tranquil pine]

Oooooo

Wait a minute, let me do this again on my notebook

[brazen plume]

Sure

[tranquil pine]

Like this

[brazen plume]

What have you done here?

[tranquil pine]

I write them in a different way from a^²+b^²/b^²+a^² to (a+b)²/(b+a)²

[brazen plume]

First of all you can’t do that, second of all the numerator is a²b² not a²+b²

[tranquil pine]

So the ending would be a²b²/b²+a²

?

Is It correct to put It as (a*b)²/(b+a)²? @brazen plume

[brazen plume]

Yes

[brazen plume]

It can be done with numerator but the denominator is wrong

b² and a² are in addition so you cannot do that

It only works in multiplication

[tranquil pine]

I didnt knew factoring could only be done in multiplication, good to know

Thank you so much for helping me, you are great 🙌

[brazen plume]

Your welcome

[brazen plume]

It can also be done for division btw, forgot to mention

[tranquil pine]

Thank you 😁

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[ancient pulsar]

a

[ancient pulsar]

hello, please help . I am taking probability, and I am struggling to find the answer of this p(AuB)

My teacher said there's a rule to find it
Help is appreciated

https://media.discordapp.net/attachments/903481105888452609/1219300817941561434/rn_image_picker_lib_temp_fd4aa00a-2c07-468f-a2b4-c30ea202ed90.jpg?ex=660acd60&is=65f85860&hm=5669a2d797a50f3fe9bb11fcd4a42489f374f6222fcfa062ae120cbbfba78f43&=&format=webp&width=555&height=416

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[stone plover]

@zenith pollen sorry bout that 😅

[zenith pollen]

pff

you can factor out anything that doesn't depend on the index

like mu^2 is fine but factoring out mu^k is bad because it changes between terms

[stone plover]

I see

I know youre only here to help out but would you happen to know any resources for solving these types of evaluation questions?

from wht Ive seen these types of series are tied to taylor series qs, but Im usingthem for a probabilty course so those resources dont really apply top me

[zenith pollen]

not really sure I just think I did enough geometric series and taylor series

[stone plover]

ok then

tysm!

have a great day/night! 🫡

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[tranquil pine]

The answer should've be 39√5 but i found 193√5, where did i commit a mistake?

[zenith pollen]

when you pull out numbers you have to take the square root of them

like sqrt(a^2*x) = a*sqrt(x)

so like this

[tranquil pine]

Ooooooooooooooooooo

Thank you so much! I'm gonna try It right now, wait a second

[tranquil pine]

Thank you! Its correct, I found the answer, youre great!

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[sacred lynx]

rhombuses diagnal is the same as its side what is the rhombuses acute angle

[misty rune]

HELP NUMBER 170

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[hidden kiln]

Can someone help me with these questions pls

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@hidden kiln Has your question been resolved?

[hidden kiln]

<@&286206848099549185>

[edgy sentinel]

yes

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@hidden kiln Has your question been resolved?

[lyric aurora]

من از پشمالو متنفرم

[robust trellis]

All of them?

Which one seems the hardest to you

[hidden kiln]

Ye all of them

I’m self studying these stuff

[robust trellis]

Where do you find yourself having problems

Setting up the equations?

Or smth else

[hidden kiln]

I don’t know what to do when it says it passes through a given point

Idk where to start in Q6 and Q7

[robust trellis]

So the equation for a quadratic is ax^2+bx+c

[hidden kiln]

Ye

[robust trellis]

When we say it passes through a point (n,m)

That’s means a*n^2+bn+c=m

Sorry I’m kinda slow typing I’m on my phone

[hidden kiln]

That’s alright

[hidden kiln]

Oh

[robust trellis]

So like if it was the point (1,2)

Actually that’s a bad example

The point (3,4)

It would mean 9a+3b+c=4

[hidden kiln]

Wait what

What does a and b represent

[robust trellis]

A is the coefficient of x^2

B is the coefficient of x

You know the different forms of parabolas right?

[hidden kiln]

Oh i thought A is a near term

[robust trellis]

Like standard vertex and factored?

[hidden kiln]

I know factored form

Is the vertex form like (x+p)^2+q?

[robust trellis]

Yes

[hidden kiln]

Oh we call it complete the square form

[robust trellis]

You can get standard form from just expanding factored form

[hidden kiln]

Or can u not just substitute the values for x and y and then expand the brackets

[robust trellis]

Wdym

[hidden kiln]

Cuz x=2 and y=-5

[robust trellis]

Yeah that works

But remember for factored form it’s c*(x-a)(x-b)

There’s a scalar multiple in front

[hidden kiln]

So what do I do next

@robust trellis

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[open yacht]

i am having trouble trying to prove this, i was wondering if my proof was correct

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[hollow hollow]

Would anybody mind explaining to do d?

i inputted the values i had for f'(x) but they did not seem to be right

Do i have to combine the datas for f'(x) and f''(x) and use that graph to get the answer?

[novel rover]

find the critical points of f'(x)

[hollow hollow]

I did, it's 0 and 9

[novel rover]

critical points of f'(x) not f(x)

[hollow hollow]

yea that's for f'(x)

[novel rover]

thats for f(x)

may i see your calculations?

[hollow hollow]

i took the derivative for fx

and used that to get the critical points

[novel rover]

buttt the question is asking for when f'(x) is at a local min/max

so to find the critical points of f'(x) we must find the zeros to f''(x)

[hollow hollow]

ohh

yea i have the values for f''(x) as well

it's 0 and 6

[novel rover]

yep!

[hollow hollow]

sorry the terms just mess me up lol

[novel rover]

now you have to find the intervals of when f''(x) is positive and negative to determine the localmin/max

[hollow hollow]

yea so its a combination of both the f'(x) and f''(x) right

Like this stuff

sorry let me re-write and draw the overall graph

its kind of messy

so im basing the answer off the info i have here?

[novel rover]

you dont need to make a graph to determine the local min/max

just the positive and negative intervals of f''(x) would be sufficient

[hollow hollow]

Wait sorry im confused

so i have the intervals for both f'x and f''x

but how do i use it so that it points me to the right answers

[novel rover]

its just asking for the local min and max of f'(x)

also i dont know why f''(x) changes from negative to positive at x=6 if thats not a zero of the function..?

[hollow hollow]

concavity?

[novel rover]

were finding when f'(x) has a local min/max

just apply the same process of determining where f(x) has a local min/max to this problem

[hollow hollow]

im sorry im so confused 😭

[novel rover]

okok

just imagine f'(x) is another function, sayyy g(x)

like just renaming it

how would you find the local min/max of g(x)?

[hollow hollow]

take g'(x), factor it and then the x are the critical points

thats from my understanding

because i thought x of f'(x) are the critical point and x of f''(x) are the inflection points thats why im a bit confused

[novel rover]

they are

BUT

its relative to f(x)

[novel rover]

yess

so if f'(x)=g(x) what would g'(x) be?

[hollow hollow]

hahah i feel like im being quizzed 🥲

umm

g''(x)???

or wait f(x)

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[novel rover]

It would be f''(x)!!

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[errant mortar]

how do i approach this; ive been on it for 3 hours please help me

[errant mortar]

the correct answer is d

<@&286206848099549185>

[zenith pollen]

cross products have all the regular multiplication laws, so you can expand it like (b-c)xa = bxa - cxa

the tricky thing is that bxa is different from axb, you have to add a minus sign

[errant mortar]

i figured it out

it was reallyt simple sadly

and i wasted that long on it

i have one question tho

when distributing vector -a

how do you know if it goes in front or back

or is it always in front

[rain compass]

a x (b + c) = a x b + a x c
(a + b) x c = a x c + b x c

it stays on whatever side it started at

[errant mortar]

oh ok i see

hold on

hm thats interesting then

[errant mortar]

because then this solution is incorrect, though it leads to the correct answer

so whaddo i do

@rain compass

@zenith pollen

[rain compass]

i have no idea what you did in that picture

i just see the original statement and then some numbers, can you write more steps

[errant mortar]

ok ok so on the right side

i factor out the negative

[rain compass]

you can't factor a negative

[rain compass]

that's like saying
(-1) * (-2) = -(1 * 2)

[errant mortar]

what about this

[rain compass]

this is fine, but they didn't factor a negative

[errant mortar]

so what would i do

two negatives make a positive?

[rain compass]

yes

[errant mortar]

so treat it as terms

not

no

wait

ok the cross product of two negative vectors produces the same vector, as if the two vectors were both positive

[rain compass]

yes

[errant mortar]

alright, and so knowing that, we have this

and

-c x -a

ok

now

on the left side

would this not be the same as a x b

because

all your doing is flipping around a

right

but it will still produce the same perpendicular vector

alright thank you so much i appreciate it

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[bleak elbow]

What did I do wrong

I think I messed up the height

5b is the original question

I started with area formula of a square

Had no idea what to do for height

Ngl my brain feels fried rn after a study session so I might not make the most sense

[bleak elbow]

This picture is the work that I did so far

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[red plover]

When solar panels rated at 230 watts of power are​ manufactured, the power of the panels is not exactly 230 ​watts, but is Normally distributed with a mean of 230 watts and a standard deviation of 6.5 watts. When solar panels are connected together in series on a​ roof, the power generated is limited by the panel with the least power. We need to connect eight panels together in series on a roof. What is the probability that the total power generated will be less than 1760 ​watts?

[red plover]

so i assumed 1760/8 which is 220

(220-230)/6.5 gives z score of -1.54

so prob of 0.06

but apparently the answer was 0.4

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[versed crater]

My classes say that if my function’s derivative exists and has continuous partial derivatives, then it has a tangent plane

[versed crater]

But what’s happening at the start of the bump on a bump function

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@versed crater Has your question been resolved?

[rain compass]

is the function differentiable with continuous partials?

if so nothing out of the ordinary

[versed crater]

Ok I’ve see a theorem about how the grad vector is orthogonal to all vectors pointing in the level set, but clearly the gradient vector is not perpendicular to all the vectors on the flat plane

[rain compass]

if you have the exact theorem maybe we can discuss it. i know that for a level set described by F(x,y,z) = c, the gradient of F is orthogonal to a tangent vector of the level set at every point

that sounds similar to what you're referring to, but im not sure if that is it

[rain compass]

im not sure i see what you're saying here
the gradient at the very edge of the bump should be 0 right? so wouldnt it be automatically orthogonal with every vector on the tangent plane

[versed crater]

Ohhh

That’s true

And that’ll work

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[main yoke]

need to find volume of this object

[rain compass]

what have you tried

[main yoke]

drawing this

but i think i did it wrong

[rain compass]

have you considered just writing it as an integral

[main yoke]

idk how

[rain compass]

4x + 6y - 2z + 15 = 0, so z = 2x + 3y + 15/2
then you want the volume under z presumably

[main yoke]

oh...

[rain compass]

so [\iint 2x +3y + \frac{15}{2},\dd x\dd y]

[soft zealot]

maximo

[rain compass]

and i think you should be able to figure out the bounds

[main yoke]

yep

thanks

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[final saddle]

@slate jasper Has your question been resolved?

[slate jasper]

How to solve this problem?

[lyric summit]

describing the area V in Cartexian coordinates is quite simple, but when it comes to calculation, your function f is a vector function, not a scalar function, so for me it means that the answer is a vector with three integral values, unless it is some strange notation of the surface integral

integrals over region V, dV denote a triple integral in my lectures, so i suspect that it is the same at you too

it requires fluency in 3d seeing, but it is classical region V

certainly i use my specific notation for iterated integrals, that is common at us

so we integrate from the right = inside, to the left = outside

but your function is a vector field, hence I can write it in a following way:

Unless your notation means something different

This form of the vector integral may, in the sense of physics, mean, for example, the values of the components of the electromagnetic field in a certain area V

i.e. typical exercise for the typical student of electricity faculty at the Polytechnique or University of Technology

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[tame mauve]

How do i proceed/integrate this?

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[untold vessel]

the question is given in the screenshot, I tried rationalizing but didn't get the answer in tan. I just need to see how to solve the question and get the answer in tan form that matches any of the options.

[rotund tinsel]

try dividing my cos 8 degrees

[ornate knot]

u can write 8 as 45-37 and simplify

[untold vessel]

ok, I'll try both and see if I get the answer!

[rotund tinsel]

that is actually a very good way

[untold vessel]

gimme 5 mins

I'm kinda new to the cos(45-37) thing, I believe we are supposed to check the quadrant first? then uh we put the sign accordingly(first quadrant is all +ve) and we get cos37? since cos(-A)=cos(A)

I think there's some big mistake going on here

[ornate knot]

cos(a-b) = cosacosb + sinasinb

thats when u have angles like 90 or 180 or 270

but if u are new , just use the sum of angles formula

[untold vessel]

ohhhh that formula

my bad

[untold vessel]

yeah I remember, I thought similar thing was going on here. totally forgot about cos(A-B) XD

[hazy hemlock]

But

It can be done in a easier way

[hazy hemlock]

Yeah this

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@untold vessel Has your question been resolved?

[untold vessel]

almost

just 2 more mins

got it

my answer is 3/4

[untold vessel]

I think tan37 is 3/4?

yeah

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[tranquil pine]

koshan time:

[chrome pawn]

bru

!15m

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[tranquil pine]

oh

sorry helpers

my bad

[chrome pawn]

is ok we forgive

[tranquil pine]

well

now that you're here

[chrome pawn]

idk how to solve this shi

[tranquil pine]

oh

ok

[chrome pawn]

wait like 3 hours hopefully someone will come, otherwise ill learn this shit for you and help you

[tranquil pine]

lol ok

thanks for the future undetermined help

[chrome pawn]

npnp

my pleasure

[lofty spade]

llet the line be y =mx + c, put in -2,-3 in the eqn

[brave shoal]

Well start by graphing those 2 lines maybe

[lofty spade]

find c in terms of m

[tranquil pine]

ok

[opaque vine]

y-y1=m(x-x1)

[lofty spade]

and then find point of intersection of this line with the 2 given lines in terms of m

[tranquil pine]

I tried to equate slopes for A to B and A to C

[lofty spade]

and then take distance between them and equate it to 20

[tranquil pine]

I understand your soln

but isn't that a lot of work

[lofty spade]

it is

but i cant think of another way

[brave shoal]

What I'd do is find y in terms of x for both equations, plug it into the distance formula for the 2 points equate it to 20

Cause we already know A

[tranquil pine]

that would give me a 4 degree eqn

not so convenient to solve

wait

there are options

[hazy hemlock]

That makes easy now then

[tranquil pine]

these are the options available

[brave shoal]

Firstly I think u can eliminate options cause u know it has to pass through (-2,-3)

So option B is eliminated

[hazy hemlock]

D too ig

[brave shoal]

Yeah

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[dapper cipher]

help

[dapper cipher]

i need to find out the length of side a

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@dapper cipher Has your question been resolved?

[dapper cipher]

no

[loud sundial]

$\tan \alpha=\frac{DC}{AC}$ and $\tan(\alpha+\beta)=\frac{BC}{AC}$

[soft zealot]

Civil Service Pigeon

[dapper cipher]

idk what to do

i only have that one part of that side

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[dapper cipher]

.reopen

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✅

@dapper cipher Has your question been resolved?

[dapper cipher]

i have no idea what to do to find out the length of any side

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[tranquil bone]

I solved this
[
\frac{d}{dt}\begin{pmatrix}x\y\end{pmatrix}=\begin{pmatrix}1&-2\1&-2\end{pmatrix}\begin{pmatrix}x\y\end{pmatrix}
]
and got
\begin{align}
x(t) = 2c_1+c_2e^{-t}\
y(t) = c_1+c_2e^{-t}
\end{align}
How can I go about solving
[
\frac{d}{dt}\begin{pmatrix}x\y\end{pmatrix}=\begin{pmatrix}1&-2\1&-2\end{pmatrix}\begin{pmatrix}x\y\end{pmatrix} + \begin{pmatrix}\cos t\0\end{pmatrix}?
]

[tranquil bone]

ugh

[soft zealot]

Faq

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[tranquil bone]

.close

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[vocal grove]

how do i solve this?

[foggy minnow]

What tools do you know for solving system of equations

[vocal grove]

elimination

[foggy minnow]

ok well we want to eliminate one of the variables so do you know how to do that

[vocal grove]

yes

but i got

x=-13-5y

which doesnt work

[foggy minnow]

Well you didn’t eliminate a variable

[vocal grove]

i tried putting them next to each other and solve

[foggy minnow]

Ok so how did you eliminate

In this equation

[vocal grove]

(3x+4y)+(-2x+y)=-6-7

[foggy minnow]

Well before you add the equations together

You need to make sure one of the variables will cancel out

[terse dagger]

try to subtract the second one from the first one until the equation you're left with has no y anymore

[foggy minnow]

so you need to modify the second equation to have how many y?

[vocal grove]

4

?

[foggy minnow]

and to get 4y, what do you need to do to the equation

1y -> 4y

[vocal grove]

so i need to multiply by -4?

[foggy minnow]

Yes

Can you show that

the resulting equation

[vocal grove]

@foggy minnow