help-33

[weary quarry]

Nevermind 💀

.close

[marsh citrus]

Channel closed

Closed by @weary quarry

Use .reopen if this was a mistake.

[marsh citrus]

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.

[abstract kestrel]

df =(z - 2.5) *m df =5
da = (z+2)*m da = 5.5
what is m and what is z

[marsh citrus]

Please don't occupy multiple help channels.

[abstract kestrel]

.close

[marsh citrus]

Channel closed

Closed by @abstract kestrel

Use .reopen if this was a mistake.

[marsh citrus]

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.

[drifting ingot]

is this the right intergral for

[marsh citrus]

@drifting ingot Has your question been resolved?

[marsh citrus]

@drifting ingot Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[marsh citrus]

Please don't occupy multiple help channels.

@slate hearth Has your question been resolved?

[marsh citrus]

@slate hearth Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[uneven vector]

what am i missing...

[uneven vector]

x = 0 right? since its between y and z?

so first option isnt true

then the second option is straight up given

but somehow im wrong

then since x is 0 third option is false

[wild zodiac]

can't x be, say, -0.5 if y is -0.6

[uneven vector]

then 4th option is false since z is positive

i guesss

[wild zodiac]

z < 0 is wrong as z > 0

[uneven vector]

but it for sure can be 0

[iron meadow]

yes 2nd option seems correct

that was marked wrong?

seems like broken question =\

[uneven vector]

yeah

[wild zodiac]

z > 0 is given in the question how can that be wrong lol

[leaden monolith]

Surely 2 is right, it’s true by assumption, it’s marked wrong

[uneven vector]

how is 2 wrong?

am i blind

[leaden monolith]

I typo’d

[uneven vector]

yeah

this is driving me crazy

in anycase

[iron meadow]

whoever made the question messed up

your answer was correct

[uneven vector]

great

but also

if i see somehitng like this again

should i be thinking that x could be a negative number as well?

or it is 0

[iron meadow]

sure, you don't know anything about x, it could be negative 0 or positive from the information given

[uneven vector]

hm okay

thanks

.close

[marsh citrus]

Channel closed

Closed by @uneven vector

Use .reopen if this was a mistake.

[marsh citrus]

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.

[mint sonnet]

help?

[shadow nest]

whats the equation of a circle

[mint sonnet]

wdym?

[shadow nest]

the equation of a circle is in the form of
$x^2+y^2=r^2$

[elfin berry]

Renz

[shadow nest]

where r is your raidus

whats the raidus of the circle in the problem?

[mint sonnet]

15^2?

,calc 15^2

[elfin berry]

Result:

225

[mint sonnet]

so x^2+144=225?

x=+-9?

,calc 9^2

[elfin berry]

Result:

81

[mint sonnet]

,calc 81+144

[elfin berry]

Result:

225

[mint sonnet]

but cant i make a right triangle?

@shadow nest what other two points?

-9,10?

-6,8?

[shadow nest]

not sure about the name two other points that must be on the circle

if the question asks any points

[mint sonnet]

maybe the triangle?

the right triangle we can make

[shadow nest]

then just try to find ordered pairs that satisfy the equation
x² + y² = 15²

[mint sonnet]

x is 9

right?

[shadow nest]

x is -9

[mint sonnet]

ohh since its on negative side

[shadow nest]

since point c is in quadrant 2

yep

[mint sonnet]

@shadow nest can these be other two points?

-9,10?
-6,8?

[shadow nest]

its on the negative side

not quite

do they follow
x² + y² = 225

sub those values in

[mint sonnet]

ohh i see

but i dont think other values work

@shadow nest 12 and 9?

[shadow nest]

ye, try that in the equation

if its equal to 225, then its on the circle

[mint sonnet]

,calc 12^2+9^2

[elfin berry]

Result:

225

[shadow nest]

its equal to 225

[mint sonnet]

but it has to be on negative coordinante, no?

[shadow nest]

then it must be on the circle

[mint sonnet]

since the right triangle is

[shadow nest]

both are positive right

[mint sonnet]

mhm

[shadow nest]

then the coordinate is on the 1st quadrant

[mint sonnet]

but it doesnt fit the blue line

[shadow nest]

now you have
(-9,12)
(12,9)

the question asks for what other 2 points that must be on the circle

[mint sonnet]

yea

[mint sonnet]

so we need one more point

[shadow nest]

this is for point C, our point (-9,12)

we have already solves that

what do you notice when you square 12

and -12

[mint sonnet]

yea but (12,9)

[shadow nest]

thats for question number 2, naming two other points

we have already solved question number 1

[mint sonnet]

yea

and also (9,12)

for question 2?

ohh yea they work

[shadow nest]

ye

[mint sonnet]

ok thx

[shadow nest]

heres what you can do to find other points on the circle

[mint sonnet]

what

[shadow nest]

just swap the negative signs

they will all work

[mint sonnet]

wdym swap

them

[shadow nest]

(9,12)
(-9,12)
(-9,-12)
(9,-12)

like this

they will still all ewual to 225 when you do x²+y²=15²

[mint sonnet]

ahh yes

i see

[shadow nest]

since the square of a positive number will still equal the square of its negative number

like

(-9)² = 9² = 81

sry if i worded that wrong

[mint sonnet]

yea

i forgot about that lol

thx tho renz

any other trig tips?

[shadow nest]

just be familiar woth the eqn of the unit circle

[mint sonnet]

always x^2+y^2=r^2?

[shadow nest]

since many trigonometric functions are defined based on x²+y²=1

[shadow nest]

thats the standard equation for a circle

but in a unit circle, the raidus is 1

[mint sonnet]

so 1^2?

like a periodic function?

[shadow nest]

so the equation of a unit circle is always
x² + y² = 1²

[shadow nest]

ye, the sine cosine functions are based on that

[mint sonnet]

ohh ok

any other tips?

[shadow nest]

+know how angles work

angle in standard position, positive and negative angles

radians vs degrees etc.

[mint sonnet]

im confused with periodic functions relating to a clock

[shadow nest]

this is a unit circle

lets say we have an angle theta

[mint sonnet]

yea

[shadow nest]

the ray of that angle where it intercepts the circle is a point right

P(x,y)

the x value is exactly cos(theta)

the y value is exactly sin(theta)

theres a short proof for it using sohcahtoa

which takes advantage of the fact that the hypotenuse of that right triangle is 1

[mint sonnet]

ill show u what i mean

@shadow nest

[shadow nest]

ok so

the hand is 1 feet long right?

and it said if its pointing to the right, the height is 10 feet above the ground

lets put it in a cartesian plane

[shadow nest]

from this, we can say that the height of the center of the clock is at 10feet

[marsh citrus]

@mint sonnet Has your question been resolved?

[mint sonnet]

@shadow nest u still there?

[mint sonnet]

yes agreed

ohh nvrm

i understand it

@shadow nest wait how during 0 and 60 minutes, height is 11?

[shadow nest]

correct

[mint sonnet]

how tho?

i dont understand

shouldnt it be 10?

[shadow nest]

so the raidus of the circle is 1 right?

since the minute hand has a length of 1

[shadow nest]

and the problem stated that if its pointing on the right, the height is 10

we can see that its perfectly alligned with the center right? which makes the height of the center 10 as well.

meaning, if the hand were at the top, we just add the height of its center (10), and the raidus (1)

[mint sonnet]

yea

[shadow nest]

10+1 is 11 so the height is 11

[mint sonnet]

but the radius is always 1

so 10+1=11 when its right?

[mint sonnet]

but every side radius is 1

[shadow nest]

we are talking about the height

not the raidus

the raidus is always 1

[mint sonnet]

yea

[shadow nest]

but look at this

[mint sonnet]

radius is always 1

so +1

[mint sonnet]

how?

[shadow nest]

the height of the center is 10 right?

and the raidus is 1 right?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[shadow nest]

the very top of the circle must have a height of 10+1

[mint sonnet]

.reopen

[marsh citrus]

✅

[mint sonnet]

@shadow nest u here

[mint sonnet]

but radius all sides are 1

so +1 every side?

[shadow nest]

look at this diagram

the red lines refers to the height right?

when its on the top of the circle, the height is 11

[mint sonnet]

yes

[shadow nest]

when at the center, its 10

[mint sonnet]

how?

[shadow nest]

while at the bottom its 9

[mint sonnet]

why is it decreasing? isnt radius 1

[shadow nest]

we are talking about the height

[shadow nest]

the length of this is 1 right?

[mint sonnet]

yes im aware but why the +1 only for the top

[mint sonnet]

yea

[shadow nest]

and the height of the center of the clock from the ground is 10 right?

so to get the top, we add those heights together

10 + 1

[mint sonnet]

but the +1 radius is on all sides of the circle

[mint sonnet]

ohh i see

but on my question

[shadow nest]

you get it now?

[mint sonnet]

we dont have a cartesian graph

[shadow nest]

you dont

i just used one so you can visualize the problem

[mint sonnet]

so what about my problem?

like without the graph

and why does the ladybug in this problem matter?

[shadow nest]

because the ladybug is standing on the end of the minute hand

the movement of the minute hand is in a circle right

[mint sonnet]

but ladybug height will always be the same

10

[shadow nest]

no, it will change depending on the clock

since the hand will move along with the ladybug

ok lets put it this way

after 15mins, the height is 10 right

because the problem said that the height of the ladybug from the ground is 10 when the hand is pointing right

get it?

[mint sonnet]

yes

i get that

but not 11

[shadow nest]

now

[mint sonnet]

nor 9

[shadow nest]

lets say another 15 mins pass

where would the hand be

[mint sonnet]

at 6

[shadow nest]

at 6, or pointing downwards right?

[mint sonnet]

mhm

[shadow nest]

remember that the length of the hand is 1?

the raidus is 1?

[mint sonnet]

yes

[shadow nest]

ok so if the center of the circle has a height of 10

[mint sonnet]

yea

[shadow nest]

and theres a raidus of length 1 that points downwards

what would be the height at the bottom of the circle

[mint sonnet]

10?

[shadow nest]

its 9

[mint sonnet]

9

[shadow nest]

see here

the red dot is the ladybug

[mint sonnet]

but why -1?

isnt radius +1?

[shadow nest]

we are subtracting because the height went downwards

[mint sonnet]

by ur logic, here the radius is -15

[shadow nest]

the hand is pointing downwards

[shadow nest]

no, the raidus is still 15, we are not talking about the height in that problem

[mint sonnet]

ohh sorry

[mint sonnet]

ohh

the height

[shadow nest]

here, we are talking about the height, or the y-value of the ladybug

[mint sonnet]

ok i see

wait

im still kind of confused

all sides radius is 1, no?

[shadow nest]

yes, its all 1

[mint sonnet]

@shadow nest

so where are u getting -1

and +1

[shadow nest]

so the height of the center is 10 right?

and we want to find the height at the bottom of the circle, since that is where 6 is, where the minute hand points after 30mins

[mint sonnet]

yes

10

[mint sonnet]

mhm

[shadow nest]

our height will move down by 1, because the raidus is 1, like in the diagram

[mint sonnet]

ohh wait i see

its supposed to represent a function

[shadow nest]

since we are going down vertically

[mint sonnet]

with x y axis

i see

nvrm lmao

i get it

should i close now?

renz?

[shadow nest]

now complete these questions

ok so

starting at 12am lets say

[mint sonnet]

wait renz

[shadow nest]

at 12am what will be height

[shadow nest]

ye?

[mint sonnet]

what if it was 10, 20, or 40 mins?

nvrm i see

nvrm lmao

[shadow nest]

thats the time where trigonometry comes in

[mint sonnet]

i forgot that top is 11

ohh yea we could use trig?

how?

[shadow nest]

or you can just use

[mint sonnet]

so is 10 minutes y?

[shadow nest]

wait no

nvm

[mint sonnet]

no trig?

[shadow nest]

you cant use x²+y²=1

[mint sonnet]

why?

[shadow nest]

you gotta use sine and cosine

[mint sonnet]

not right

[mint sonnet]

how?

[shadow nest]

ye its not right

mb

[mint sonnet]

how do we use sine and cosine

[shadow nest]

wait leme get a pic

[mint sonnet]

ok thx

[shadow nest]

so we have an angle theta right?

[mint sonnet]

mhm

and radius 1

[shadow nest]

if you draw the ray of the angle, and find where that ray intersects the circle, you will get a point P(x,y)

[mint sonnet]

i dont get what u mean

[shadow nest]

you see this ray

[mint sonnet]

yea i see that?

[shadow nest]

its end point, which touches the edge of the circle

it can be represented as P(x,y)

where
x= cos(theta)
y = sin(theta)

[mint sonnet]

but cant we use sin(x)=y/z

or smth like that

like we need value for theta

[shadow nest]

ye, we are essentially using that

[mint sonnet]

but we need value

[shadow nest]

when you actually do that, you will get that x= costheta and y=sintheta

[shadow nest]

right

we need an angle theta right?

[mint sonnet]

mhm

[shadow nest]

it means

we gotta find this angle

if we want to know the height of the ladybug at 10 mins

so a clock can be divided into 12 right?

[mint sonnet]

yeas

[shadow nest]

what do you think is the angular measurement of a circle

1 whole circle is how many degrees?

[mint sonnet]

360

?

,calc 360/12

[elfin berry]

Result:

30

[shadow nest]

its 30

[shadow nest]

meaning that this angle is 30 degrees

[mint sonnet]

which angle?

[shadow nest]

since its from 2 to 3, which is a single part of what we divided

[shadow nest]

this one, the red one

[mint sonnet]

but specfically where?

the whoel triangle is red

[shadow nest]

here

thats 30 degrees right?

[mint sonnet]

but why specfically there?

[shadow nest]

do you know angle in standard position?

an angle is said to be in standard position if its initial position is at the positive x-axis, and its vertex is at the center of the circle

[mint sonnet]

ohh ok

[shadow nest]

the inital position should be the horizontal red line

[mint sonnet]

ohh i see

so now what?

sin(30

[shadow nest]

while the terminal side is the one rotated 30 degrees

[mint sonnet]

or cosine(30)?

[shadow nest]

we will use

[mint sonnet]

=

[shadow nest]

sin(30)

[mint sonnet]

why sin?

[shadow nest]

remember

P(x,y)

x = cos(thetha)

y=sin(theta)

[mint sonnet]

whats thetha

[shadow nest]

our angle

[mint sonnet]

thats theta?

[shadow nest]

yep

[mint sonnet]

ok

yea

so out theta is 30

[shadow nest]

treat theta as a variable

correct

[mint sonnet]

we dont have a hypotnuse

[shadow nest]

now whats sin of theta?

[mint sonnet]

sin(30)=?

[shadow nest]

yes

solve that

[mint sonnet]

we are solving for hypp?

@shadow nest sin(30)=1/x?

[shadow nest]

we are solving for the y-value

no it's directly the y-value of that point

y = sin(30)

[shadow nest]

that point right there

[mint sonnet]

but sin is length of opposite side/length of hypotenuse h

[shadow nest]

okay lets do that

[mint sonnet]

yea

[shadow nest]

i just enlarged the triangle

[mint sonnet]

but we dont have hypp

this isnt a right triangle

[shadow nest]

its a right triangle

remember this diagram?

[shadow nest]

the orange lines will form a right angle

meaning, 1 will be our hypotenuse

now apply sin = opposite/hypotenuse

[mint sonnet]

its a ight triangle?

ok so we are solving for adj?

[shadow nest]

yes

we are solving for opposite

[mint sonnet]

so sin(30)=x/1?

[shadow nest]

correct, but use y

[mint sonnet]

so its just sin(30)?

[shadow nest]

sin(30) = y/1

[mint sonnet]

,calc sin(30)

[elfin berry]

Result:

-0.98803162409286

[shadow nest]

yes

[mint sonnet]

i got a neg number

[shadow nest]

thats in radians i think

[mint sonnet]

i got .5

now what?

thats it?

[shadow nest]

meaning, the y value is 0.5

[mint sonnet]

so height is .5?

wouldnt it be 10+.5?

[shadow nest]

the y-value of that hand is 0.5 compared to the center, meaning you have to add them to get the height

[shadow nest]

exactly!

so at 10mins, height will be 10.5

[mint sonnet]

ok can we please try one more?

[shadow nest]

ok how about at after 5 mins?

[mint sonnet]

40 mins?

[shadow nest]

nono

after 5mims

[mint sonnet]

why?

[shadow nest]

like

12:05am

calculate the y-value of the ladybug at 5mins

[mint sonnet]

no after 40 min?

like 12:40?

[shadow nest]

wym after 40mins

[mint sonnet]

thats a right triangle?

what if it was 10, 20, or 40 mins?

[shadow nest]

ohhh ok

lets do 40mins ig

[mint sonnet]

yea thank you

[shadow nest]

ok so

wheres 40mins in the clock

[mint sonnet]

triangle for me is hard to make

8

[shadow nest]

yes

[mint sonnet]

@shadow nest ?

so its also 30

[shadow nest]

our angle is this now right?

[mint sonnet]

huh?

what time?

[shadow nest]

40mins

[mint sonnet]

40 minutes after 12

so 12:40

[shadow nest]

yes

[mint sonnet]

what angle did u make

[shadow nest]

until 8

since remember, we need an angle in standard position

[mint sonnet]

like 90 degrees?

[shadow nest]

this

[mint sonnet]

but why 3:40?

why not 2:40?

or 12:40

[shadow nest]

huh

the angle must always be starting from the positive x-axis

and measure the angle from there

[mint sonnet]

so u picked 3:40?

[shadow nest]

it should always start at the positive x-axis

[mint sonnet]

and u picked 3 as positive x?

[shadow nest]

i did not "picked" 3 as positive x

3 is the positive x

[mint sonnet]

how?

[shadow nest]

think of the clock like a cartesian plane

[mint sonnet]

OHHHH

so how do we connect triangle?

[shadow nest]

the positive side of the x-axis should be the angle' ray

we can make a triangle here, but we dont actually need

just use the formula

y = sin(theta)

whats our theta here?

[shadow nest]

here

[mint sonnet]

30?

[shadow nest]

not quite

[mint sonnet]

how?

-30?

[shadow nest]

ok so from 3 to 2 how big is the angle?

[mint sonnet]

i dont get what u mean

[mint sonnet]

-.5?

[shadow nest]

ok lets go back to the angle

[mint sonnet]

since 2 was 10.5

and 3 is 10

[shadow nest]

we know thay from 0 to 1, the angle is 15 degrees

from 1 to 2 its 15 degrees

from 2 to 3 its 15

[mint sonnet]

mhm

[shadow nest]

etc.

now, measure the angle from 8 to 3

8 to 9 is 15 so thats 15

9 to 10 is 15, thats another 15

[mint sonnet]

im getting confused now

[shadow nest]

etc.

[mint sonnet]

this is too complicated

renz thx for the help tho

really appreaciate it

[shadow nest]

ah i see

i recommend watching a vid

[mint sonnet]

where ru from?

[shadow nest]

on unit circles

[mint sonnet]

because its getting late

here

[shadow nest]

country?

ah

[mint sonnet]

yea

[shadow nest]

im from philippines

[mint sonnet]

ohh nice

take care

renz

.close

[marsh citrus]

Channel closed

Closed by @mint sonnet

Use .reopen if this was a mistake.

[marsh citrus]

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.

[vestal mist]

how would i do this

[vestal mist]

not sure how

[elfin ivy]

what kind of series is this? you might know a theorem about error bounds on this kind of series

[marsh citrus]

@vestal mist Has your question been resolved?

[vestal mist]

alternating

[elfin ivy]

do you recall how to find an alternating series error bound

[marsh citrus]

@vestal mist Has your question been resolved?

[vestal mist]

.close

[marsh citrus]

Channel closed

Closed by @vestal mist

Use .reopen if this was a mistake.

[marsh citrus]

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.

[vital fiber]

i cant understand the calculation for P(R|M,N)

[marsh citrus]

@vital fiber Has your question been resolved?

[marsh citrus]

@vital fiber Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[whole compass]

Which question?

[white pivot]

C

X^-1 in denominator right

When rewriting

[whole compass]

Yes

Ans is -1?

[white pivot]

Yes but I need to show work

[whole compass]

Ok

[white pivot]

So denominator approaches 1/-infinity right

Would that just be 0

[whole compass]

Just cancel the x^2

[white pivot]

But before I differentiate

[whole compass]

And put X= - infinty

[whole compass]

Yeah

[white pivot]

What’s the indeterminate form here

[whole compass]

0/0

[white pivot]

Ah ok

[whole compass]

Ln 1 is 0

[white pivot]

Yeah

[whole compass]

1/X is 0

[white pivot]

I got that

Now lemme differentiate

[white pivot]

Where did 1/x^2 come from in numerator

[whole compass]

Differentiating ln (1-1/x)

[white pivot]

I forgot chain rule

I’ll redo now

Ok I see now

So just

-1/(1-1/x)

[whole compass]

Yes

[white pivot]

Ok I got it -1

Thank you

.close

[marsh citrus]

Channel closed

Closed by @white pivot

Use .reopen if this was a mistake.

[marsh citrus]

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.

[still temple]

.close

[marsh citrus]

Channel closed

Closed by @jade mulch

Use .reopen if this was a mistake.

[marsh citrus]

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.

[obtuse mirage]

Does anybody know the formula for this? I was absent during our gen math class so i have no idea what to do

[marsh citrus]

@obtuse mirage Has your question been resolved?

[marsh citrus]

@obtuse mirage Has your question been resolved?

[obtuse mirage]

is this the formula for semi annual or monthly?

or are they the same?

and another thing, following that formula i somehow get 740 for this question

[marsh citrus]

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.

[sharp whale]

Can anyone explain how i'd go about answering this ?

[marsh citrus]

@sharp whale Has your question been resolved?

[marsh citrus]

@sharp whale Has your question been resolved?

[marsh citrus]

@sharp whale Has your question been resolved?

[marsh citrus]

@sharp whale Has your question been resolved?

[marsh citrus]

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.

[fervent rampart]

= has one meaning

in 2 days you would walk (2 miles/day) • (2 days) = 4 miles

[sleek lake]

i don't see the thing you're seeing

distance = 2 days reads like you're saying it's defintiely 2 days, so distance = 4

so like you substitute miles for distance
miles = 2 × days
then you add coefficient of 1
1 mile = 2 days

why 2 distance

you mean 1 distance

basically = isn't used in this sense

you would just write it in words

your main mistake is reading days as a unit

suppose it said
2 in = 5.08 cm
this is correct in the sense that it's short for
2 in × (1 in/in) = 5.08 cm × (0.3937 in/cm)

and like, as far as I know it's not used in this sense, you wouldn't see 2 in = 5.08 cm

but maybe i'm wrong

[marsh citrus]

@hidden shuttle Has your question been resolved?

[sleek lake]

.close

[marsh citrus]

Channel closed

Closed by @sleek lake

Use .reopen if this was a mistake.

[marsh citrus]

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.

[whole sleet]

Reminder that 4! = 1×2×3×4

Oh wait, but yeah it's still not obvious even after that

[elfin berry]

nox💫

[sand fable]

isn’t it?

once you cancel out the 2s and 4s, that is

[whole sleet]

Ah didn't see the alternating

[sand fable]

ah

[normal sky]

the missing numerator is 2 * n!

factor out a 2 from the numerator to see

[whole sleet]

Alternating series test ought to put a stop to this series

[mystic minnow]

(2^n)(n!)
?

[normal sky]

oh yes oops

[whole sleet]

I was thinking about how the denominator can be the product of the first n odd numbers

[normal sky]

im kinda lazy but isn't this telescoping

if you keep it as the product of odds, and rewrite with partial fractions

[mystic minnow]

no, you won't get any cancelation like a telescoping series.
as far as I can tell anyway.

[marsh citrus]

@fresh fiber Has your question been resolved?

[elfin berry]

nox💫

[mystic minnow]

nope. Factorial's don't distribute like that

[elfin berry]

nox💫

[mystic minnow]

Use the definition of factorials to help.
[2(n+1)]! = (2n+2)! = (2n+2)(2n+1)(2n)!

[candid plank]

the part of 2+24+24*6 ig u can try to solve its recurrence

after that just use leibnitz criteria to see if converges or diverges

the progression should be

$a_{n+1}=2(n-1)a_n $

[candid plank]

i just dont know how to solve this for a_n

ugh from where did (2n+2)! come from?

[elfin berry]

nox💫

[candid plank]

oh

wait then

just

$\limit_{x \to \infty}\frac{2^n(n!)}{(2n!)}$

$\lim_{x \to \infty}\frac{2^n(n!)}{(2n!)}$

[elfin berry]

MECànica CQ4N7ICA

[candid plank]

this limit ismt zero

so it diverges

just for leibnitz criteria

wait nvm

it converges

[marsh citrus]

Channel closed

Closed by @fresh fiber

Use .reopen if this was a mistake.

[marsh citrus]

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.

[past estuary]

Hello I was wondering if anyone was willing to explain how differential equations really work

[past estuary]

Like how they show up in around certain topics

And the idea behind them

Also some stuff on how derivatives can be manipulated to solve differential equations

Right now I am just looking at simple first order examples so stuff too complicated probably won't make sense to me

[whole sleet]

Let's look at Newton's law of cooling. If we call the ambient temperature 0°, then a hot object will cool over time

[past estuary]

Ummmm

[whole sleet]

dT/dt = kT

[past estuary]

What is Newton's Law of Cooling

Oh cool

[whole sleet]

The hotter the object, the faster it cools

[past estuary]

Is the ambient temp. the T value?

[whole sleet]

yeye

[past estuary]

Okie

[whole sleet]

Then dT/dt is it's cooling rate at any time t

[past estuary]

So I have a question

[whole sleet]

We see that the cooling rate of the object actually depends on how hot the object is. In other words, the derivative of the function T depends on the value of T

We call that a differential equation

[past estuary]

When we work with dT/dt do we treat it like a symbol like we would treat f(x) as in we really don't think of it as a value or do we think of dT/dt as a fraction that we can multiply by dt to cancel out dt

This is probably a really elementary question

But I am trying to teach myself

[whole sleet]

dT/dt is a function.

It is related to the function T through the derivative

[past estuary]

So it is not a fraction

Right?

[whole sleet]

(That being said sometimes we split dT and dt up like it's a fraction. This is an abuse of notation that we use sometimes. dT/dt is not a fraction)

[past estuary]

Ohhhh

Okay

Thats why they did that

That is why I was asking

Okay

So what is going on in the background

When we do that step

[quaint elm]

(there is a big debate over whether dy/dx is a fraction... if you want to think about it as one you probably won't get into trouble for a very long time)

[past estuary]

Hmmmm

[quaint elm]

um, some of the things happening involve the chain rule

[past estuary]

Well what is the official way when we are dealing with differential equations

[quaint elm]

if it's separable, the closest thing to an "official" way is to just separate and integrate

[past estuary]

Because canceling out the "denominator" of dT/dt seems weird

Wait

So we can separate

But how do we do that part

[quaint elm]

if you can get it into the form of like... $(stuff) \dd{T} = (other stuff)\dd{t}$

[elfin berry]

lemonsaurus enthusiast

[quaint elm]

then you can just integrate both sides

[past estuary]

Yeah

But how do we get to that point, like the separation(unless we just cancel the dt on both sides)

[quaint elm]

i'm going to say something that will make some mathematicians very angry but that's their fault for making me mod

you can just multiply by dt on both sides

so, canceling it out

[past estuary]

Ummmm

Okay

But is there another way?

Just in case

[quaint elm]

i mean kinda but it's effectively the same, you can keep the dT/dt on the left and integrate both sides dt
then you use the chain rule on the left to justify cancelling the dt's

it's basically u-substitution

[past estuary]

So when we have a differential equation it is like dT/dt [f(T,t)] = kT for example

That is the full version right?

[quaint elm]

sure yeah that's a good example

[past estuary]

So we take the integral and the derivative cancels out

[quaint elm]

if your function takes both T and t then you're not going to be able to separate them out like this though

[past estuary]

Hmmmmm

[quaint elm]

let's try a concrete example

[past estuary]

d/dx [f(x)] = x^2

Like that?

Easy example

[quaint elm]

that is an easy example, yes

[past estuary]

So integrate and get f(x) = integral of x^2

[quaint elm]

dx, yes

[past estuary]

Oh yeah

Ohhhhhhh

I get it now

[quaint elm]

okay, let's try one that was like what you were trying to do earlier

[whole sleet]

If you don't like the idea of "splitting the not-fraction"

Solving through separation of variables is basically just using the chain rule, except we're hiding a lot of that detail

[quaint elm]

$\sin(t)\cdot\dv{T}{t} = kT$

[elfin berry]

lemonsaurus enthusiast

[past estuary]

So when you multiply we have dx on the left and when we right the integral we just ignore writing the dx at the end

[quaint elm]

no

hang on let me write out the full steps

[past estuary]

Okay

[quaint elm]

\begin{align*}
\dv{x} [f(x)] &= x^2 \
\dd{} [f(x)] &= x^2 \dd{x} \
\int \dd{} [f(x)] &= \int x^2 \dd{x} \
f(x) &= \f13x^3 + C
\end{align*}

[elfin berry]

lemonsaurus enthusiast

[past estuary]

So in the third step we just put the integral sign in the front of the x^2, and ignored that we usually put a dx when writing integrals

[quaint elm]

there is a dx already there

[past estuary]

Yeah

[quaint elm]

much like there is a d[f(x)] on the left

[past estuary]

Wait

So what happens to the d in front of the f(x)

[quaint elm]

well, it gets integrated, in the same way that if you integrated "dy" you'd get y

in fact, if you replace f(x) with y in that, it may be more palateable

[past estuary]

Hmmmm

[quaint elm]

technically I could put like +C on the left and +D on the right, but they'd both get combined since they're arbitrary constants

[past estuary]

Yeah

If f(x) was instead y we would have a dy at the end

So an empty integral

[quaint elm]

an integral of dy

or if you like, an integral of 1 dy

[past estuary]

I think I am thiking of this wrong

Whn we write integrals do we always put a d(something) at the end

[quaint elm]

they always need something like that

[past estuary]

I just thought that was just there to let us know what it is with respect to

[quaint elm]

but here i can show you a slightly different way where we do always write down both things

[past estuary]

Okay

[quaint elm]

(sort of? it's talking about the width of the rectangles in the Riemann sum)

[past estuary]

Okay

[quaint elm]

(which is infinitesimal)

[past estuary]

Oh

What about discrete functions

I guess at every horizontal step the derivative would be 0

[quaint elm]

,, \begin{align*}
\dv{x} [f(x)] &= x^2 \
\int \dv{x}[f(x)] \dd{x} &= \int x^2 \dd{x} \
f(x) &= \f13x^3 + C
\end{align*}

[elfin berry]

lemonsaurus enthusiast

[past estuary]

Ohhhhhhhhhhhhhh

Thats what I was thinking

[quaint elm]

yeah i mean that way works

[past estuary]

Now I see why the dx cancels out

Okay

[quaint elm]

yep! it's just a slightly different way of doing things

ok now try this one: $\sec(t)\cdot\dv{T}{t} = kT$

[elfin berry]

lemonsaurus enthusiast

[past estuary]

Okay

Divide by sec(t) right?

No

Wait

[quaint elm]

you could, seems like a reasonable start

[past estuary]

Okay

[quaint elm]

i'm going to give you that sec = 1/cos for free

[past estuary]

Yeah

I am going to get a paper

[quaint elm]

$\dv{T}{t} = kT \cdot \cos(t)$

[elfin berry]

lemonsaurus enthusiast

[past estuary]

Okay

Thanks

[quaint elm]

but don't let me stop you from getting paper

[past estuary]

Yup

int. 1/kT dT = int. cos(t) dt

Right?

[quaint elm]

yeah that seems good

[past estuary]

Okay

ln(kT) = -sin(t)

Is that right?

[quaint elm]

well for one thing you're missing the +C

[past estuary]

Oh yeah

Oops

Hehe

[quaint elm]

and for the other, is that LHS correct?

[past estuary]

What is LHS?

[quaint elm]

left hand side

[past estuary]

Oh by "ln" I mean natural log

[quaint elm]

yeah i know

[past estuary]

I am confused

[quaint elm]

if you take d/dT of ln(kT) , you get 1/T

[past estuary]

Does it have to k*ln(T)?

[quaint elm]

i think it's ln(T) / k

because you just pull the 1/k out from the start

and then do your integral

[past estuary]

Oh yeah

Thanks

[quaint elm]

that one's tricky, i've messed it up a lot

anyway

oh yeah third thing, you didn't do the trig integral quite right either

just a sin error

[past estuary]

So it is (ln(T))/k + A = sin(t) + B

[quaint elm]

err, sine error :)

sign*

[past estuary]

Oops

Edited

[quaint elm]

ok great

now generally we'd want to solve for T

[past estuary]

So I can move the A onto the other side and just make it one costant right?

[quaint elm]

yep

[past estuary]

(ln(T)) = k(sin(t) + C)

T = e^k(sin(t) + C)

[quaint elm]

you are also welcome to integrate the k into the C, if you want

[past estuary]

Is that correct

Wait integrate?

Again

[quaint elm]

no sorry

i mean integrate as in combine

[past estuary]

Oh okay

[quaint elm]

like when you have k(ln(T) + C)

you can distribute the k and, well, kC is just C right?

[past estuary]

Oh yeah

T=e^(k*sin(t) + C)

[quaint elm]

yeah great

and you could check your work by calculating dT/dt

[past estuary]

So that is the value for T

[quaint elm]

yep

often these differential equations will be paired with an initial value

so you can calculate what C is

[past estuary]

So that means the derivative of what I wrote is the first one

Okay

[quaint elm]

well....

it means that if you calculate dT/dt

[past estuary]

yeah

[quaint elm]

and then plug T, t, and dT/dt into that original equation

then it will work

[past estuary]

Okay

[quaint elm]

i guess you wouldn't plug t in, but T and dT/dt

[past estuary]

Oh yeah

Wait

Why not

[quaint elm]

well just that like

t is your variable?

[past estuary]

No

[quaint elm]

you plug in T and dT/dt to make both sides in terms of t

and then check they're equal

[past estuary]

Okay

[quaint elm]

remember this was the original: $\sec(t)\cdot\dv{T}{t} = kT$

[elfin berry]

lemonsaurus enthusiast

[past estuary]

So can I just say T=2

[quaint elm]

no

T is a function of t

[past estuary]

Okay

Ohhh okay

I just do this

sec(t) * dT/dt = k* e^(k*sin(t) + C)

Is the correct

[quaint elm]

yeah, so you'd calculate dT/dt

just like you've done before, using the chain rule and stuff

[past estuary]

Okay

[quaint elm]

and then substitute that in

and then do a ton of boring simplification

[past estuary]

So when solve this equation what does that mean in context of this example

Just so it is easier to understand

[quaint elm]

this example represents like... a roast turkey in an oven that fluctuates in temperature

,w graph e^(1*sin(t) + 3) from t=0 to t=10

[past estuary]

So when I solved the first one that would be how fast the temp. of the turkey was fluctuating

[elfin berry]

Results provided by WolframAlpha

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

Requested by kitten.in.a.teacup

[quaint elm]

which first one sorry?

[past estuary]

The sec one

[quaint elm]

i think in both of them you were finding T(t), the temperature as a function of time

[past estuary]

So the sec(t) * dT/dt = kT was the first one

[quaint elm]

was there a second one?

[past estuary]

I think we were just about to do one

After plugging in T

[quaint elm]

oh, that was just for verification

[past estuary]

Oh okay

I think I have to go now

Thank you so much for the help

[quaint elm]

no problem! i think you understood well

[past estuary]

Yeah

I am just in 9th grade

So I think it was a good start

[marsh citrus]

@past estuary Has your question been resolved?

[marsh citrus]

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.

[halcyon tiger]

Stats testing a hypothesis for a proportion.
No clue how to do the bottom section with the choice between A and B, and the example problem they give is no help either.

oh I got it nvm

.close

[marsh citrus]

Channel closed

Closed by @halcyon tiger

Use .reopen if this was a mistake.

[flat pulsar]

Wait I was trying to figure this out. z0 is just the test statistic but what is za? I don't think I've seen that notation before.

[halcyon tiger]

Neither have I

I think it has something to do with the level of significance, and I used the table to figure out it's za=1.28. I honestly still don't understand it.

[whole sleet]

za is the z-score at probability a

[halcyon tiger]

ah

[flat pulsar]

I was about to say that. And "za/2" is just the z-score at probability a/2.

[halcyon tiger]

Yeah

I think I get it now?

[marsh citrus]

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.

[fading spear]

For this question, I'm assuming you have to minimize the perimeter?

[crimson valley]

We are minimizing the width of the rectangle

Real

[fading spear]

I'm writing up my work neatly. I've done it in a way that's only legible to me 💀

can you give me a minute?

and I'll share what I have

[crimson valley]

Np

[small berry]

That window question is in literally every Cal 1 class

[desert dirge]

respect the jokes

[late geode]

#chill

!redir

[marsh citrus]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[fading spear]

LMAO

This is what I have till now

[fading spear]

do I just sub in r into the perimeter and see when it's minimized?

reminder this was the q

[fading spear]

yo guys

any help 💀

[fading spear]

sorry for pinging you but could you please check what I have till now?

guys why did you hijack this channel wtf 😭

💀

imma just go to another channel

.close

[marsh citrus]

Channel closed

Closed by @fading spear

Use .reopen if this was a mistake.

[quaint hill]

sorry about that.

[crimson valley]

I believe that P is 2h+2r + pir
If it was 2(2r+h) + pir then that would mean we are going around the entire rectangle when getting the perimeter

[marsh citrus]

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.

[sleek lake]

you are a deviant

and a reptile

not unlike a komodo dragon