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[proven mango]

what part of the question are you stuck on

[placid flame]

idk how to calculate the half circles or that rectangle in the middle

[proven mango]

so perimeter or area or both

[placid flame]

both

[proven mango]

so for perimeter

we know that the two edges of the rectangle would be 4ft each

we just need to add the arc from the semicircles

do you have an idea in how to find this arc?

[placid flame]

does it have to do with the diameter of the half circle

[proven mango]

yep

we can use the circumference formula here to help us find that arc

[placid flame]

c=pi d

[proven mango]

yep

so for each individual arc

each semicircle

it would be the circumference over 2

since it is only half of it

[placid flame]

i see

how do you find the diameter or the radius?

[marsh hill]

it says it in the problem 😄

[proven mango]

i believe its stated there as 15

yeah

[placid flame]

oh that’s the dismater

i see

the rectangle perimeter is 38 right

[proven mango]

well we dont need to add the two 15s there

its not in the perimeter

[marsh hill]

well the perimeter of rectangle is 38 but part of that 38 is inside the rest of the shape

[placid flame]

ohhh

[marsh hill]

perimeter is essentially the length of the border of the shape

so you only find the length of all the walls and add them together

[placid flame]

for the half circles i got 47.1

[marsh hill]

wonderful

[placid flame]

and then i add the 2 4’s and i got 55.1

[marsh hill]

Bingo

Now do a similar approach for the area

seperate it into its rectangular and circular parts

do you know the equation for the area of a circle? keeping in mind a semi circle is just half of a circle

[placid flame]

a=pi times radius squared

since it’s semi divided by 2 for each circle

[marsh hill]

yup 😄

[placid flame]

the radius is 7.5

thanks!

[marsh hill]

wonderful

also something you can do

you can see that the 2 individual semi circles have the same radius so you know in total its just 1 big circle so you can save some time on that

great job though 😄

[marsh hill]

oo that is fun

[placid flame]

for the rectangle area i know the area is 27 but the shaded takes up 1/2 so i know we add 13.5 to whatever’s in the square

[marsh hill]

I am not sure if i can help you through the entire thing cuz i gtg soon but ill try

[placid flame]

okay

[marsh hill]

yup

the square is the difficult part though

ok want to hear what im thinking?

[placid flame]

sure!

[marsh hill]

So firstly you see that the part inside the square is half the square + a little white bit right?

[placid flame]

yes

[marsh hill]

hold on 1 second lemme write some stuff on a note thing and show u

you see that part in purple right?

sorry i dont have a good writing application on my computer

that purple area is half of the square

does this make sense?

I just labled the side lengths

[placid flame]

the other side would be 24.5

(area)

[marsh hill]

I just wrote it all out

Let me know if anything does make sense or if you are stuck on something

[placid flame]

oh the 4 is the length of A

Ty so much!

but what’s the answer i got 10.5

OH

NVM

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[quiet saddle]

hi

[dull seal]

If you have any math question post it

[quiet saddle]

how

[dull seal]

Write with your hands the question?

If it include an image take a screenshot and paste here

[quiet saddle]

ok

1 sec

https://tenor.com/view/multiple-kernels-grid-math-calculations-equation-gif-17234477

I need help

[dull seal]

Give all the context and what are you suppose to achieve

[quiet saddle]

so I've seen these everywhere I don't understand it it's on my homework

[fathom saddle]

We'll need all the context, in order to help

[quiet saddle]

what do you mean

ok so I don't understand it and the -2

[dull seal]

You have to explain the problem, not just put a gif with numbers that appear for 1 second

Make a question properly

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[naive bison]

Whats the difference between a cardiod and a dimpled limacon?

[naive bison]

like the look of the graph

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[naive bison]

<@&286206848099549185>

[naive bison]

.close

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[fickle adder]

is my logic right?

if this was a perfect cone, it would just be pi * the integral of (R-y)^2dy on the interval [0, h]

R - y = x is just y = -x + R, a downward linear line that hits the x axis at R

[stiff musk]

is it really just R - y = x? i think you need to involve h and r as well

the slope of the diagonal side is not 1, is it?

[fickle adder]

"if this was a perfect cone"

[stiff musk]

even if it was

[fickle adder]

is it not ?

[stiff musk]

that would only be true if it were a 45 degree cone

[fickle adder]

how would i find the slope

[stiff musk]

well the x value changes by (r - R) and the y value changes by h
so change in y over change in x would be h/(r - R)

[fickle adder]

okay yeah i can see that now

wait isnt it (R - r) though

[buoyant pewter]

try this too:

rotating around x - axis is more natural

for me

[fickle adder]

man doing this on x and y axis was so easy, but trying to comprehend rotating about different axes has actually been so hard for me im starting to lose understanding of how it works on the original axes

genuinely

[buoyant pewter]

that is not worth to do here

[fickle adder]

i mean in general

ive been doing a lot of these for homework today

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@fickle adder Has your question been resolved?

[vale cosmos]

it is hard but once you understand where the formula comes it is easy to understand

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[fickle adder]

how wrong :(

[fickle adder]

integral is the line describing the slanted part of the frustum, which is going about an axis at x = r

then you add the volume of the inner cylinder which is pi*r^2*h

so either my integration is wrong or the integral is wrong

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@fickle adder Has your question been resolved?

[fickle adder]

new attempt

still wrong

[buoyant pewter]

i show you solution in a few minuts i only write LaTex

in the meantime i give you final result, too

[fickle adder]

where the hell does that come from

[buoyant pewter]

read and analyze it

in fact, it was very fast, just LaTex writing slow it down

[fickle adder]

i got (R-r)/h * y - r
where did you get R - ... instead of ... - r

[buoyant pewter]

x axis

[fickle adder]

why integrate on x axis instead of y

[buoyant pewter]

i repeat: it is natural way

just draw it in system of coordinate

i was doing it around x - axis

notice that when you rotate it the same graph, around y that requires more

is less natural way

but if you that correctly, you get the same answer

[fickle adder]

.close

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[cerulean lynx]

May I have help with number 4 and then others maybe later?

[cerulean lynx]

I don’t know the method for a lot of these as I was absent

[amber palm]

well then you might wanna learn substituion and elimination methods

[cerulean lynx]

its just the fractions that are making me confused

and the exponents

if you know how to help that would be greatly appreciated

:)

[amber palm]

i dont really remember those methods but the first thing i saw was

i would just move 3/y to the other side and then multiply with 1/2

so you get 2/x = 3/2y

which you can input in the second equation

[cerulean lynx]

wait ur a genius

[amber palm]

6/x + 2/x =2
8/x = 2
x=4

[amber palm]

no 😭

[cerulean lynx]

yessss

what about 5 though :p

i know i missed that day

[amber palm]

you can square y in the first equation

y^2 = (-3 - 2x) ^2

[cerulean lynx]

i have to square everything else in the first equation then too right

[amber palm]

yep

[cerulean lynx]

yess like that

[amber palm]

.

and then you input the result in second

[cerulean lynx]

let me see if i can do this

can I do this with the radicals or no

hellppp :c

[amber palm]

sorry

what did you do

[amber palm]

first equation

[cerulean lynx]

added the radicals to the y^2 and the other side

wait no yes x^2

i equated the 2

now that they both equalled y^2

[amber palm]

no

basically when you have y^2

just input it into second equation

[cerulean lynx]

wait what

like how

[amber palm]

actually

that wouldnt work hm

[cerulean lynx]

since bith on the right side equal y^2 then cant i just equal them?

[amber palm]

you can

but that wouldnt solve it

[cerulean lynx]

oh okay :c

shoot im stuck

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@cerulean lynx Has your question been resolved?

[spiral vigil]

no that will work

you can equate them and solve for x

you'll get two possibilities but that's fine

[cerulean lynx]

so I can do the square root thingy?

wait the x^2 is negative😭😭😭😭

what do i do bruh

Also yes I solved it by intuition but I still wanna solve it normally

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[torpid compass]

What would be the theoretical probability of rolling a die 50 times

[torpid compass]

compute the mean, variance and deviation i need to compare mine

[brave crater]

and getting what?

[torpid compass]

idk that's the question

[brave crater]

oh well my bad, im not sure then

[torpid compass]

very confusing

[gritty rose]

The question is asking for probability distribution, not theoretical probability

probability distribution has a formula

[torpid compass]

oh but im looking for the theoretical result

to compare mine

[gritty rose]

It's just the discrete uniform distribution

https://openforecast.org/sba/distributionUniform.html

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[twin wolf]

I’d like help with question 10, how do I begin?

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@twin wolf Has your question been resolved?

[twin wolf]

.close

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[amber palm]

.reopen

did you figure it out ?

@twin wolf

[twin wolf]

.reopen

[full forum]

✅

[twin wolf]

nope

[amber palm]

oh

i wanted to know too

lets think a bit together

[twin wolf]

alright

[amber palm]

is this from a particular chapter?

[twin wolf]

Yes just the beginning of antiderivatives although I’m familiar with integration and all that from my self study alone

[amber palm]

ah

should have known

i wonder if throwing dt to the other side will help

[twin wolf]

I’m just confused by the “find x when t=4” but in the function dx/dt = (t-3)^2 I don’t see an x anywhere apart from the dx obviously

[amber palm]

which is why anti derivate

if you integrade dx

you get x

integrating the other side will also give you a proper equation

[amber palm]

perhaps it wants you to integrate with the gives values as lower and upper limits?

where one lower/upper limit is unknown?

[twin wolf]

Hm

Oh so if we say anti differentiate both sides we get x = (insert antiderivative) ?

[twin wolf]

Hm I don’t think it’s that complicated since the chapter never actually covers “integrals” and all that yet

[amber palm]

no you throw the dt the other side

so you get dx on one side

and (t..) dt on other side

this is the only way i can think of

[twin wolf]

I still think there’s an easier way or something we’re overlooking

[amber palm]

i wonder

if you can graph this

nah

doyou have solutions

[twin wolf]

I think so I’ll check

So I checked and it just has the value for x

Not any working out

[twin wolf]

So wouldn’t do us much good here unfortunately

<@&286206848099549185> any ideas

[main ginkgo]

Integrate both sides with respect to t

[twin wolf]

What do I get if I integrate dx/dt?

[main ginkgo]

x

[amber palm]

.

[amber palm]

.

[twin wolf]

[amber palm]

he is saying what i said

[twin wolf]

Then what though?

[main ginkgo]

Find the constant of integration

[twin wolf]

how do I do that again

[main ginkgo]

You know that at t = 0, x is 7

Use that to find it

[twin wolf]

I got C = 16

[twin wolf]

What next?

[main ginkgo]

Find the answer

[twin wolf]

I don’t get it how does the constant help me get the answer for x when t = 4

[hallow ferry]

you got the function x(t) right?

just evaluate x(4)

[twin wolf]

Oh like this is the function?

[main ginkgo]

Yes

It’s literally like f(t) = …. It’s just different letters

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[strong prism]

How can I prove that the product of any 4 consecutive integers is divisible by 24?

[leaden aspen]

4 consecutive integers will have multiple of 2, multiple of 4 and a multiple of 3

So their products can always be expressed as 24k where k is some integer

[open igloo]

When a number(positive integer) is divided by 4 and r is the remainder, it can be written in form of 4n+r

Also r can take certain values only

[strong prism]

aight

yeah i got it ty

.close

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[rancid flame]

i need to prove this. so, i need to start from the left side and arrive at the right side. can someone walk me through this specific problem and maybe tell me some general strategies for this?

[cursive nacelle]

When I do these I try to have my identies on the side

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[faint dock]

i first tried finding the volume by integrating on dxdydz

frist i integrated on dz using the limits that are already shown

then i used polar coordinates on 2D

i'm not sure what are the limits for rho though

after integrating on z and changing to polar coordinates i get double integral of 2r -r^3 -r^2

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[viral zephyr]

can k be 0? here so I mean
can scaler matrix be like
[0 0 0]
[0 0 0]
[0 0 0]

pls assume it as 33 matrix

[viral zephyr]

it's a quick doubt ehehe if any one have time pls address it first eheheh

[torn jolt]

ye

[torn jolt]

k can indeed be 0

it's just a 0 matrix

that exists yea

[viral zephyr]

ohh cooll thank you, sir 😄

[torn jolt]

🙀

ur welcome lol

[viral zephyr]

so 0 matrix can be a scaler matrix

[torn jolt]

yeah

a scalar is any number with a magnitude and not a direction

that has a magnitude

0 is still a size

it's my size 😢

[viral zephyr]

any number means real number?

[torn jolt]

i tell that to myself all the time in the mirror 😢

[torn jolt]

ye

any real number

[viral zephyr]

sorry to hear that 😅

[torn jolt]

😿

[viral zephyr]

oki doki sirr
thank you so muchhh

<33

[torn jolt]

lol stop calling me sir 💀

how old are you 😭

[viral zephyr]

just 18

newly adult 😂

[torn jolt]

bro why are you calling me sir 😭

i turn 17 this year

😭

[viral zephyr]

oh gosh

[torn jolt]

lol

[viral zephyr]

it's okii

thank youuu!!

.close

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[lucid sierra]

how do i find the inequality expression

[lilac sun]

I need help

[lucid sierra]

x>=1
y>=1 right

[wise saffron]

nvm i didnt even read the Q

[lucid sierra]

what does integrate mean

so then 6x+4y<=24 right?

but that one line i cant see it where it ends off

[lucid sierra]

xd

would u help me though

[wise saffron]

Sure

Lets take it setp by step ig

[lucid sierra]

okay

i think i've found 3 inequality already?

[wise saffron]

Whats the equation of the line for the one you can see the x and y axis

[lucid sierra]

uhh

its x>=0 and y>=0

[wise saffron]

That yes

Now you need to find the 2 lines

[lucid sierra]

the second graph is

6x + 4y <= 24

[wise saffron]

Is what im guessing

[lucid sierra]

andd, i dont know the next one, the line cutsoffs idk how to find them

[wise saffron]

Im guessing you have to visualise

You know they intersect at a certain point

[lucid sierra]

(3.2) ?

[wise saffron]

being 2,3

[lucid sierra]

oh yeah 2,3 sorry

ohhh so 2,3 and 0,4

[wise saffron]

You can find the gradient with that

no?

[lucid sierra]

how to?

i can see, every 2 x it goes up 1 y

[wise saffron]

y2 - y1 / x2 - x1

[lucid sierra]

so it would end at (8,0) ?

[lucid sierra]

ohhh

which one is y2 and y1

[wise saffron]

that will give you m (gradient)

doesnt rlly matter

Its more of a
2,3 and 0,4

x y x2 y 2

It can also be

x2 y2 x y

as long as its like the 1 are together and 2's are together

[lucid sierra]

kk,,

[wise saffron]

Once-
You find the graident throw it into

y-y1 = m (x-x1)

[lucid sierra]

lets try it

4-3/0-2 right?

[wise saffron]

yeah

[lucid sierra]

1/-2

or - 1/2

[wise saffron]

its the same thing

-1 /2 = 1/-2 = -(1/2)

[lucid sierra]

then y+3 = -1/2 (x+2)

right?

[wise saffron]

Yeah

[lucid sierra]

uhh how to do them now

[wise saffron]

Expand the right side

y+3 = ?

[lucid sierra]

y+3 = -1/2x + 1

[wise saffron]

y +3 = -1/2x -1

[lucid sierra]

oh sorry

[wise saffron]

and then bring the 3 over

[lucid sierra]

y = -1/2x -4

[wise saffron]

yep

And now you need to find out if its bellow or above

What you want

[lucid sierra]

its below right

from the visual

idk next step to find the equation

[wise saffron]

UhhI made a mistake somewhere

Or something

[wise saffron]

Oh this is (x-2)

[wise saffron]

which will get you this

So y = -1/2x + 4

[lucid sierra]

wait isnt it -2

oh

[wise saffron]

y-y1 = m(x-x1)
You plugged in 2,3

[lucid sierra]

i thought it were negative because the y2-y1/x2-x1 equation

sorry

[wise saffron]

y-3 = m(x-2)

nw

[lucid sierra]

okay so y = -1/2x + 4?

[wise saffron]

Yes

And now you want the bottom

Of the graph

Is it <= or =>

[lucid sierra]

<=

right?

[wise saffron]

yeah

[lucid sierra]

uhh idk how to do it

[wise saffron]

Idk,
either but ig they want you to list it

so $$y\le-\frac{1}{2}x+4$$

$$y\le-\frac{3}{2}x+6$$

[glossy valve]

Equity

[wise saffron]

and the x and y

$$x\ge0$$

$$y\ge0$$

[glossy valve]

Equity

[lucid sierra]

uhmm

where di you get the -3/2x from

is it the lists of the inequation?

[wise saffron]

Its your 6x + 4y <= 24

Just rearanged

[lucid sierra]

ohh kk

[lucid sierra]

how to make the inequation we found like this

[wise saffron]

I made y the subject

What you did is just looked at the x and y axis

And said 6x and 4y

and then multipled by eachother i guess

to get 24

Or something i dont know

I use y=mx +c

[lucid sierra]

ohh

[wise saffron]

Just search up how to find equation of a straight line on ytb

[lucid sierra]

right i multiplied each other

[lucid sierra]

thankks

[lucid sierra]

can we do -4 <= -(1/2x) -y
or 2y+x => 8 ?

[wise saffron]

$$2y+x\le8$$

[glossy valve]

Equity

[wise saffron]

Its the other way

[lucid sierra]

ohh i forgor

thanks for the help

[wise saffron]

If you divide the other side by a negative

Inequality swaps arround

But you can move - and + around ez

just divide no

[lucid sierra]

kk thanks for the reminder

u helps a lot thanks!

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[lucid sierra]

Yes

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[static pendant]

When doing chemistry, and your trying to find the percent abundance of 3 isotopes with only mass, what do you do.

[gritty flax]

mass of isotope/total mass of element * 100, or im wrong ?

[static pendant]

Hm wait a sec

[gritty flax]

you calculate it for each isotope and you'll get the percent of abundance for all of three isotopes

Where the total mass of an element is the sum of the masses of all its isotopes if i have great memory xd

oh and by the way, the percent abundance of an isotope can change over time due to natural processes such as radioactive decay or human activities such as nuclear reactions so it will probably help to understand chemical reactions

[static pendant]

The issue is, you don’t know the mass of each after the abundance calculation

[static pendant]

Yeah I know

[static pendant]

This won’t work sadly

[gritty flax]

you have the masses of these three isotopes right ?

[static pendant]

Yes

I know each isotope

[gritty flax]

and you don't have their natural abondance ?

[static pendant]

No

I’m getting their avg mass from the periodic table

Ik how to do 2 but idk 3

If it helps I can give an example

Oxygen-16 and oxygen-17

Avg mass can be like 16.3

You do

(x)(16)+(1-x)(17)=16.3

Then you distribute

[gritty flax]

okay so x= 0.7

[static pendant]

Yeah

Smth like that

But that’s 2

Not 3

[gritty flax]

for the third one can't you write it like ((1-2x) * ... amu ) ?

instead of 1-x like the second one

[static pendant]

Can I?

Wait how does that work

That only works if 2 isotopes are equal

Right?

[gritty flax]

yes aren't they ?

[static pendant]

I’m trying to find if they aren’t

Is that possible?

[gritty flax]

as we find x= 0.7 in both way ig it's not

[static pendant]

So we need to know if they are equal or bite

Not*

[gritty flax]

yes you need to know if they're equal

[static pendant]

Alright

Thanks

[gritty flax]

your problem is solved ?

[static pendant]

I just needed to know if it was possible

[gritty flax]

it's possible only because they're equal, then from the equation
(x * amu) + (y * amu) + (z * amu) you get (x * amu) + (x * amu) + (x*amu) then for the first x which is the third one to solve for u, instead of 1-x you'll express it like 1-2x because 100% - x - x = 100% -2x

In fine, you'll get : (x . amu ) + ((1-x) * amu) + ((1-2x) * amu)

that's kind of demonstration,

[gritty flax]

np

[static pendant]

Thanks

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[hazy lantern]

how did theta become 290 degrees?

[tired sedge]

360-70

idk but it is what it is

[median tapir]

from diagram, it ask abt major arc so, u gonna take angle of that , (360 - 70) = 290

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[glossy valve]

bob420

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✅

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[gritty rose]

This is correct

But the limit of the function can still go to -inf

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[maiden peak]

I need help

[maiden peak]

.help

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[maiden peak]

.help

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[mint sage]

ask your question

[maiden peak]

Do you know this?

[mint sage]

what do you think is the asnwer

[maiden peak]

wht I wrote

[mint sage]

think about it

if x is greater than -3 it could be 6

which isn't in the range

[maiden peak]

wdym

im confused

[mint sage]

you wrote

[maiden peak]

I found a video

[mint sage]

wait

my fault

that then works

[maiden peak]

its Inqualites

[mint sage]

yeah

that should work then

[maiden peak]

ok thx

what about this?

@mint sage

[mint sage]

might wanna doublecheck the 3 >= x part

[maiden peak]

How

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[noble sleet]

Did I do this correctly?

[spiral vigil]

you dropped a 6

[noble sleet]

Man

[spiral vigil]

happens

[noble sleet]

Thank you

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[crystal gate]

Have a feeling I may have messed up

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[hearty onyx]

pls help 🙏🏻

[serene hazel]

just use a calculator when you plug the numbers into the x-value

[proven mango]

the slope of the secant line is really just the avg rate of change from 2 to x here

[hearty onyx]

i did f(1.9)-f(-1)\1.9-2

but idk if i’m right

[proven mango]

why f(-1)

you have to use the point P

and -1 itself is already the y coordinate

[hearty onyx]

ohhh

aight so

i should do f(1.9)- -1 /1.9-2

it’s cuz i saw this formula

[hearty onyx]

i

[proven mango]

yep

[proven mango]

f(a) is the y coordinate of a point

since you’re already given the y coordinate

you don’t need to plug it into the function again

[hearty onyx]

alr bet

is that the new genshin character

[proven mango]

no its an old one

[hearty onyx]

oh ok

thx for help

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[harsh elk]

if a height of 150 mm is scaled by 80% 3 times do i do
150(.8)^3
150(1-.8)^3
?

[harsh elk]

how is it the former?

i always learnt when something is decreasing it subtracts by 1

like a car deprecating

[balmy rose]

if we scale it once, we get
h=150
h'=150 * 0.8
if we scale this new height, we get
h''=h' * 0.8=(150 * 0.8) * 0.8 = 150 * 0.8^2
so if we scale it thrice, we would get
h''' = h * 0.8^3

[harsh elk]

so its the first formula?

[balmy rose]

and that will make it smaller and smaller, since 0.8 is less than 1

[balmy rose]

yes

[harsh elk]

how tho?

i always learnt when something is decreasing it subtracts by 1
like a car deprecating

[balmy rose]

can you give an example?

multiplying by 0.8 makes it smaller

[harsh elk]

a car starts at 25000 and depcreates at a rate of 10% each year

[balmy rose]

ah ok

[harsh elk]

25000(1-.10)^x

[balmy rose]

then in this case, the height would deprecate by 20% each time

so you would do 150 * (1-0.2)^3

[harsh elk]

what?

,calc 1-.2

[glossy valve]

Result:

0.8

[balmy rose]

with the car, you could say:
the car's value gets multiplied by 0.9 each year
same effect as deprecating by 10%

[harsh elk]

huh?

im not understanding it

also what if i wanted to rescale it?

[balmy rose]

if something shrinks by x%, then we do *(1-x)
if it gets multiplied by something, we just multiply

what do you mean by rescaling?

[harsh elk]

yea and it is shriking no?

[harsh elk]

what do i multiply by to get original size

[balmy rose]

if we multiplied by 0.8 to scale it
then we would do the opposite to undo that
opposite of multiplying is dividing

x*0.8/0.8=x

[harsh elk]

why?

[balmy rose]

why?

0.8/0.8=1

multiplication and division are inverse to each other

they cancel each other out

thats why n/n=1

for every n except 0

[harsh elk]

@balmy rose is this 54500(1+.6)^x?

,calc 54500(1+.6)^2

[glossy valve]

Result:

1.3952e+5

[balmy rose]

yes, good job
if it shrinks we do 1-x, if it grows, we do 1+x
so in this case *(1+0.6)

1.3952e+5=139.520

[harsh elk]

which is 1850?

[balmy rose]

what?

[harsh elk]

what would be the population of florida in 1850

139?

[balmy rose]

nope

[harsh elk]

i add it with 54000?

[balmy rose]

we started in 1840
it increases by 60% each decade
you used an exponent ^2
that means you were looking at the population ater two decades
1840 + 2 decades = 1860
so 139.520 is the population in 1860

[harsh elk]

how is it 139 people?

[balmy rose]

not 139
139 thousand and 520

[harsh elk]

ohh ok

wait but my first question

@balmy rose

i was scaling by 80%

so 1-.8

[balmy rose]

scaling is not the same as something shrinking or growing by x%

if we scale something by let's say 80%, we multiply it by 80%

that is what scalign is

scaling basically is multiplying

[harsh elk]

but if i do 150*.8

thats 120

so 150-120?

[balmy rose]

why would you do 150-120?

[harsh elk]

to get the size

[balmy rose]

the initial size is 150
after scaling by 80%, we get 120
so 120 is the new height
if we do 150-120, we would get the difference in height

[harsh elk]

ok so i cant do 1-.8 because scaling is not growing or shrinking?

[balmy rose]

here is some visualization

if we would do 150 * (1-0.8)
that would mean "a height of 150 m shrinks by 80%"
but our task was "a height of 150 m gets scaled by 80%"

[harsh elk]

@balmy rose where do i practice exponetial decay and growth?

[harsh elk]

so scaled just means multiply

ok got it

[balmy rose]

i think khan academy is quite good
i have not used them but i heard good stuff about them

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay

[harsh elk]

but how did u learn

it

[balmy rose]

i don't know on what level this is though

[harsh elk]

algebra 2

[balmy rose]

i learned it in school without other material

[harsh elk]

u learned scaling?

[balmy rose]

well

scaling is just multiplying

[harsh elk]

but i didnt know that

[balmy rose]

in german, we dont really make a distinction between multiplying and scaling
so for me it was always the same

[harsh elk]

ohhh

i didnt learn it in US

like that

[balmy rose]

we do have the word "skalieren" which means scaling, but we don't really used it (although i really like it)

[harsh elk]

im not german

so what do i do

like how do i practice

[balmy rose]

well, now you know that scaling = multiplying

[harsh elk]

yea but

i want to practice

[balmy rose]

i got these from ChatGPT:
Initial Investment Growth:
You invest $5000 in a savings account with an annual interest rate of 5%. If the interest is compounded annually, what is the total amount after 3 years?

Distance Reduction:
A car travels at a speed of 60 miles per hour. Due to traffic congestion, its speed decreases by 10% each hour. How far will the car have traveled after 4 hours?

Salary Increase:
Sarah earns $50,000 per year. If she receives a salary increase of 8% annually, what will be her total earnings after 5 years?

Bookshelf Space Decrease:
Jane has a bookshelf with a capacity of 120 books. If she donates 15% of her books each year, how many books will be left on the shelf after 4 years?

Temperature Drop:
The temperature drops by 2 degrees Celsius every hour in a refrigerated room. If the initial temperature is 24 degrees Celsius, what will be the temperature after 6 hours?

Discounted Electronics:
An electronic store offers a discount of 15% on laptops. If the original price of a laptop is $1200, what is the discounted price?

Weight Loss Journey:
Mark weighs 200 pounds. If he loses 5% of his body weight every month, what will be his weight after 8 months?

Forest Area Reduction:
A forest loses 12% of its area each year due to deforestation. If the initial area is 500 square kilometers, what will be the remaining area after 7 years?

[harsh elk]

well this is using 1+x% or 1-x%

[balmy rose]

correct

[harsh elk]

i know that

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[still reef]

Im either getting 43 or 85 as the magnitude

So, for the number 1010101 I'm guessing that the complement is 0101011, is 0 + 32 + 0 + 8 + 0 + 2 + 1 = 43.

The number 1010101 = -64 + 0 + 16 + 0 + 4 + 0 + 1 = -43, as required.

[neat axle]

,tex $1010101 \to 2^6 + 2^4 + 2^2 + 2^0 = 64 + 16 + 4 + 1 = 85$

[glossy valve]

@neat axle

[neat axle]

,tex $0101010 \to 2^5 + 2^3 + 2^1 = 32 + 8 + 1 = 41$

[glossy valve]

@neat axle

[neat axle]

Am i doing this wrojng

[still reef]

Am I supposed to use that original number or after I’ve conveyed to 2s complement

[neat axle]

I think the complement would be flipping each bit, then finding the number in base 10

[still reef]

I think it’s plus 4 as well

[neat axle]

No, 4 in binary is 100

The third digit from the right should be 1

[still reef]

I’m either getting 43 or 85

[sudden stirrup]

You’ve written 2^1 = 1 there, and don’t forget in 2’s complement you also need to add 1 after flipping all the bits

[sudden stirrup]

Yeah I’m not sure if the first bit is supposed to be negative or not. It’s not clear from the problem you’ve sent

[still reef]

Only other instruction is that calculating magnitude refers to converting the decimal to binary

[neat axle]

The 2^1 is necessary, but ya i forgot to add 1

[sudden stirrup]

Yes, but 2^1 = 2

[still reef]

Do you know if I’m supposed to use the original number or once I’ve inverted it to 2s complement

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@still reef Has your question been resolved?

[still reef]

no

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@still reef Has your question been resolved?

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@still reef Has your question been resolved?

[still reef]

<@&286206848099549185>

For magnitude is it 7

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[slim harbor]

Could someone help me with left invariance and one parameter subgroups?

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[slim harbor]

Help please

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[cobalt frost]

I had a math problem on today's regional Olympiad that I sadly didnt have time to solve 😦 Could you pls help me?
So I need to prove that there is/there is no such natural number n that is bigger than 10^100 and so n^2 and (n+1)^2 are the same but with the numbers rearranged, for example 13^2 and 14^2 are 169 and 196
But I need n to be more than 10^100

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Please don't occupy multiple help channels.

[rugged void]

!1c

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Please stick to your channel.

[cobalt frost]

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[rancid basin]

How do I do this

[rancid basin]

Number 8

[tiny crest]

You wanna eliminate all the zeros so you can have an easier equation

To do this, right now think of where your decimal point is. In this scenario all of these are at their far right, so there is no decimal point.

Draw that in if it makes it easier, and then shift over that decimal point one by one by one through each number and count how many times you've done that so far

Once you get to the 7, however many spots you moved your decimal point, you put 7.0 because you moved the decimal to the closest to the 7, and

[summer sigil]

i think # of numbers after the 1st digit is the power

is it

[tiny crest]

do that times 10 to the power of negative how many you jumped

[tiny crest]

thats acc very simple way to see it

[summer sigil]

so like

for that 77077 one

its 10^4*7.7077

shifting that decimal 4 places to the right

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[iron wigeon]

if for a differentiable function $$f:\mathbb{R}\to\mathbb{R}$$ it is true that $$f\left(x^2\right)-f^2\left(x\right)\ge \frac{1}{4}$$, how do I prove that $$f'(0) = f'(1)$$

[glossy valve]

TubyconB

[idle kelp]

I have no idea where you would have gotten an inequality like that from, but no, it is not true.

[balmy rose]

i was trying to find a counter example, but i couldnt find a function for which that inequality holds true 😦

[iron wigeon]

well I have to prove that if that inequality is true, then the tangent lines at points A(0, f(0)) and B(1, f(1)) are parallel

[idle kelp]

Oh I misread your question

[iron wigeon]

pretty sure I just have to prove that the derivatives at those points are equal, I am supposed to use the fact that at local maxima and minima, the derivative is 0

we call it Fermat's theorem but pretty sure Fermat's theorem means something else globally

<@&286206848099549185>

[mint sage]

p sure ur not supposed to ping

but

[iron wigeon]

15 minutes have passed

I can ping now

[mint sage]

i can try

[iron wigeon]

go ahead

it's supposed to be high school math question, I don't think it uses any higher math

[cobalt frost]

What f' means?

[iron wigeon]

derivative of f

[cobalt frost]

Bruh I don't know so many English math words

[mint sage]

nope

[cobalt frost]

English isn't my native 😦

[iron wigeon]

you probably dont know about those yet

[mint sage]

fermat has multiple theoroms

dyk which one ur talking about

[cobalt frost]

Yep, I translated it and as fur as I know we would study those in 10th grade. I'm only in 9th

Dunno how grade system in your country works, it might be different

[iron wigeon]

essentially the one that says that if for some point a, f(a) is a local maximum or minimum, then the derivative f'(a) is equal to 0

[iron wigeon]

I guess this would be a 12th grade problem

[cobalt frost]

In your country or in mine?

[iron wigeon]

listen this isn't the issue

no need to try to figure out something you havent learned about

[cobalt frost]

?

[cobalt frost]

Yea, it's just always interesting to study new things

[balmy rose]

TubyCon, did you find some functions for which the inequality is true?
i could only come up with constant functions until now, for those, this property holds true of course

[mint sage]

im stuck on two equations:
f'(0)(1-f(0))>=0
f'(1)(1-f(1))>=0

dont know what local max or min would have to do with this

[iron wigeon]

no but the idea is that, since $$f(x^2)-f^2(x)-\frac{1}{4}\ge0$$ then, for the function $$g(x) = f(x^2)-f^2(x)-\frac{1}{4}$$, there must be some x=a so that g(a)=0, and since $$g(x)\ge0$$ then g'(a)=0

[glossy valve]

TubyconB

[iron wigeon]

because g(a) is the minimum

[mint sage]

i got it

[iron wigeon]

I essentially have to find that g(1) = g(0) = 0 somehow

[mint sage]

nvm

i did not get it

but i got f(0)=f(1)=0.5

can u do something with that

[iron wigeon]

probably not

anyway, no big deal. I will just ask my teacher

[mint sage]

im close

[iron wigeon]

the exercise could be wrong you know

[mint sage]

nope

all i got to was f'(0)>=0 and f'(1)>=0

[iron wigeon]

it's ok, thanks for your effort, I have much more to do anyway so I'm just going to move on

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[odd wolf]

need help to find L somehow

[little mica]

10

They are adding previous numbers in clockwise direction

[odd wolf]

you're brilliant

thanks a lot

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[wary urchin]

may someone help

[wary urchin]

i have a few questions

and i literally cant understand through text

can someone call for less than 10 minutes please

bruh

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[hidden harbor]

.maybe if you state your problem as it is clearly marked in the help channels, you would get help

.If you think i didnt see that or that the mods dont have logs, you're mistaken @wary urchin

[wary urchin]

ok dude myb im stressed

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[wide latch]

need to know the shell height

$\left(\frac{y^{2}}{2}\right)-\left(\frac{y^{4}}{4}-\frac{y^{2}}{2}\right)$

[glossy valve]

jacks

[wide latch]

idk if its plus or minus

[full forum]

@wide latch Has your question been resolved?

[tepid plover]

Looks good to me. Because to get the "posive height", subtract the equation with the lower values of x to the other equation with the higher values of x.

[glossy valve]

poypoyan

[wide latch]

the drawing was in the book i just copied it

i'm not very good at drawing 😭

[tepid plover]

Oops... this is my mistake

[wide latch]

no problem

alright thank you for the help

i just needed help on the setup i can calculate the rest

have a good day!!

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[verbal valley]

I'm sorry but I do not know how to approach this problem. In the prior Smullyan Island problems, each native can only be a knight or a Knave so it's simple to define

A means the islande is a Knight, $ \neg A $ means that the islander is a Knave.

However in this case with three possible choices for each islander how can we create a truth table that has more than just True or False. So how do we incorporate the possibility of Normal?

(This is a assignment on Gradescope, hence the points, I can submit this as many times as I want before the deadline)

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@verbal valley Has your question been resolved?

[verbal valley]

This is from my Descrete math class

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[twilit cypress]

hello, ive pointed the step im stuck on

[viral jasper]

Try another u-substitution

w=3u+1

[twilit cypress]

that was the substitution given in the question

[viral jasper]

!original'

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

[twilit cypress]

Question 2c

[viral jasper]

,rotate

[viral jasper]

You have two routes then: \

1. Know how to solve $\int \sqrt{au+b}du$ \
2. Use another substitution and solve $\int \sqrt{w}dw$

[glossy valve]

SWR

[twilit cypress]

im not sure im very confused

ummm if you scroll up u can see the step i got to

but im not sure how to integrate that

[viral jasper]

Do you know how to integrate $\int \sqrt{x}dx$?

[glossy valve]

SWR

[twilit cypress]

(X)^1/2

So dy/dx is 1/2(x)^-1/2

[viral jasper]

yup

yup. So you need to basically do that with $\int\sqrt{3u+1}du$

[glossy valve]

SWR

[twilit cypress]

So its -1( 1/2(3U+1)^-1/2)

Times by 3

So -1(3/2(3U+1)^-1/2)

[viral jasper]

Oh wait. This is actually incorrect. This is derivative of sqrt(x). I asked for integral

[twilit cypress]

2/3 X^3/2

Is the one for root x

[viral jasper]

yup

[twilit cypress]

-2/3 (3u+1)^3/2

is the solution bank doing the other method u asked for

[viral jasper]

Close. Problem is that 3u+1 is in the root, not just u itself. You need to account for that

[viral jasper]

Yeah. Looks like

[twilit cypress]

i dont quite understand, can you reword?

[viral jasper]

Note how you wrote -2/3 and the answer wroye -2/9

That's the basic problem

[twilit cypress]

do u multiply the denomiator of 3 by 3 as it is the derivative of the bracket?

[viral jasper]

yes

In general, for any differentiable function $f(x)$, $$\int f'(ax+b)dx=\frac{1}{a}f(ax+b)$$

[glossy valve]

SWR

[twilit cypress]

so its the (1/3)x (-2/3) that gives -2/9

all these little things are so hard to remember lol

even if i get these questions down now its like i doubt il remeber this in the exam and drop marks

the solution bank says the power at the end is still 1/2 though

[viral jasper]

The fundamental thing to remember is that integral is just the antiderivative. When in doubt, take the derivative of your answer to confirm if you got it right

[twilit cypress]

fair enough

[twilit cypress]

but you see how somehow after integration the power of 3u +1 is still 1/2 instead of 3/2, how is that

[viral jasper]

hm

That should not be

This is a typo

The power should be 3/2

[twilit cypress]

yeah fair enough

il also check with my teacher in school

i was thinking that looks wierd

thank you very much

[viral jasper]

👍

[twilit cypress]

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[torn jolt]

hello. my name is anthony. i have math problem on homework #8 week 3

[torn jolt]

here is the issue

i know that there is theory that work backward

let me see if i find

ayyyy

is this backward of problem 3

i dont know if true that backwards version work

[summer wraith]

why do you think its the backwards of problem 3 mr anthony

it looks the same to me

[torn jolt]

because one gives you the integral first and the other give you the function first

[gritty rose]

This is false

[idle kelp]

You should have learned that any continuous function is riemann integrable with up to a finite (or countable) number of discontinuities

[gritty rose]

Come up with a function and interval where sometimes the function is positive and sometimes negative

[torn jolt]

where does it say this function is continuous

[idle kelp]

It doesn't

[torn jolt]

ahh so then why bring it up. i dunno understand

[idle kelp]

Because the fact that the integral exists and has a a value greater than 0 tells you something about the function itself. Namely that it is continuous up to some number of discontinuities, which is not the same as saying the function is continuous.