help-0

[dense meteor]

Anyone here who can help

[cerulean breach]

#❓how-to-get-help

thanks

[dense meteor]

I don’t understand how to do it

[karmic pulsar]

So z=sqroot (x²-12x+100)

[dense meteor]

So how can someone help me

[karmic pulsar]

Post in a channel that's available

[cerulean breach]

click under the math help available and click an open one

[karmic pulsar]

Now, replace the values of y and z in y²+z²=x²

[cerulean breach]

ahhhh i seeeeeee

[dense meteor]

Can someone teach me how to do it

[cerulean breach]

bro this making mad sense

[karmic pulsar]

Bruh

[cerulean breach]

no way

#help-27

try that

[dense meteor]

Ok and then

[cerulean breach]

ask there

[dense meteor]

What do i do after

Ok

Thank you

[cerulean breach]

ask in that channel

yeah

[karmic pulsar]

Back to the triangles, lmk what you get

[cerulean breach]

idk if im doing it right

bottom righ

right

[karmic pulsar]

Nope, you can't just sqroot a single term

[cerulean breach]

oh so it'd be z=x+3.5x+10

[karmic pulsar]

Noooo, that's not how you do square roots

Leave it as is, you should study how sqroots work

[cerulean breach]

ok

[karmic pulsar]

For now we want z² so that's just x²-12x+100

Also, y²=100

[cerulean breach]

ok thanks for your time

[karmic pulsar]

So y²+z²=x²-12x+200

And that's x²=x²-12x+200

Left side is the side squared and right side is the sum of the other two sides squared

[cerulean breach]

ohhh okay thank you

[karmic pulsar]

The x² cancel each other so you get 0=-12x+200

Can you solve for x?

[cerulean breach]

yeah

16.7=x

approximately

[karmic pulsar]

,w 200/12

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by ralvrz#3477

[karmic pulsar]

We can use 50/3

[cerulean breach]

i think i have to put it in decimal form

[karmic pulsar]

Finally, find z

Ok then

[cerulean breach]

8 squared +10.7 squared = z squared

[karmic pulsar]

Substitute x and solve

[cerulean breach]

13.4=z

[karmic pulsar]

That's it, you found x, y, and z

[cerulean breach]

thanks so much

extra credit babyy'

[karmic pulsar]

[lone heart]

@cerulean breach Has your question been resolved?

[lone heart]

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[coarse elm]

How do you solve this 3x^2 + 24x + 45 = 0

[coarse elm]

(Finding the x intercepts)

I factored it and got 3(x+3)(x+15)

Im confused about the coefficiant 3 that is infront of the brackets because without the 3 i know x = -3 and x = -15

but what about the 3 at the start

[wanton tusk]

are u sure

[tacit arch]

,w expand 3(x+3)(x+15)

[coarse elm]

uh

oops

3(x+3)(x+5)=0

but im still confused on how to continue to solve to find x intercepts

[lone heart]

@coarse elm Has your question been resolved?

[wanton tusk]

you’ve alr factored

(x+3)(x+5)

set each factor =0 and solve for x

those will be the roots

[lone heart]

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[void agate]

Can someone help me out here?

[void agate]

The correct answer according to the answer sheet is 2:5 but I don't see why.

Ignore my other statement just noticed something

But yeah

I dont know how to do it

[rotund gorge]

Ooh, I think I know

If ABX is similar to CDX

and u were to draw these two triangles side by side

AX would be similar to XC

Right

And XC is also shared by BCX

AX is 2
XC is 5

since XC is a side of BCX and CDX the conversion factor is the same for both

[void agate]

This is going right over my head.

😦

[rotund gorge]

well

if u wanna solve it out mathematicallu

Then

Ok so ABX is similar to CDX

[waxen flame]

Give me a moment. I'm going to make a graph.

[rotund gorge]

Alright

[void agate]

Thank you guys

[rotund gorge]

It's j like

ABX is like CDX
This includes the sides w 2 and 5
The 5 is a part of both triangles so by knowing that a side increases by 5/2 times u know the whole area increases by 5/2 times

[void agate]

Ohhhh

That does make sense

I wanna see what @waxen flame has to say

[void agate]

It makes sense but its a bit hard for me to fully wrap my head around

I wanna see if there's an easier method

[rotund gorge]

If u had the measurements of the other sides of BCX you'd see they'd also be inflated by 5/2 times

[void agate]

Cuz the way I'm used to finding the ratio of areas is by squaring the ratio of sides

[rotund gorge]

er rather if u calculated them out to find the area

[waxen flame]

Rotate the triangle AXB around X and you will see which sides correspond with which side.

[void agate]

Can we say BX = 2?

[rotund gorge]

No, not necessarily

[void agate]

Argh

[void agate]

Yeah but there are some missing sides so you cant draw up a ratio comparing their lengths

[rotund gorge]

bc having 2 side lengths of a triangle actually doesn't mean anything for the third

[void agate]

Alright thanks so much for the help @rotund gorge

I think yours is the most comprehensive answer

I'll be off now

.close

[lone heart]

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[polar otter]

<@&286206848099549185>

[lone heart]

@polar otter Has your question been resolved?

[polar otter]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

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@polar otter Has your question been resolved?

[lone heart]

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[dusky elk]

https://cdn.discordapp.com/attachments/791204354757361684/1050582712697765968/20221208_181945.jpg

[dusky elk]

i need help for surface area

[rocky grove]

Alrighty

You're given 3 lengths only?

20, 15, and 17.8?

[dusky elk]

yep

is this the side triangles?
1/2BH
1/2 x 15 x 17.8
A = 133.5cm

[rocky grove]

Nope doesn't work

[short gust]

15 cm for which line ?

[rocky grove]

I think the side perpendicular to 20 is also 15

[dusky elk]

oh

what would the first step be

[rocky grove]

First since we have all sides at the base 15 cm, we find the area of the triangle with height 20

It's the usual (1/2)bh

b = 15 and h = 20

[dusky elk]

oh ok

i got 150

[rocky grove]

Alright, keep it aside for now

[dusky elk]

k

[rocky grove]

We then calculate the base triangle area

[dusky elk]

right

i have to use pythagoras?

[rocky grove]

You can

But there is already a known formula for area of an equilateral triangle

[dusky elk]

oh

how can i use that?

[rocky grove]

$$\frac{\sqrt{3}}{4} s^2$$

[ocean seal]

VulcanOne

[rocky grove]

s is your side

Which is 15

[dusky elk]

replace s with 15?

oh ok

97.428

[rocky grove]

Alrighty

Now the last 2 areas are equal

[dusky elk]

theyre also 97.428?

[rocky grove]

Nope

[dusky elk]

oh yeah theyre 150

[rocky grove]

Nope too

[dusky elk]

wait no

[rocky grove]

They're different than the 2 triangles we have

They are the side triangles

[dusky elk]

right

[rocky grove]

Now you'll need to use Pythagoras with 20 and 15/2

[dusky elk]

k

20^2 + (15/2)^2 = c^2?

[rocky grove]

Yep

[dusky elk]

sqrt(456.25)

[rocky grove]

21.36

[dusky elk]

ye

[rocky grove]

Now we will use a trick involving angles

[dusky elk]

k

[rocky grove]

Wait nvm

We will use Pythagoras again

[dusky elk]

oh ok

with which triangle?

[rocky grove]

Side 20, height of equilateral triangle, and the missing edge

Basically cutting the prism in half

[dusky elk]

20^2 + 21.36^2 = c^2?

[rocky grove]

Nope

Lemme draw it

[dusky elk]

k

[dusky elk]

so i would do 15^2 + 15^2 ?

[rocky grove]

Nope

It cuts the 15 in half

[dusky elk]

ohh so (15/2)

[rocky grove]

Ye

And keep in mind that 15 is the hypotenuse here

[dusky elk]

(15/2)^2 + b^2 = 15^2?

[rocky grove]

Ye

[dusky elk]

k

[dusky elk]

sqrt(168.75)

[rocky grove]

Hmm

Something went wrong

[dusky elk]

?

[rocky grove]

Ye I had something wrong in my calculator

You're correct

Ok 12.99

[dusky elk]

k

[rocky grove]

Now 2 more Pythagoras

[dusky elk]

oh

is it 12.99^2 + b^2 = 20^2?

[rocky grove]

Yee

[dusky elk]

15.207 = b

[rocky grove]

Wait no

You use 20 hypotenuse, 17.8 leg 1 and x leg 2

20^2 = 17.8^2 + b^2

That's "Pyth1"

[dusky elk]

oh

[dusky elk]

b = sqrt(83.16)

[rocky grove]

Ye

Now how do you get Pyth2?

[dusky elk]

is it sqrt(83.16)^2 + b^2 = 20^2?

[rocky grove]

Nope

You will get back you 17.8 again

[dusky elk]

oh yeah

[dusky elk]

what would the equation be?

[rocky grove]

First you need to know the sides of the triangle that contains pyth2

[dusky elk]

12.99- sqrt(83.16)?

[rocky grove]

Yep yep

What's the second side?

[dusky elk]

17.8?

[rocky grove]

Yep

[dusky elk]

k

3.87^2 + 17.8^2 = c^2?

[rocky grove]

Mhm

[dusky elk]

k

[dusky elk]

18.216

[rocky grove]

Yep

[dusky elk]

whats next?

[rocky grove]

Area using half perimeter

You ever heard of it?

[dusky elk]

idts

[rocky grove]

$$s = \frac{15+18.216+21.36}{2}, , Area = \sqrt{s(s-15)(s-18.216)(s-21.36)}$$

[ocean seal]

VulcanOne

[rocky grove]

Here

Area using half perimeter

s is the half perimeter

[dusky elk]

i got 27.288

for s

[rocky grove]

You use this formula when you have all sides of a triangle but no angles

[dusky elk]

oh

[rocky grove]

Ye

The square root part is usually the hardest part to memorize but a couple of practice runs on it will make it memorable

Because it is super helpful

[dusky elk]

oh ok

thx

[dusky elk]

wait do u have the answer?

sry i gtg in 4 minutes

[rocky grove]

You should practice more with triangles

Get familiar with them

And make sure to enjoy them

They're pretty fun

[dusky elk]

yeah im new with the subject lol

thx very much man

i have a test tmrw lol

[rocky grove]

I can help you whenever you need

[rocky grove]

Good luck :)

[dusky elk]

thanks 🙏 🙏

[rocky grove]

[dusky elk]

goodnight

for me lol

[rocky grove]

Good night :)

[dusky elk]

.close

[lone heart]

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[jagged cobalt]

4^x=2 or 4^x=3, do you know how to use logarithms?

[rocky grove]

@wind bloom you still have this channel open so if you have anymore problems feel free to send them over

[lone heart]

@wind bloom Has your question been resolved?

[low quartz]

@wind bloom do u get sol

[lone heart]

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[unkempt temple]

hiiii can i get a help?

[unkempt temple]

<@&286206848099549185>

[rose sigil]

haii you should just post your question 🙂

[unkempt temple]

im confused on how will i compute this

what will i do with the ( )

[tall topaz]

rewrite this as y = f(x) then see what values of x are not allowed

[alpine sable]

Pure got new drip 😮

[tall topaz]

calm

[alpine sable]

Serene

[tall topaz]

[low quartz]

did you solved this?

[unkempt temple]

nah

it is the given problem

[tall topaz]

this

[low quartz]

yes

pure is right

y=f(x)

[unkempt temple]

y = -1 (x^2-4) ????

[low quartz]

then f(x)=1/x^2-4

find the domain of f(x)

[alpine sable]

[
y(x^2-4) = 1
]
[
y = \frac{1}{x^2-4}
]

[ocean seal]

♡LexQa♡

[low quartz]

yes

like this

[unkempt temple]

OHHHH

okayyyy

[low quartz]

see this

[unkempt temple]

i will not change the sign, right?

[low quartz]

no

well the domain

the function is not defined when x=2

so it will define on every number except +2 and -2

[unkempt temple]

where did u get the 2???

howd u do that

[low quartz]

try putting x^2-4=0

x will comes out to be

+2 and -2

but

if we put x=2 or x+-2 in the equation

it will not define

cuz it will become 1/0

which is not define

did you understood?

@unkempt temple

[unkempt temple]

ohh okay i got it

thankyouuu!

[low quartz]

np

:).

[unkempt temple]

i sent u a friend request :))

thank u again

[low quartz]

okk

np

:).

[unkempt temple]

.closed

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[somber spoke]

I don’t really know how to be rigorous here

If u just pick many balls at random

And divide the number of blue balls by red balls

That should give u the ratio?

And as u start to pick an infinite number it will get closer to the actual answer

[lone heart]

@somber spoke Has your question been resolved?

[naive valley]

"drawing balls at random" needs qualification if there are infinitely many balls

there's no uniform distribution on a countably infinite set

[wooden crag]

Good ol' Bertrand's Paradox.

[wooden crag]

The rigorous part comes in defining how exactly this procedure happens, because when you're drawing at random with infinity involved, there are multiple procedures that can give you different distributions
So you must first pick a distribution/procedure to use

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[somber spoke]

.reopen

[lone heart]

✅

[somber spoke]

How can u make the procedure different

If ur just picking at random

[wooden crag]

Essentially you'll have to define exactly what "picking at random" means here
Like Bungo said, there is no uniform distribution for a countably infinite set

So you'll have to choose a distribution to use

[lone heart]

@somber spoke Has your question been resolved?

[lone heart]

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[violet citrus]

help

[violet citrus]

im bad a math

.close

[lone heart]

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[wooden crag]

what is your question bruh

[lone heart]

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[tulip hound]

if f(-1)=f(1001)
what is f(-1001)?

[delicate jacinth]

not enough info

[tulip hound]

y=f(x) quadratic function

[tulip hound]

and this is known

answer is f(2001) but I wanna know how

[gaunt sparrow]

you need to use the general equation for quadratic formulas

[delicate jacinth]

This info tells you the symmetry axis

[gaunt sparrow]

ax^2 + bx + c

substitute x for -1 and 1001 and equate the two

simplify then you should get the answer

[delicate jacinth]

Nah, easier

take the average between -1 and 1001

you'll find the symmetry axis

f(-1001) will be on the other side of the axis

[tulip hound]

Won't it be a 500

[gaunt sparrow]

?

[delicate jacinth]

nah, im dumb

[gaunt sparrow]

how do you know the axis of symmetry is between -1 and 1001?

[gaunt sparrow]

did you try this? @tulip hound

[tulip hound]

I don't know math english terms pretty well so I couldn't understand

[gaunt sparrow]

it's ok

do you know what the general equation for quadratic formulae is?

[tulip hound]

ax²+bx+c

[gaunt sparrow]

correct

in the question, it's given that f(-1) = f(1001)

that means when you put 'x' as -1 and 'x' as 1001, they're both equal

a(-1)^2 + b(-1) + c = a(1001)^2 + b(1001) + c

if you rearrange the terms, you should get the answer

[tulip hound]

Aighty I'll try that, thank you so much

.close

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[lime light]

calculator says the answer is 2 * cos^2(x) - 1

[soft quarry]

If you sub sin^2(x) = 1-cos^2(x) you will see they are equivalent

Into your answer

Basically you are right

[delicate jacinth]

you want $[\sin(x)\cos(x)]'$?$

[ocean seal]

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

[lime light]

yes, wait is this an identity?

[delicate jacinth]

yes, from $\sin^2x+\cos^2x = 1$

[ocean seal]

sopinha

[lime light]

ah & the 1 is negative due to sine being negative?

[delicate jacinth]

yes

[lime light]

hang on

oh yeh they r

tysm guys

.close

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[raw bone]

hi guys what is a vanishing polynomial

[raw bone]

.close

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[surreal vapor]

Is it possible to make two different direction fields for the equations of a 2x2-matrix of differential equations?

[livid narwhal]

as in x' = Ax?

[surreal vapor]

yes

[livid narwhal]

I dont think so

[surreal vapor]

Both equations in the system depend on 2 variables so i find it hard to have the axises x(t) and t.

[livid narwhal]

if you let the matrix be

[surreal vapor]

Since x_1'(t) depends on x_1 and x_2 and vice versa for x_2'(t)

[livid narwhal]

$$
A = \begin{bmatrix}
a_{11} & a_{12} \
a_{21} & a_{22}
\end{bmatrix}
$$

[ocean seal]

Shell

[livid narwhal]

then you have $F(x_1, x_2) = (a_{11}x_1 + a_{12}x_2) \vec{i} + (a_{21}x_1 + a_{22}x_2) \vec{j}$

[ocean seal]

Shell

[livid narwhal]

is your field

[surreal vapor]

True.

[livid narwhal]

t doesn't really matter because for the dirfield you want it on the x_1, x_2 plane

t only matters when you want the vector value at a specific point

[surreal vapor]

My e^tA matrix is

\begin{bmatrix}
\frac{\sin(t\sqrt{\frac{\beta}{\alpha}-1})}{\sqrt{\frac{\beta}{\alpha}-1}}+\cos(t\sqrt{\frac{\beta}{\alpha}-1}) & -\beta\frac{\sin(t\sqrt{\frac{\beta}{\alpha}-1})}{\sqrt{\frac{\beta}{\alpha}-1}}\
\frac{\frac{1}{\alpha}\sin(t\sqrt{\frac{\beta}{\alpha}-1})}{\sqrt{\frac{\beta}{\alpha}-1}} & -\frac{\sin(t\sqrt{\frac{\beta}{\alpha}-1})}{\sqrt{\frac{\beta}{\alpha}-1}}+\cos(t\sqrt{\frac{\beta}{\alpha}-1})
\end{bmatrix}

[livid narwhal]

or the parametric equation

[ocean seal]

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

[livid narwhal]

jesus

[surreal vapor]

This is my phase portrait

[livid narwhal]

are these the flow lines?

[surreal vapor]

But my associate professor wants me to make two different direction fields

[surreal vapor]

They are solutions for different initial conditions (arbitrary)

[livid narwhal]

sure

[livid narwhal]

how so though?

[surreal vapor]

idk 😦

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[delicate marsh]

Stuck at 3 so far I've done 1 and 2 not sure if I did them correctly though

[feral wind]

Twice = 2
The difference between 2x and 5 = 2x - 5

[delicate marsh]

Uh

So what I write

5=2x-5?

Uhm

How about 4 and 5

[feral wind]

No, that would be 2 times the difference between 2x - 5 or (2x - 5) + (2x - 5) = 2(2x-5) = 4x - 10

[delicate marsh]

What I write in my notebook then

[feral wind]

Wait, 2x - 5 not 2x + 5

[delicate marsh]

Yea

Noticed that

[feral wind]

Im on the phone 😔

[delicate marsh]

Me too

So I write (2x-5)=2(2x-5)=4x-10?

[feral wind]

4x-10

But any of the three, they are equivalent

[delicate marsh]

Oh

[feral wind]

(2x-5) + (2x-5) = 2(2x-5) = 4x-10

[delicate marsh]

Aight

I won't close this channel just yet if I can't figure out 4 and 5 I'll just ask here

[feral wind]

The ratio of a and b = a/b = a divided by b

[delicate marsh]

b = a/b

Right?

Is what I write

[feral wind]

The product of a and b = ab = a times b

[delicate marsh]

They ask me to write it in mathematical symbols

[feral wind]

No, i'm just giving you enough information for you to finish the rest

[delicate marsh]

Confused af though

Aight

[feral wind]

With what i wrote you should be able to figure out the rest

[delicate marsh]

@feral wind is my answer for 5 correct

[feral wind]

Looks good, yes

[delicate marsh]

Aight thanks

@feral wind now did I do 4 correctly

[feral wind]

4 also looks good

[delicate marsh]

Aight thanks

Done

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[vapid steppe]

can sets have imaginary values

[vapid steppe]

so like {3,7,2+5i}

[alpine sable]

yeah that would be a complex set

[vapid steppe]

ok ty

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[toxic lotus]

.reopen

15. I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

[toxic lotus]

having a bit of trouble in linear equations

[toxic lotus]

now this is the question

this the solution

Solution:

Let the number of ₹5 coins be x.

Then,

Number ₹2 coins = 3x

and, number of ₹1 coins = (160 – 4x)

Now,

Value of ₹5 coins = x × 5 = 5x

Value of ₹2 coins = 3x × 2 = 6x

Value of ₹1 coins = (160 – 4x) × 1 = (160 – 4x)

According to the question,

5x + 6x + (160 – 4x) = 300

⇒ 11x + 160 – 4x = 300

⇒ 7x = 140

⇒ x = 140/7

⇒ x = 20

Number of ₹5 coins = x = 20

Number of ₹2 coins = 3x = 60

Number of ₹1 coins = (160 – 4x) = 160 – 80 = 80

i get how the entire problem works

but having trouble in why

[vale wigeon]

why what?

[toxic lotus]

the value of rupee 1 coin is 160-4x

[vale wigeon]

the number of 1-rupee coins is (160-4x). do you understand why this is true?

[toxic lotus]

no

thats my question

[vale wigeon]

you said value and not number at first but ok

[toxic lotus]

yes sry bout that

its the number of 1 rupee coins

[vale wigeon]

the number of five-rupee coins is x and that of two-rupee coins is 3x. do you understand this?

[toxic lotus]

yes

[vale wigeon]

in total, the number of 2- and 5-rupee coins is 4x. do you understand this?

[toxic lotus]

how is it 4x

that isnt given

[vale wigeon]

it's x + 3x

[toxic lotus]

oh shit

im dumb

thank you for that

also

1 more question has arrised

[vale wigeon]

yes?

[toxic lotus]

5x + 6x + (160 – 4x) = 300

⇒ 11x + 160 – 4x = 300

⇒ 7x = 140

⇒ x = 140/7

⇒ x = 20

how did 140 come into the equation

[vale wigeon]

subtract 160 from both sides

you will have 300-160 on the right

[toxic lotus]

oh ok so we're transposing 4x and 160?

[vale wigeon]

we are not "transposing" anything.

11x - 4x on the left was simplified into 7x, and in the same step 160 was subtracted from both sides

[toxic lotus]

ah k

alright

ty for this

ik this was really dumb

thx a lot

for your time

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[humble falcon]

please help me with this question

[low quartz]

solve it using

differential equation

find the general form of the differential eqaution

[humble falcon]

and then--?

[low quartz]

then use the given inputs

[humble falcon]

okie i'll try

[low quartz]

show me the general equation

i will tell

what to do then

[humble falcon]

okay

[low quartz]

yup

[humble falcon]

something like this?

??

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[humble falcon]

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[undone cliff]

Idk where can i start, give me some clue

[undone cliff]

[worldly sparrow]

It's 69i

[undone cliff]

Can you explain the step?

[low quartz]

wait

for a cubic equation

[undone cliff]

okay

but

[low quartz]

for this equation

try using it

[undone cliff]

ok wait

ye

[undone cliff]

so should i get a equation to get like this from the = 6 thingy?

[low quartz]

no

use the

[low quartz]

equation this one

and compare it with your cubic equation

find the values of a,b,c

[undone cliff]

ye i got it

already

[low quartz]

then find this

[undone cliff]

already

[low quartz]

and use it in the

[undone cliff]

ohh

wait

p = -6?

[low quartz]

r u getting alphabetagamma = p

[undone cliff]

its gamma * alpha * beta

so

-p = 6

[low quartz]

yes

check your answer

you have to find p

so it is -6

[undone cliff]

alright

thanks alot

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[low quartz]

is it coreect? @undone cliff

i mean answer

[undone cliff]

yez

there is the option

[low quartz]

nice

[undone cliff]

[low quartz]

beluga

:).

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[wanton valley]

what is your question

[crisp widget]

i tried so many times to do that

in different ways

but it's not working

idk what's the mistake

[low quartz]

whta

[alpine sable]

simplify numerator first

[low quartz]

simplify the num first

[crisp widget]

how?

[alpine sable]

x-1/10

[low quartz]

lcm

[crisp widget]

i can't simply it or?

[low quartz]

it will become 10x-1/30

[crisp widget]

aha

[low quartz]

yup

[crisp widget]

i'm gonna try, like i was looking for an easy way, cos there's too many ways to it

my teacher tought me a way

to take all the terms like 3x5x10=150

and multi it

[undone cliff]

or you may multiply all of it by x3 and x5

and simplify it

[low quartz]

yup

you can

[crisp widget]

X3?

And x5?

[low quartz]

i dont think this will be hard

than multply or increasing complications

[crisp widget]

Ok

Imma try to do it by myself

I got help from the bot place(idk what it called )

[crisp widget]

Thanks a lot

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[dapper tide]

Can someone rephrase these questions for me

I’m trying to figure out what “c” is

Nvm i got it the phrasing of the question was just wonky

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[open wharf]

<@&286206848099549185>

Need step-by-step how to get answer.

[hollow lodge]

To use linear programming to solve this problem, we first need to identify the variables, the objective function, and the constraints.

The variables in this problem are the number of skateboard A and skateboard B that should be manufactured. Let's call these variables $x$ and $y$ respectively.

The objective function is the profit we want to maximize. This is the sum of the profits from skateboard A and skateboard B. Since the profit on each skateboard A is $30 and the profit on each skateboard B is $40, the objective function is $30x + 40y$.

The constraints in this problem are the maximum number of skateboard A and skateboard B that can be made, as well as the maximum number of hours of labor available for skateboard production. Since each skateboard A requires 3 hours of labor, the maximum number of skateboard A that can be made is $\frac{96}{3} = 32$. Since each skateboard B requires 2 hours of labor, the maximum number of skateboard B that can be made is $\frac{96}{2} = 48$.

The constraints can be written as follows:

$x \le 32$

$y \le 48$

$3x + 2y \le 96$

We can now use these equations to set up and solve the linear programming problem. To maximize the objective function $30x + 40y$, we want to find the values of $x$ and $y$ that satisfy the constraints and give the maximum value of the objective function. This can be done using a variety of methods, such as the simplex method or the graphical method.

Using the graphical method, we can plot the constraints on a graph with $x$ and $y$ as the axes, and then find the values of $x$ and $y$ that give the maximum value of the objective function by finding the point where the objective function line is tangent to one of the constraints.

In this case, the maximum value of the objective function is $30x + 40y = 30(32) + 40(48) = 1920$. This is achieved when $x=32$ and $y=48$, which means that the optimal solution is to manufacture 32 skateboard A and 48 skateboard B.

@open wharf

[ocean seal]

MeatBagFrank

[open wharf]

ok

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[alpine sable]

hello,

[boreal verge]

whats the question?

[alpine sable]

Im finding it hard to understand what a degree of accuraccy while findinng out in decimals, can someone help me?

[boreal verge]

also jesus christ my man wrote more than i ever could

[boreal verge]

whats the example

[alpine sable]

for example (this is actually coming up on my test) find the degree of accuracy of 1.724

[boreal verge]

how many decimals are after 1?

[alpine sable]

three

[boreal verge]

so the degree its rounded to is?

[alpine sable]

three?

[boreal verge]

yes thats pretty much it

also if its less than 5 round down and more round up

and if its 5 just pick whatever you wanna

[alpine sable]

(thats chatgpt)

ok thx

[boreal verge]

(dunno what that is 😭)

[alpine sable]

(ai thats wrong most of the time)

[boreal verge]

(oh amazing)

[alpine sable]

anyways

what grade is everyone here in

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

[tame quarry]

Count of Distinct Integers

Given a board with an integer n written on it, select an integer x from the board. For each, /from 1 to x, if the remainder when x is divided by /is 1, add the integer (x-1) to the board. Find out the maximum number of distinct integers that can be present on the board.

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[crude jungle]

so for integrating by parts

[crude jungle]

i learned it ETAIL which which comes first is what dv =

eqxponetination, trig, alg, inverse, log

my question is what are times this doesnt work

as ETAIl doesnt awlays work

[alpine sable]

dont use that as a rule or whatever, just do whatever makes sense to you and see if it works or not

and then check for alternatives if it doesnt

[crude jungle]

hmm ok

thanks

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[alpine sable]

can someone please help me with this

[alpine sable]

https://cdn.discordapp.com/attachments/653280042050387969/1050793767046750248/image.png

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@alpine sable Has your question been resolved?

[alpine sable]

lol

great server

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[cobalt loom]

I need help

[cobalt loom]

ill be able to answer in 15

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[vapid steppe]

guys

[vapid steppe]

for 89

is it f(-2)+h(-2) or (f+h)(x) and then you plug in -2

[karmic pulsar]

(f+h)(x) at -2

[vapid steppe]

yea ik

but like is that f(-2)+h(-2)

[alpine sable]

yeah

[vapid steppe]

i hate this notation

[alpine sable]

well think about how polynomials add and it kinda makes sense

if you add the functions together

and evaluate at -2

[vapid steppe]

can you do (x^2+5x-14)+(x-1)

and then plug in -2

[alpine sable]

yes

[vapid steppe]

i got different answers tho

[alpine sable]

can i see your work

[alpine sable]

this is not very much work shown lol

[vapid steppe]

OH OOPS

i used g(x)

wait

so is it right that it’s -13

[alpine sable]

thats what i got

[vapid steppe]

ty

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[strange rampart]

partial fraction decomposition of 1/(x+3)^2 ?

[strange rampart]

It seems like this isn't possible

[jovial burrow]

its jst 1/(x+3)(x+3)

and so do it normally

youll get a / (x+3) and b/ (x+3)^2

a = 0

b = 1

[strange rampart]

Oh

Let me try

[jovial burrow]

no point

[strange rampart]

Yeah... cuz it's the same thing

[jovial burrow]

the answer is 1/(x+3)^2

Yea

LOL

u tryna int it or sometin

[strange rampart]

I was gonna try it to confirm but I don't see how it would lead to any other result from this

So, what's the conclusion?

We can't decompose 1/(x+3)^2

?

[jovial burrow]

i mean u can but the values will make the other term vanish

so ur just left with that thing again

so basically u cant decompose it into anything useful

[strange rampart]

:/

thanks i guess

.close

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[wanton falcon]

Which one is correct?

[wanton falcon]

I'm confused

[abstract fractal]

-4x³ = -4(x³)

Only the x is being cubed

[wanton falcon]

so -4(2)^3 is correct ?

[abstract fractal]

Yes

[wanton falcon]

What about

-x^4

is it -1(x)^4 ?

[abstract fractal]

Again, only the x is being cubed

So yes, it's -1(x)⁴

[wanton falcon]

okey thank you 👍

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[cobalt loom]

yes

[last ether]

Based name

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[shadow oak]

Bit confused on how sin^-1 (and cos tan) work...I get how to use the arcsin function but like how do you get from sin(theta) = o/h to sin^-1(o/h) = theta

[abstract fractal]

arcsin(x) is the inverse of sin(x)

Just like how x² = a implies x = √(a) (almost)

sin(x) = o/h --> arcsin(sinx) = arcsin(o/h) --> x = arcsin(o/h)

[shadow oak]

Oh

OH i get it

Ty

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[cursive wharf]

How did we go between those two steps

[tacit arch]

It's actually like 5 calculations scrunched up into one

do you know what $\delta_{ik}$ is?

[ocean seal]

riemann

[cursive wharf]

Not really, but I’ve seen it in the definition for the identity matrix

Does the delta stand for each individual coefficient in the matrix?

[tacit arch]

$\delta_{ik} = 1$ if $i=k$ and 0 otherwise

[ocean seal]

riemann

[tacit arch]

if you write that out for $i=1,2,..., n$ and $k=1,2,...,n$, that describes the identity matrix

[ocean seal]

riemann

[tacit arch]

Might help you if you wrote out the 9 entries of a 3x3 matrix using $\delta_{ik}$ for $i=1,2,3$ and $k=1,2,3$

[ocean seal]

riemann

[cursive wharf]

You mean like this?

[tacit arch]

correct

[cursive wharf]

Right, I’m getting what $E_{ik}$ is intuitively

[ocean seal]

astral

[cursive wharf]

Still more sure about how to combine that with $A_{kj}$

[ocean seal]

astral

[cursive wharf]

Not*

[tacit arch]

just focus on the first case when E is delta.

$E_{ik} A_{kj} = \delta_{ik} A_{kj}$

[ocean seal]

riemann

[tacit arch]

can you simplify the right side?

[cursive wharf]

Would it be just $A_{kj}$

[ocean seal]

astral

[cursive wharf]

Since the delta represents the entries in the k x k matrix

[tacit arch]

use this as $\delta_{ik}$

[ocean seal]

riemann

[cursive wharf]

No clue sorry

I thought an identity matrix multiplied by any matrix was the matrix itself

[tacit arch]

it is!

[cursive wharf]

And delta ik in the first case is the identity matrix

[tacit arch]

you just have the wrong index

k is the summation index

if you have an $m \times n$ multiplying an $n \times p$ matrix, $k$ is the index for $n$

[ocean seal]

riemann

[tacit arch]

the result is $m \times p$ with indices $i, j$

[ocean seal]

riemann

[cursive wharf]

So $A_{ij}$

[ocean seal]

astral

[lone heart]

@cursive wharf Has your question been resolved?

[cursive wharf]

Thanks for the help so far if you see this riemann, guess you had to go, I’ll ask in #linear-algebra in a bit

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[unkempt sundial]

im trying to get Un in terms of n, and i got this, can i write it in a more compact way?

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[alpine sable]

.close

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[neon smelt]

what does point of intersection mean?

[woeful pulsar]

it's (x, y) where x, y satisfy both equations

[neon smelt]

so this point (x, y) would both be on the line of each respective equations?

[woeful pulsar]

yeah like that

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[timid swift]

i need help

[hidden heart]

with?

[vale wigeon]

@timid swift good for you but you should post your problem(s) not just scream into the void like that

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[peak mist]

limits help

[peak mist]

why do we change the limit

and how do we know when to change the limit

[tacit arch]

That's how u sub works

[peak mist]

so evrytime we use u sub we have to do this?

[merry depot]

you don't have to, but you can. and sometimes it simplifies your work

if you don't change the limits, then you have to convert back to x before you plug in the bounds

[gray isle]

and also be careful with how you indicate your bounds in your intermediate work

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[ocean seal]

bryce

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[lucid depot]

Hi. how do i get from 1 to 2

I tried distributing but at some point i reach a loop

[royal plank]

consider it like
(a+b)*(a+c)
and solve it using the more common math laws of distribution

it behaves the same until the very end

but makes it much easier

[lucid depot]

I'm sorry but why would i consider it like that

[royal plank]

you get the result in 2

[lucid depot]

Why would that behave the same way? is there a proof for it?

[royal plank]

it doesn't behave the same way

a^2 is a for example

but its close enough

otherwise, I can show you on tablet, just takes a sec

with set laws

[lucid depot]

yes but the distributive law does not state that. that's my only objection. i get that i can reach the result I want but i would like to have proved each step along the way

[royal plank]

alright, second

[lucid depot]

ok

[royal plank]

here

the first 3 steps

afterwards its only 2 more

do you understand everything I've done so far?
in the 3rd line I use commutativity to ignore the outer brackets

[lucid depot]

i have a problem with the first step
i don't get why it behaves just like algebra

if i do it i would go like that

a sec

last two lines

[royal plank]

well you just did it right to left

[lucid depot]

oh that makes sense

😂😂

[royal plank]

your next line should be the exact same, just other ordering

where you distribute the 2 sub-terms over the union

[lucid depot]

okay how would i continue then

because after a couple of steps

[royal plank]

.

no

[lucid depot]

i get a loop

[royal plank]

you don't

just do the next step as I told you

[lucid depot]

let me try and come back to ypu

[royal plank]

distribute the sub-unions

ok

[lucid depot]

i reached a loop on the question mark then i tried working on the left a bit

but i dont seem to reach anywhere

am i doing anything wrong? @royal plank

[royal plank]

,rcw

[royal plank]

jesse what

[lucid depot]

what

[royal plank]

yes the 3rd line

sorry the light makes a little hard to rea

d

but the 3rd line is wrong

[lucid depot]

where exactly

3 under the blue writing?

[royal plank]

what is that lol

yes, the line right after you went do it

[lucid depot]

b complement union b

[royal plank]

ah wait then its right

oh my wait

[lucid depot]

let make take a better picture

[royal plank]

nono I see it

the line after

4th line

wait i make tablet again

[lucid depot]

ok

[royal plank]

what symbol do you use for Universe?

U?

[lucid depot]

yes