help-13

[crimson sedge]

$\lim_{h \to 0+} \frac{\sqrt{h}}{h}$

[wraith dagger]

Bleidorb

[glad kestrel]

.

.

[crimson sedge]

why am I not allowed to get rid of the absolute value sign?

[glad kestrel]

because you can't just get rid of some part of the equation and expect it to be the same

that's like asking why the graph of x^2+4x+2 isn't the same as the graph of x^2

can't just get rid of 4x+2 and expect it to be the same

[crimson sedge]

true

[glad kestrel]

you can evaluate the absolute value, though...

through simplification

what is |-h|?

[crimson sedge]

|-h| = h

[glad kestrel]

right

and |h|?

[crimson sedge]

= h

[glad kestrel]

so your left hand limit is now...?

[crimson sedge]

left hand limit is now some small number divided by negative number

that goes near 0

like, if we choose number 0.01 for h

[glad kestrel]

refer to what you did here

[crimson sedge]

then we get:
sqrt(0.01) / -0.01

[glad kestrel]

for the left and right hand limits

it's still applicable

but now you have different equations

well one of them is different

[crimson sedge]

left hand side limit:
0 / -0 = -infinity 🤔

[glad kestrel]

?

[crimson sedge]

I don't really know how to substitute properly

when I have this kinda situation

[glad kestrel]

you have $$\lim_{h \to 0^-} \frac{\sqrt{|-h|}}{-h}$$

[wraith dagger]

a disappointing son

[crimson sedge]

yes

[glad kestrel]

which is $\lim_{h \to 0^-} \frac{\sqrt{h}}{-h}$

[wraith dagger]

a disappointing son

[glad kestrel]

so now just do what you did before, multiply both top and bottom by sqrt(h)

this time it's not the square root of a negative number though

and the h on the bottom is negative

[crimson sedge]

I got limit h -> 0- - (1 / sqrt(h))

$\lim_{h \to 0-} -\frac{1}{\sqrt{h}}$

[wraith dagger]

Bleidorb

[crimson sedge]

-1 / 0 = minus infinity

[glad kestrel]

-1/0 doesn't equal -infinity, but the limit does

[crimson sedge]

$\lim_{h \to 0-} -\frac{1}{\sqrt{h}} = -\infty$

[wraith dagger]

Bleidorb

[crimson sedge]

so you mean this 🔼

$\lim_{h \to 0+} \frac{1}{\sqrt{h}} = \infty$

$\lim_{h \to 0} \frac{\sqrt{|h|}}{h}$ = does not exist

[wraith dagger]

Bleidorb

[glad kestrel]

yes

[crimson sedge]

why is there a signum function?
am I doing this right?

[glad kestrel]

do the same thing for this one, |h|=h, multiply by sqrt(h), simplify

[wraith dagger]

Bleidorb

[crimson sedge]

d.n.e. = does not exist

[crimson sedge]

Now, I only need to know how they got this form lim h->0 (1/|h|sgn(h))

sgn(x) = x/|x| = |x|/x

is sqrt(|h|) = | |h| |

double absolute value?

[floral thistle]

that would be useless

also that’s not what it is

it’s just sqrt(|h|)

[crimson sedge]

$\lim_{h \to 0} \frac{1}{|h|sgn(h)}$

[wraith dagger]

Bleidorb

[crimson sedge]

how can I get this form?

[crimson sedge]

they are not even equal?

[crimson sedge]

I probably just have to ignore this, since this is not equal to the limit h->0 (sqrt(|h|)/h)

.closed

.close

[cedar kiln]

Channel closed

Closed by @hot socket

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[untold comet]

This is my last attempt on this problem. May someone please help me validate that it is indeed 0.07?

[untold comet]

I've tried 0.69 & -0.69, also -7.

I plugged in 31 into dp/dx for b

then plugged in 32 into dp/dx for part c

31 = 2.24

32 = 2.1705

2.24 - 2.1705

[cedar kiln]

@untold comet Has your question been resolved?

[untold comet]

.close

[cedar kiln]

Channel closed

Closed by @untold comet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[untold comet]

May someone please help me solve this?

[graceful karma]

Do you know where to start @untold comet

[cedar kiln]

@untold comet Has your question been resolved?

[untold comet]

Sorry was away

Let me see

[bright surge]

uh
use a calculator, i suppose

[untold comet]

never thought of that thanks

🤡

i know how to do this with t he total cost but confused with the average cost

ok no i don't know

how to start this problem

@graceful karma

[graceful karma]

Wouldnt you just multiply it by 300 @untold comet

[untold comet]

??

To g et the total cost?

Then solve like normal?

[graceful karma]

Yeah that sounds right

They don't specify exactly what they want but I assume its the marginal total cost

Not just the marginal cost of a single unit

[untold comet]

side question since i just finished working this problem

and i get only one attempt

before it randomizes and i have to do it over again

it is inelastic

bc n < 1

but i don't know which inelastic to pick

[graceful karma]

Well if something is inelastic the demand wont change when the price changes right?

And if thats the case the total revenue would increase

Because price is increasing and demand is steady

[untold comet]

u make way more sense than my textbook

[graceful karma]

Lemme double check though

Im not an econ type person

Yeah I think that checks out

[untold comet]

so C

[graceful karma]

Yeah

[untold comet]

hope i did my math right

got them both wrong

hot damn

[graceful karma]

[untold comet]

idk what i did wrong there...

i followed a book example

:l

[graceful karma]

Hmm

[untold comet]

i can send pic of my work

genuinely don't know what i di dwrong

i realized what i did wrong

i did 100(-0.1) instead of 100(-0.2)

it's supposed to be -20e

lol...

[graceful karma]

Thatd do it

[untold comet]

the book example had -0.1

-_-

[graceful karma]

Oh

Yeah I randomly write stuff Im looking at or thinking about too

Like if Im typing to someone and I start thinking about something Ill just randomly type what Im thinking about

[untold comet]

GAH

this is time consuming and i have 4 other classes kms

all this due friday

OK

back to the other question

[graceful karma]

Thats so annoying that it randomizes every time

[untold comet]

right?

[graceful karma]

Does it at least tell you the answer to the old one?

[untold comet]

nope

[graceful karma]

Thats evil

[untold comet]

ok back to the avg cost question

so what i need to do is

multiply everything by 300

except c

or also c?

[graceful karma]

Well wouldnt you just multiply C by the number of products

Or do you mean both sides of the equation

[untold comet]

both sides of the equation

if we only multiply one side

[graceful karma]

I suppose you could do that

[untold comet]

i get 90000e^x/300

[graceful karma]

If it makes more sense

[untold comet]

ok i multipled

300c=90000e^x/300

now what

find the derivative?

since marginal cost?

then sub in 300?

[graceful karma]

Yeah

Id honestly just ignore the c

Its just there to show what the whole equation is

I would maybe write

T=90000e or whatever

[untold comet]

so dy/dx of 90000e^x/300 = 300e^x/300

then plugin 300 into x?

[graceful karma]

Yeah

[untold comet]

ok i get 300e

then multiply 300 * e

815.484

[graceful karma]

Yeah thats what I got

[untold comet]

"Round your answer to the nearest cent."

that mean .48 right

[graceful karma]

Ye

[untold comet]

question wrong

🙁

[graceful karma]

Hmm

Maybe they really do just want the marginal cost per unit

[untold comet]

ok what i do

new randomization

same concept

[graceful karma]

The same procedure but without the * # of goods ig?

[graceful karma]

So just differentiate 200e^x/200

I hope thats the correct solution

[untold comet]

e^x/200

then sub in 200?

[graceful karma]

Yeah

[untold comet]

200e

200*e

543.656

do 543.66

[graceful karma]

Wait

Its just e right?

Cause its e^200/200

[untold comet]

i plugged in 200 into x then calculated

and i got 200e

wait

u right

for some reason it was inputting 200 before everything when i pasted

:L

e^1 = 2.718

2.72

is that the answer??

i've tried 2.72 in the past and said it was wrong

[graceful karma]

Pain

So yeah maybe we were right before

But it still didnt work

[untold comet]

??

[graceful karma]

Hmm what in the world

I see no reason why multiplying by the number of products wouldnt work

Theres no example in the book right?

[untold comet]

<@&286206848099549185> who wants $20 helping me solve 4 derivatives problems

[graceful karma]

LOL

[untold comet]

at this rate i'm screwed

[graceful karma]

Random image online of this problem

[untold comet]

what

does it tell you waht to do

[graceful karma]

It links to that super sketchy chegg website

[untold comet]

yooooooo

[graceful karma]

Surely your textbook has some kinda thing for this

Maybe check the index for marginal cost or smthn?

[untold comet]

that's what i've resorted to

yo might have found

[graceful karma]

|| <@&268886789983436800> this guy with the grinch pfp||

[untold comet]

alr papa

i think i found it

one sort of like it

but part of the question ma-

this thing says total cost not average cost

papa how do we go from avg cost to total cost

[graceful karma]

I mean I can only imagine its multiplying by the number of products

Nothing else makes sense

[untold comet]

hm

https://tenor.com/view/not-sure-hmm-thinking-gif-5730421

dinkleberg...

[graceful karma]

Do you get infinite attempts

[untold comet]

100 submissions

used 5 so far

[graceful karma]

Maybe it was a rounding fluke in the system or smthn

Cause it should always be e * number of products

[untold comet]

i wasted

so much time

on this problem

still need help

anyone

[graceful karma]

https://www.youtube.com/watch?v=uPp1QZZKc8E

I mean this guy has a tutorial on something similar

He basically just says that average cost = total cost / units produced

And that marginal cost is the derivative of the total cost

Which is what we did

[cedar kiln]

@untold comet Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unique cypress]

find the derivative

i need help doing the derivative for this probglem

i dont know how to do it

[bright surge]

you know the derivative of arcsin, right?

[unique cypress]

yes 1/sqrt(1-u)^2

[bright surge]

yeah

use product rule for derivative of x arcsin(x)

what would you have?

[unique cypress]

so would you get yeah so like

[bright surge]

(eh - ping me when you've got the answer pls)

[unique cypress]

ok

1(arcsin(x)) + (x)(1/sqrt(1-u)^2

@bright surge \

[bright surge]

what's u?

[unique cypress]

i mean x

[bright surge]

i think that's supposed b=to be x

oh ok

[unique cypress]

then u just add the second part?

oh nah wait

[bright surge]

you know how to rewrite a radical?

[unique cypress]

elaborate pls

[bright surge]

it's just an exponent

[unique cypress]

oh

yeah

[bright surge]

a square root of something is just that something to the power of 1/2

[unique cypress]

yeah

[bright surge]

you know that, right?

[unique cypress]

yessir

[bright surge]

then just use chain rule

[unique cypress]

ok

so would the answer be

well

for that part

its 1/2(1-x^2)(2x)

@bright surge

should i just put it all together now

[bright surge]

add those together

sum rule

and if you're right a beautiful thing should happen

[unique cypress]

yeah i think the problem is

i dont know how to add them all together

its not fitting together

@bright surge

[bright surge]

what did you get?

(also do you know latex? it's a bit hard to look at plain text)

[unique cypress]

no sorry

[bright surge]

uh

[unique cypress]

ill put in paint sreenshots

[bright surge]

that's ok

[unique cypress]

i can write it out with my mouse hah

[bright surge]

doesn't matter

[bright surge]

(as long as it's readable...)

[unique cypress]

so would you multiply the chainrule out?

[bright surge]

wait what?

[unique cypress]

uhhhhhhhhhhh

[bright surge]

i think you have a mistake with the chain rule part

[unique cypress]

isnt chainrule f'(g(x)) (g'(x))

[bright surge]

yeah

that's right

[unique cypress]

so

[bright surge]

so what would you choose as f and g?

[unique cypress]

well

(sqrt(1-x))

is just (1-x)^1/2

oh wait

[bright surge]

that's right

[unique cypress]

i use chain rule right here right

[bright surge]

yeah

[unique cypress]

did i stick a x^2 in there

[bright surge]

isn't it supposed to be $\sqrt{1-x^2}$ though?

[wraith dagger]

Adavocowana

[unique cypress]

oh yeah

ohhhh

completely forgot to power rule

[bright surge]

nah

you can keep the radical as it is after applying chain rule

[unique cypress]

so i can just keep it at 1/2?

so when i bring down the power using power rule

i can keep the exponent at 1/2?

casue chain rule?

[bright surge]

i mean

you don't have to bring down the exponent

just use chain rule

[unique cypress]

so

sqrt(1-x^2) = (1-x^2)^1/2 (2x)

[radiant topaz]

Write d/dx on left side and you differentiate wrong

[bright surge]

wait no

i mean

[unique cypress]

wym sam

[bright surge]

you still have to bring down the exponent in f'(g(x))

[unique cypress]

so 1/2(1-x^2)^-1/2

how do you do these things

looks cool

[bright surge]

$\frac{\dd}{\dd x}(\sqrt{1-x^2}) = \frac{1}{2 \sqrt{1+x^2}} \frac{\dd}{\dd x}(1+x^2)$

[wraith dagger]

Adavocowana

[bright surge]

just calculate the other derivative

multiply

and then add that to the derivative of x arcsin(x)

[unique cypress]

.close

[cedar kiln]

Channel closed

Closed by @unique cypress

Use .reopen if this was a mistake.

[unique cypress]

i will just go to sleep and pray

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dapper berry]

How do I do quality of fit?

[dapper berry]

I need to get the quality of fit for a line, and I have no idea how to do that.

[cedar kiln]

@dapper berry Has your question been resolved?

Channel closed

Closed by @dapper berry

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[idle quartz]

I'm reading about sums of infinite series from a textbook, the textbooks takes the partial sum of 1/(n*(n+1)) as (1/i) - (1/(i+1)), why is this?

[idle quartz]

I understand how it split into (1/i) and (1/(i+1))

but why is it subtracting them from each other if it should be a partial sum?

ohhhhhh

nevermind i think i got it

I completely forgot you have to substitute and solve the system of equations

.close

[cedar kiln]

Channel closed

Closed by @idle quartz

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[idle quartz]

you can use identities

cos^2(x) = (1+cos(2x))/2

then you just factor out 1/2 and you're leeft with the integral of 1 + cos(2x)

np

[cedar kiln]

Channel closed

Closed by @quick lagoon

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[severe flume]

gotta find what this angle and how much does this add up to?

[cedar kiln]

@severe flume Has your question been resolved?

[severe flume]

<@&286206848099549185>

.close

[cedar kiln]

Channel closed

Closed by @severe flume

Use .reopen if this was a mistake.

[crimson sedge]

so you are trying to find x + y ?

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[severe flume]

nah i alreay did that but yu can help me with a different one?

[crimson sedge]

sure

[crimson sedge]

is this the full picture?

[severe flume]

ye

[crimson sedge]

well let's start with a since that's the easiest

[severe flume]

ok

[crimson sedge]

you know that the sum of 30 + 50 + a = 180 right?

[severe flume]

ye

[crimson sedge]

so solving for a you'd get 180 - 50 - 30 = a

[severe flume]

yep

[crimson sedge]

I'll leave the solving to you, so that's one down

now e

[severe flume]

ok bet

[crimson sedge]

since 30 and e lie on the same "U" shape, if you were to continue the line the right line of the triangle downwards the angle below e would be 30

and so e + 30 = 180

[severe flume]

does e equal 150 degrees because it a co-interior angle?

[crimson sedge]

hell yes

[severe flume]

lesh go

[crimson sedge]

now since e is the exterior angle of d

150 + d = 180

but there's another easier way to solve that

since d and 30 lie on the same z shape

[severe flume]

d=30 degrees

[crimson sedge]

d must = 30

[severe flume]

yep

[crimson sedge]

as shown here

and then c is the same thing

lies on the same z-shape with 50

and to be certain you are correct check that your a + c +d = 180 since all the angles of a triangle must sum up to 180

(it is btw)

[severe flume]

ye

whats a equal tho?

[crimson sedge]

.

which becomes 100

[severe flume]

ohh

ok

then c =50 degrees because if you a+d= 130 degrees then 130-180=50 degrees?

[crimson sedge]

yessir

[severe flume]

nice

so were finished?

[crimson sedge]

seems like it

[severe flume]

thank you very much

[crimson sedge]

anytime

[severe flume]

@crimson sedge

.close

[cedar kiln]

Channel closed

Closed by @severe flume

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gleaming cave]

some points exist in an n-dimensional space, given some of the distances between the points, find the smallest possible value of n

[gleaming cave]

probably has a wikipedia article, but I don't know its name so i cant search for it

[cedar kiln]

@gleaming cave Has your question been resolved?

[fair geyser]

i don't get it

it's 1

what possible distance would invalidate n=1

[tropic oxide]

4 points all 1 away from each other

[gleaming cave]

oops forgot to mension euclidean space/distance

actually if the popular problem is noneuclidean thats fine aswell

i know its known math because my psychology book said some words about it when psychologists calculated the # of dimensions human emotion lies on

the math in that instance is obviously
A) more complicated due to imprecision
B) easier due to bashing

[cedar kiln]

@gleaming cave Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[white hornet]

ya

I got

something

but not sure

is correct

OF = j+k

ED = -j-k

AG = i+k

but feel wrong

oh

ty

.close

[cedar kiln]

Channel closed

Closed by @white hornet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gray vine]

A straight line passes through the point (3, 5) and has the slope a/3. Determine a so that the line also goes through:
a) point (5, a)
b) the point on the y-axis where y = -4a
c) the point on the x-axis where x = 3-a.

[gray vine]

$$f\left(x\right)=\frac{a}{3}+m$$
$$5=a+m$$
$$5-a:=:m$$

[wraith dagger]

Theophania

[gray vine]

Is this correct steps in the beginning?

[gray vine]

Okay I solved question a), but I don't know how to solve b).

[cedar kiln]

@gray vine Has your question been resolved?

[cedar kiln]

@gray vine Has your question been resolved?

[gray vine]

Btw, we write the equation in this form here in Sweden:
y = kx + m, as opposed to y = mx + b

[cedar kiln]

@gray vine Has your question been resolved?

[spiral orbit]

First, figure out what is the general equation of a line that goes through the point (3, 5) with a slope of a/3. This can be done by the point slope formula

For part b), you are given that the line goes through another point.
Can you figure out what the coordinates are of the point that lies on the y-axis and y=-4a?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ivory pollen]

can anybody help me out on ii, i dont understand the question and dont know what to do 😦

[ivory pollen]

I already solved i but have no idea at all how to solve ii

[drifting marlin]

Is it not just differentiating f' and solving?

[ivory pollen]

uhh can you elaborate a bit

[drifting marlin]

What part doesn't make sense?

You're given f'; differentiating that gives you f", from which you can solve f"(x) = 4 with high school algebra

[umbral pulsar]

.open

.help

[cedar kiln]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[umbral pulsar]

.reopen

.tag

.tag hi

.help tag

[cedar kiln]

Usage: .tag ...
Manage factoids.
Sub-commands:
.tag add <name>
.tag alias <name> <newname>
.tag delete <name>
.tag edit <name>
.tag info <name>
.tag top
.tag unalias <name>

Type .help tag <sub-command name> for more info on a sub-command.

[umbral pulsar]

.help open

[cedar kiln]

No command called "open" found.

[umbral pulsar]

.tag add hi

.help

[cedar kiln]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[umbral pulsar]

ok wat

Is this symetrical or anti-symetrical?

Id say its none

since it doesnt even have a proper diagonal

oh

nvm wait

.close

[ivory pollen]

.close

[cedar kiln]

Channel closed

Closed by @ivory pollen

Use .reopen if this was a mistake.

[ivory pollen]

there @umbral pulsar

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[umbral pulsar]

Posted in another 👌

[umbral pulsar]

.close

[cedar kiln]

Channel closed

Closed by @umbral pulsar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crimson sedge]

Did I do this correctly?
i just wanna know if i did it right

[fossil dirge]

Yup looks good to me @crimson sedge

[crimson sedge]

Looks good

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wintry wasp]

How can i prove tan(pi(x-(1/2)) and its inverse 1/pi (arctan(x)) + (1/2) are injective functions from (0,1) to R and from R to (0,1) respectively?

[wintry wasp]

This is the inverse btw

<@&286206848099549185>

[steady imp]

What level of math is this

@wintry wasp

[wintry wasp]

University BAphysics year 1 idk lol

its uhh

set theory

[steady imp]

I would just make a claim that it's monotonic increasing i.e. bijective

[wintry wasp]

see we only ever saw that bijective = injective and surjective

never the monotonic increasing thing

[steady imp]

Do you know derivatives?

[wintry wasp]

Is there a link online about monotonic increasing i can refer to?

i do

[steady imp]

Do you know continuity?

[wintry wasp]

yeah

[steady imp]

Your proof would look something like this

[late wing]

monotonic increasing=injective

[steady imp]

Basically the derivative is strictly positive

[wintry wasp]

yeah but is there any website that i can link to that claims that

since its for a task

[steady imp]

So it's injective

[wintry wasp]

the full task is prove [0,1] is equinumerous with R and the deadline is in less then 2 hours lol

[steady imp]

using continuity and bounds you should be sufficient

yeah just use

1. continuity
2. strictly positive derivative

and you should be set

maybe an argument by contradiction

Does any individual part not make sense?

[wintry wasp]

Well, im not how i would prove continious and increasing over intervall = injective

[steady imp]

You can make an argument by contradiction

[wintry wasp]

So i claim a function is injective while not having a strictly positive derivative?

[steady imp]

otherway around

show that a function that is not injective while continuous increasing is not possible

i.e. consider two points x and x+h

that's how I would do it

namely it's going to be bijective so the inverse should prove true as well

[wintry wasp]

Im lost sorry man, i really dont grasp the concepts talked about in class yet

maybe a better solution for me is to go about proving the equinumerousity between R and [0,1] differently

[steady imp]

I'm trying to think how I can help you without telling you how to do it

[wintry wasp]

Rn i was going to prove an injection from R to (0,1) and vice versa using that tan function and its inverse

[steady imp]

What's your approach to do that?

[wintry wasp]

according to the schroder cantor whatever theorem there exists a bijection between the 2 sets if thats true

[steady imp]

That is true

[wintry wasp]

and then i'd refer to the hotel paradox thing and claim that adding elements to this set doesnt change the cardinality so id just add 0 and 1 to the (0,1) interval to make [0,1]

[wintry wasp]

no idea tbh

injective means for a,b element of a set, f(a) is not equal to f(b)

[steady imp]

https://proofwiki.org/wiki/Continuous_Real_Function_on_Closed_Interval_is_Bijective_iff_Strictly_Monotone

[wintry wasp]

whats that

[steady imp]

that's as much I can help you without telling you the solution

[wintry wasp]

alright thanks

[cedar kiln]

@wintry wasp Has your question been resolved?

Channel closed

Closed by @wintry wasp

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[upper knot]

does anyone know how to make a sin wave more linear?

[graceful karma]

Wdym

Like a triangle wave?

,w triangle wave

[upper knot]

I guess. Sin waves ease in and out

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[graceful karma]

Sus

,w plot triangle wave

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[upper knot]

o perfect

[graceful karma]

Like that?

[upper knot]

what is the most basic form if I may ask

[graceful karma]

Lemme see

[floral thistle]

,w plot arcsin(sinx)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by quantum#6320

[floral thistle]

@graceful karma @upper knot

[upper knot]

u guys r friggn awesome!

[graceful karma]

Yeah that

I didn't actually know that was a way to write it

But I guess it is

I've always defined it using mod

[floral thistle]

how would you do that

[graceful karma]

Through some weirdness

,w |(x mod 2) - 1| - 0.5

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[floral thistle]

oh lol

interesting

[graceful karma]

It's kinda just the abs value of a sawtooth wave

With some extra stuff on top

,w plot sawtooth wave

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[cedar kiln]

@upper knot Has your question been resolved?

Channel closed

Closed by @upper knot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[polar marsh]

im trying to solve this system of equations but the only thing i can think of is trying all possible values of b and d (-1 and -20, -2 and -10, -5 and -4, 4 and 5, 10 and 2, 20 and 1 (and the other way around)) to solve, i am just asking if there might be a faster way?

[polar marsh]

than N is supposed to be a Z my bad

like this

[cedar kiln]

@polar marsh Has your question been resolved?

[void whale]

Plug a = -c everywhere, so $c(d - b) = 1$ by third equation ; since both are integers, $d - b = \pm 1$ et $bd = 20$, therefore $b,d = (4,5) ; (5,4) ; (-4, -5) ; (-5, -4)$, and $c = \pm 1$. So $b + d = -9$ or $9$. By equation 2, $b + d = -9$. So you just have to check $(-4, -5)$ and $(-5, -4)$.

[wraith dagger]

polikuj2

[polar marsh]

thats really smart thanks

.close

[cedar kiln]

Channel closed

Closed by @polar marsh

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crimson sedge]

Excuse me how may i do figure out this area

[upper abyss]

Do you know the area of a rectangle?

[crimson sedge]

Can’t remember

Is it base x height

[sudden magnet]

you basically need to separate that into 3 rectangles and 2 triangles, calculate the area of every one of them, then add them up

[crimson sedge]

Yea I just figured that out

Thank you for helping me

[sudden magnet]

np

[crimson sedge]

.close

[cedar kiln]

Channel closed

Closed by @atomic quest

Use .reopen if this was a mistake.

[crimson sedge]

.close

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crimson sedge]

m = -1/a²
how can I find all the points

why is -1/a² = -1/4?

[upper abyss]

Any line perpendicular to y = 4x - 3 has slope -1/4

[crimson sedge]

how is the slope of y = 4x - 3 equal to -1/4
I thought it is m = 4

y = mx + b

[upper abyss]

It isn't

But any line perpendicular to it has slope -1/4

[crimson sedge]

yes, I get that.

but how did they got -1/4 as slope?

[upper abyss]

Any line perpendicular to y = 4x - 3 has slope -1/4

[crimson sedge]

y = m(x - x_0) + y_0?

[upper abyss]

So if your line is perpendicular to y = 4x - 3...

We are looking for lines perpendicular to y = 4x - 3. Therefore we are looking for lines with slope -1/4

[crimson sedge]

oh

I thought parallel 😅

I get it

-1 = 4 * ...

[upper abyss]

Kek yeah I thought that might be happening.

[crimson sedge]

omg

[upper abyss]

I do that too

[crimson sedge]

thank you so much

.close

[cedar kiln]

Channel closed

Closed by @hot socket

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gray vine]

f(x) is a linear function whose graph passes through the point (0, 4) and intersects the graph of g(x) = -x - 2 at a right angle. What is f(x)?

[gray vine]

Right answer should be f(x) = x+4

[dense wing]

what have you tried?

[crimson sedge]

what do i do when my confidence interval contains my null hypothesis but my p value rejects my null hypothesis?
im doing a basic poisson counting experiment thing where background expected is 1.5 events
i see 4 events
my 90% cl interval is 1.35 to 9.15
my p value with a test size of 0.10 is 0.06565

[gray vine]

...

[gray vine]

so if its right angled, i assume we have a scenario of $k_1\cdot k_2=-1$

[wraith dagger]

Theophania

[dense wing]

what's k?

[gray vine]

-1

of g(x)

so f(x) has k value 1

[dense wing]

Oh the coefficient of x

[gray vine]

yeees

[dense wing]

then yes

[gray vine]

we use kx+m

so we should then have f(x) = x + m, and then 4 = 0 + m, so m = 4

m being the y-intercept

[dense wing]

yeah, that's right

[gray vine]

okay it's right, thanks for the help

.close

[cedar kiln]

Channel closed

Closed by @gray vine

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[astral dagger]

show that

[astral dagger]

i dont know how you approach this

[void whale]

What's your definition of sin and cos ?

[astral dagger]

?

[cinder talon]

well

[astral dagger]

if you are asking if there is anymore to this question then no, this is it

[cinder talon]

you could use th eformula

[astral dagger]

i think you are supposed to use trig identities to prove this

[cinder talon]

sin(a+b) = sin(a)cos(b)+cos(a)sin(b)

and

plug in the values

π/2 and x

[astral dagger]

ohhhh

i think i get this now

[cinder talon]

yeah

oh no

that

[astral dagger]

so is A = pi/2, B = x?

[cinder talon]

yep

[astral dagger]

ok i think i might understand this

[cinder talon]

then just simplify

[astral dagger]

ye hold on ill try and figure it out

[astral dagger]

ive ran into a problem

@void whale could you help me out? the other dude went

q) show that

so im doing cos^2A + sin^2A = 1 to find out cosA
cos^2A + (pi/2)^2 = 1
cos^2A + = 1 - (pi/2)^2
this gives me a negative which cant be square rooted

[void whale]

No

cos^2A + (sin(pi/2))^2 = 1

[astral dagger]

but i thought sinA = pi/2

[void whale]

No, A = pi/2

[astral dagger]

ohh damm

i just noticed

cheers for that

[astral dagger]

im suck now because i cant workout cosB due to sinB = x

(pi/2)(cosB) + x = Cosx

this is what im working with

[crimson sedge]

you could just show a graph

draw graphs

ez

[astral dagger]

im not good with graphs unfortunately but im pretty sure im supposed to do using identities

[crimson sedge]

draw a circle radius 1

[astral dagger]

its a skill i need to learn

[crimson sedge]

I mean using simple equations is worse than using graphs

[astral dagger]

i hate graphs tho the only one i like is the circle graph

[crimson sedge]

the teacher would give you a much higher score if you properly know how to use graphs

[astral dagger]

cast is it?

i forget what the graph is called

[crimson sedge]

doesn't mean you don't need to do it 🤷‍♂️

[astral dagger]

well its not a name for the graph its more of a name for the quadrants

so you know which one sine is positive in and which one it isnt

well idk the teacher wanted it in identities but i do have much harder questions that will require graph format

[crimson sedge]

ok I'll just do in graph war

way

can you imagine a circle on a graph that has a radius of 1 and point at (0,0)?

[astral dagger]

ye

[crimson sedge]

you know that on that graph sinx is the y coordinates?

cosx is x coordinates

[astral dagger]

i didnt know that

[crimson sedge]

uhhh

Well ok uh

[astral dagger]

well i could switch questions to the one that requires a graph and ill finish off that one tomorrow

[crimson sedge]

look sinx is y coords

[astral dagger]

yup

[astral dagger]

cosx isnt in the x coords tho

[crimson sedge]

what

radius is hypotenuse

and it's also 1

so x coords would be cosx

[astral dagger]

ok

[crimson sedge]

well uhh that coords at the top isnt correct trust me

anyways

just concentrate at the graph

only the grpah

couldnt get better pics

[astral dagger]

looks sus

[crimson sedge]

you see the triangle with points O, K, Q right?

angle AOK is basically pi/2 + 0 right

[astral dagger]

ye i know

[crimson sedge]

if an angle goes above pi/2 just think of the triangle like KOQ

don't think of the whole angle just that triangle

if you look at y coords it's supposed to be sin0

but in that situation y coords became cos0

pi/2 + 0 becomes triangle KOQ instead of PMO

so you need to think in that triangle

[astral dagger]

im confused on why the triangles are important here

[crimson sedge]

well we are trying to get trig values right?

wouldnt we need to use triangles

[astral dagger]

ahh so you are working in triangles

[crimson sedge]

yea

[astral dagger]

pretty smart

if you ask me

[crimson sedge]

graphs can be complicated at first

but trust me

it helps a lot

[astral dagger]

im just worrying because if i learn the graph way of doing stuff like this im worried i wont be able to use the identities when i need to. I dont know if in higher maths i will need to

[crimson sedge]

Graphs require identities

Wanna know how these identities are proven?

Graphs.

[astral dagger]

lol

[crimson sedge]

You can understand identities and properly use them if you use graphs

also in higher math levels you'll get to use graphs more

The best thing in making people understand is to use visual images

and that's what graphs do :))

[astral dagger]

ok ok

[crimson sedge]

i am def a graph lover wee

ok uhh I just came by to tell you how to prove that in a graph way

so like uhh

yeah im heading out lmao

[astral dagger]

but i still dont know

[crimson sedge]

ok i guess im stuck here

[astral dagger]

could you label the graph in my situation

and then ill get a better idea on how to solve it

[crimson sedge]

if anyone can come by and summarize what I just said

it'd be cool

[astral dagger]

ye i understand but could you show me a example of plotting it first

that'd be really helpful

[crimson sedge]

wdym

[astral dagger]

could you show me how you would do this on a graph

[crimson sedge]

i just told you

think of triangles

[astral dagger]

show

[crimson sedge]

damn your teacher tells you to prove these, what a low-quality teacher

smh

[astral dagger]

well she told me to do it using identities

[graceful karma]

What was the issue with using your identities

[astral dagger]

this is my first time using a graph

[crimson sedge]

so no graphs

[graceful karma]

It should be a 3 line proof

[astral dagger]

3 line!!?!?!?!?

[crimson sedge]

Well i was teaching him the graph way

[graceful karma]

Dun dun dunnn

[crimson sedge]

the graph solution

[astral dagger]

ok hold on let me find it

im suck now because i cant workout cosB due to sinB = x
(pi/2)(cosB) + x = Cosx

[crimson sedge]

you know this is better to go on by using graphs right

[astral dagger]

...

i understand it might be better but i want to learn the identity way first

[crimson sedge]

such a low-quality teacher man

can't make you use graphs

[astral dagger]

lol

[graceful karma]

sin(pi/2 + x) = cos(x)
sin(pi/2) cos(x) + cos(pi/2) sin(x) = cos(x)
Do you get to here?

[astral dagger]

yes i worked out cosA also

[crimson sedge]

wouldnt we need to prove sin(pi/2 + x)= cosx

or is it already just, given

[graceful karma]

You gotta prove it

So whats sin(pi/2) and cos(pi/2)

[crimson sedge]

ok well tbh I'd rather use graphs but your teacher has an enormous skill issue and low social credit score not allowing you to use graphs

im heading out

[astral dagger]

lol this guy

[graceful karma]

Adios

[astral dagger]

i used the sin^2A + Cos^2A = 1 formula to work out cosA which i got cosA = 1
but i cant work out cosB because sinB = x

hence im left with (pi/2)(cosB) + x = Cosx

[graceful karma]

So youre starting by converting sin(pi/2+x) to sin(pi/2)cos(x)+cos(pi/2)sin(x)

And then using the squared identity to simplify?

[astral dagger]

how do you know that cosA = cos(pi/2) and how do you know that sinB = sinx(x)

sin(a+b) = sinA * cosB + cosA * sinB

how do you know the last 2 in that equation

ahh

ok mb

i see it now

[graceful karma]

Epic

[astral dagger]

whats next tho

[graceful karma]

Evaluate cos(pi/2) and sin(pi/2)

[astral dagger]

hmm how

[graceful karma]

Using your unit circle or smthn like that

[astral dagger]

hm

[graceful karma]

Whats pi/2 radians in degrees

[astral dagger]

90

[graceful karma]

So whats the x value of a point on a circle, radius 1, at 90 degrees counterclockwise from the positive x axis

[astral dagger]

x being ?

oh you mean on the x axis

[graceful karma]

Yeah

[astral dagger]

the greenline is still at the origin tho

on the x axis

[graceful karma]

Yes

[astral dagger]

so 0?

[graceful karma]

Yeah

[astral dagger]

oh wow that was right

[graceful karma]

So cos(pi/2) is 0

And sin(pi/2)?

[astral dagger]

if sin is the y so 0? (previous guy said sin is the y) if im wrong dont give answer i have another approach

[graceful karma]

It shouldnt be 0

[astral dagger]

oh 1

mb

when cos is 0 then sin is 1

right?

@graceful karma

[graceful karma]

Yes

So what does that do to the equation for the angles

[astral dagger]

does it have to do with multiplying by 0 and 1

[graceful karma]

Yes

[astral dagger]

so do we get 0 + 0 or 0 + 1

well we dont know sin(x)

[astral dagger]

1 * cos(x) + 0 * sin(x)

[graceful karma]

Other way

[astral dagger]

oh yeah i see

[astral dagger]

we still need to figure out cos(x) tho

[graceful karma]

Wdym

[astral dagger]

how do you know what the equation equals if there is a missing value

if cos(x) = 0 then our answer changes same with if cos(x)= 1

@graceful karma ^

[graceful karma]

Well youre proving that the functions are equal

And now you have cos(x)=cos(x)

[astral dagger]

ohhh thats genius

yo proofs are fun as hell

dude that is actually insane

ive got quite a lot more to go through but it makes sense

thanks

[graceful karma]

Np

[astral dagger]

hey would you be able to help me out with one more question. its one of the last questions on the sheet and i want to know how to do it

[graceful karma]

One sec

Hmm

This ones tougher

Well R sin(wt+a) can be expanded

R[sin(wt)cos(a) + cos(wt)sin(a)]
Rsin(wt)cos(a) + Rcos(wt)sin(a)

So you want to find a value of a such that

R*cos(a)=8

R*sin(a)=15

Do you follow

[astral dagger]

let me think hold on

[astral dagger]

ahh i see what you are kinda doing here

its that rule

remember that identity

ok

[graceful karma]

Which one?

The angle addition one we used

[astral dagger]

this one

[graceful karma]

Yeah that one

[astral dagger]

so i understand up until this line

Rsin(wt)cos(a) + Rcos(wt)sin(a)

what do we do next?

[graceful karma]

Well so thats in the same form

The coefficient is entirely determined by R*cos(a)

And R*sin(a)

Right?

[astral dagger]

ye that makes sense

[graceful karma]

So you can write a formula

Rcos(a)=8
Rsin(a)=15

Or

R cos(a) = R sin(a) - 7

R[cos(a) - sin(a)] = 7

cos(a) - sin(a) = 7/R

And uhhh

[astral dagger]

🤔

[graceful karma]

We're in a similar situation thats slightly simpler

[astral dagger]

how do you put this in the form that they want tho

@graceful karma

[graceful karma]

This is gonna come out nastily

[astral dagger]

i have the answer and it is nasty

but i dont know how you get it into that format

how do we turn this Rsin(wt)cos(a) + Rcos(wt)sin(a) into that format

[graceful karma]

Lemme try smthn else

R cos(a)=8
R sin(a)=15

R=8/cos(a)
R=15/sin(a)

8/cos(a)=15/sin(a)

8sin(a)=15cos(a)

sin(a)/cos(a)=15/8

Taking in the convenient fact that sin(x)/cos(x) = tan(x)

tan(a)=15/8

a=arctan(15/8)

[astral dagger]

dude thats genius

i understood everything

thats genius as hell

[graceful karma]

Les go

[astral dagger]

do we have to do something else?

[graceful karma]

Just plug it back in

[astral dagger]

ohh i see

ohh

ye

[graceful karma]

Oh wait

[astral dagger]

are we doing this to workout R ?

[graceful karma]

We still gotta solve for R yeah

[astral dagger]

R=8/cos(a)
R=15/sin(a)

plug it in

[graceful karma]

Which should be easier

So R=8/cos(arctan(15/8)

,w 8/cos(arctan(15/8)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[graceful karma]

Oh

Reasonable

[astral dagger]

thats nice