help-41

[prime pecan]

and idk how to do it without so oooooo

[crimson cloak]

nooo lets try this

[prime pecan]

if a future question asks for me to do it without calculator

[crimson cloak]

I can take you through this

[prime pecan]

then we will do it without

😦

r u fr @crimson cloak

do we have to bruh

[crimson cloak]

we gotta find the x-intercept of (a)

[crimson cloak]

if you want to solve the problem 😭 🙏

[prime pecan]

but like i will on the calc

but on discord i js need to visually see what it would look like

come on man pls my for me 🙂

?

[weak abyss]

it wont take you much time really

[prime pecan]

ok fine

[weak abyss]

you just draw two points and a lime

[crimson cloak]

y=3/4x+6, so y=0 means 3/4x+6=0 or 3/4x=-6 or x=(-6)(3/4)=-9/2

[weak abyss]

line

[prime pecan]

but SOMEONE has to put a photo of the final result at the end

[crimson cloak]

so when y=0, x=-9/2 or (-9/2,0) ok?

[prime pecan]

WHAT

the fuck

haah AHA WTF

[crimson cloak]

I thought it would be a simpler coord 😭

[prime pecan]

ee bruh

guys dont even bother explaing to me how to plot them both

@weak abyss pls generate the photo of the final result labeled pls

[crimson cloak]

so you can plot them?

[prime pecan]

on the calc

Yes 🙂

[weak abyss]

i promise I will after you solve it

[prime pecan]

okkkkkkkkk

OK

[weak abyss]

but only after

[prime pecan]

bet

LETS DO this

[weak abyss]

see this easy

[prime pecan]

OKay what do i do

[weak abyss]

a) was

[crimson cloak]

this is what it looks like

[prime pecan]

A is 0/6

0,6

coords

[prime pecan]

i need all the lables and everything

clear

[crimson cloak]

but write out the graph

[prime pecan]

like all the coords all of everything but nano said we wokring it out

[crimson cloak]

I'm not giving you the answer, just guiding you towards it

[weak abyss]

lets work it out its simple

[prime pecan]

k

[weak abyss]

first off, draw some cartesian graph in the sheet

[prime pecan]

its alr there

[weak abyss]

cool

so a) was

[crimson cloak]

mark off your x-intercept and y-intercepts

[weak abyss]

y= 3/4x + 6

when x =0, what was y?

[prime pecan]

we actually didnt solve when x = 0 for A bc we moved on

lol

so idk

[weak abyss]

we did

[prime pecan]

bruh

[weak abyss]

thats the one we solved

[prime pecan]

ok

x int - 4

y int 6

?

thats for B

[weak abyss]

6

so a dot in the graph is

[prime pecan]

A x int is 6?

[crimson cloak]

for (a), 0=3/4x+6, 0=3x+24 or 3x=-24 and x=-8

[weak abyss]

(0,6)

mark down that dot

[prime pecan]

ok

[weak abyss]

then y = 3/4x +6

[crimson cloak]

so lets gather our intercepts, (-8,0), (0,6) for (a) and (-4,0) and (0,6) for (b)

[weak abyss]

when y=0, x=-8

so (-8,0) is another dot

mark it down

[prime pecan]

ok

[weak abyss]

so you have two points that connect a line

just draw a straight line that crosses both points

and thats it

thats a)

[prime pecan]

yep

[weak abyss]

for b) just do the same

mark down both intercepts

and draw a line that goes through them

[prime pecan]

ok

well

my lines are like parralell

A and B dont cross

for me

[weak abyss]

they shouldnt be?

[prime pecan]

oh ok good

[weak abyss]

if 3x -2y = -12

[prime pecan]

so whats the coords of the meeting point
?

[prime pecan]

mhm

[weak abyss]

whats the coord when y = 0

[prime pecan]

-4

[weak abyss]

and x = 0

[prime pecan]

6

[weak abyss]

did you draw a line that went through both points

show the graph you made

[prime pecan]

yep

ok

valid?

[weak abyss]

bottom one is a or b?

[prime pecan]

B is top

A is bottom

-8 and 6

[weak abyss]

a was y = 3/4x + 6

if x is 0

y is 6

[prime pecan]

yes

[weak abyss]

Is that point in your graph?

[prime pecan]

yes

[weak abyss]

not for A

[prime pecan]

bruh

its labeled

Oh

wait

I got my points mixed up

1s

ok

so the meeting point is (6,6)

[weak abyss]

nope

[prime pecan]

br

o

how is this wrong

[weak abyss]

x=6 is very far away

x = ?

[prime pecan]

ok listen to my list of ints

A, x int -8 y int 6

B, x int -4 y int 6

correct>

[weak abyss]

the graph is perfect

you did it

[prime pecan]

oh ok

[weak abyss]

but they dont meet at 6,6

[prime pecan]

how

for me they do

[weak abyss]

x = 6 is a point much more at the right side

[prime pecan]

where do the ymeet

[weak abyss]

at the point where they meet

what is x

[prime pecan]

idk

[weak abyss]

you do

[prime pecan]

-4?

-8?

[weak abyss]

look at this, look at your graph, and state the meeting point again

[prime pecan]

where is the meeting point

0,0

[weak abyss]

no

[prime pecan]

for the 1 above

[weak abyss]

yes yes

[prime pecan]

ok

[weak abyss]

but in your graph

whats the meeting point

[prime pecan]

in my graph both lines dont have an X meeting point

only a y meeting point

[weak abyss]

wdym?

[prime pecan]

X never meets

until it hits the Y

[weak abyss]

thats right

but when they meet

x is equal to something, no?

[prime pecan]

yhe

0

[weak abyss]

and y?

[prime pecan]

6

[weak abyss]

YOU DID IT

[prime pecan]

meeting point (0,6)

[weak abyss]

[prime pecan]

les fricking GO

COME ON BRUH

now u put in uR PHOTO

of the finished graph

this is 4 marks

[weak abyss]

but you already graphed it

[prime pecan]

so its 4 marks of 1, label it all, 2 put A and B down, 3 solve it, 4 say what the meeting point is

[weak abyss]

your graph is exacty correct

[prime pecan]

ok dw about it

[prime pecan]

but this is it right

[weak abyss]

mhm

mark down the intercepts for each line

dont confuse A and B

[prime pecan]

yes yes

[weak abyss]

graph and state the meeting point

[prime pecan]

yes 1s

ok

next question

is the top bit right>?

[weak abyss]

so the water is leaking

[prime pecan]

and even min

200ml gains

[weak abyss]

and the volume of water is increasing

[prime pecan]

so 1m is 2200

2 is 2400

and so on right>

[weak abyss]

thats a contradiction

less water will mean less water

[prime pecan]

ok

[weak abyss]

how much less water?

[prime pecan]

but the top bit is correct doe right

the blue rrighting

[prime pecan]

200

[weak abyss]

no no, thats what im explaining

[prime pecan]

how is the blue writing wrong

[weak abyss]

so if you had 2000ml

and lost 200

[prime pecan]

OH leaks AWAY

[weak abyss]

now you have

[prime pecan]

so its

MINUS

200

for EACH

not GAIN

MINUS

[weak abyss]

right

[prime pecan]

bc less

IS

LESS

not less - MORE

its less - LESS

by 200

yes!?

[weak abyss]

perfect

[prime pecan]

ok 1s

ok

back

help me graph it

pls

@weak abyss

dependent variable is Y axis and independent is X axis

[weak abyss]

@prime pecan hi sorry

[prime pecan]

hi

what is the dependent and independent

[weak abyss]

i have to get ready for my own classes

[prime pecan]

for this scenario?

wait what ur leaving me!?

[weak abyss]

but ill help you with this last one

[prime pecan]

ok bet

❤️

[weak abyss]

you need to find the equation

and graph its intercept

[prime pecan]

plot the volume of water remaining against time

but first i need to label graph propperly

whats at the bottom, time or water

[weak abyss]

you have 2000, right?

[prime pecan]

x) water or time>

?

[prime pecan]

yes

[weak abyss]

does time depend on how much water you have

[prime pecan]

yes

[weak abyss]

you sure

time passes anyways

[prime pecan]

nbr juh

does doesnt

depend

time

doesnt

[weak abyss]

thats right

so it goes in x axis or y axis

[prime pecan]

Y

[prime pecan]

oh damn cheers

[crude kite]

That's useful

[prime pecan]

yeah

Y is Time X is Water

[weak abyss]

nope

[prime pecan]

right @weak abyss

wait

why

[weak abyss]

because time doesnt depend on anything

it just passes

how much water there is

[prime pecan]

oh yeah we said its not dependent

[weak abyss]

depends on time

[prime pecan]

yeah yeah

mb i forgot

[weak abyss]

so y axis or x axis for time

[prime pecan]

Water is Y time is X

[weak abyss]

yes

[prime pecan]

ok now we have that sorted

so i just fill out the graph

like how u normally would

based off what we got

the - 200 part

[weak abyss]

you have to graph all the points

[prime pecan]

yer

[weak abyss]

x = time
y = volume

when x = 0

volume = ?

[prime pecan]

whats the equation relating with the Time and the volume?

[prime pecan]

200

[weak abyss]

you forgot a 0

[prime pecan]

2000*

yeh

[weak abyss]

right

and x=1

volume = ?

[prime pecan]

x = 0

or x = 1?

u mean 0 right

[weak abyss]

if x=1

that ks

that is

[prime pecan]

oh

[weak abyss]

time = 1 hour

the volume is?

[prime pecan]

0

right

bc we will lose all the water within 1 hour

[weak abyss]

mmm

does it decrease by minute or hour

[prime pecan]

min

[weak abyss]

then nvm

when time = 1 min

volume = ?

[prime pecan]

2000 - 200

1800

[weak abyss]

yes

and time = 2min?

[prime pecan]

1600

[weak abyss]

so just graph all those points

[prime pecan]

yeh thats ez

dw about that

[weak abyss]

and you make a line that connects them

[prime pecan]

yeh

ofc

bc its continuous

[weak abyss]

you need the equation?

[prime pecan]

so whats the equation relating the time w voluime

indeed

[weak abyss]

you start with 2000 and decrease from there

so its gonna be

2000- something right?

[prime pecan]

2000 - 200

thats the equation?

[weak abyss]

thats just a substraction

[prime pecan]

.-.

whats the equation bru

[weak abyss]

well have 2000- ?

[prime pecan]

.-. idk

[weak abyss]

at 1 you substract 200

at 2

200 two times

[prime pecan]

yes

[weak abyss]

at 3

200 three times

[prime pecan]

200 3 times

soooo...

[weak abyss]

so you lose 200 times the minutes

[prime pecan]

2000 - 200^1

?

[weak abyss]

what gives the minutes? y? or x?

[prime pecan]

mins is X

bc its indeoendent

[weak abyss]

mhm

[prime pecan]

yea?!??

[weak abyss]

so you have 2000- what

200 times the minutes that have passed

how would you write that

if minutes that have passed is equal to x

[prime pecan]

idk

ngl

im stumped

whats the equation lollllll

[weak abyss]

youre just substracting 200

but each time, more

[prime pecan]

ye

ye

but how can i write that as an equatio

n

2000 - 200 - 200 -200 -200

6 times?

2000 - 200/6

?

[weak abyss]

thats a number not an equation

[prime pecan]

brooooooooooooo

Nano pls just tell me the awnser

[weak abyss]

srry

[prime pecan]

how can i figure it out

isnt an equation number

or is it like y - x - 200

[weak abyss]

think about exactly this

[prime pecan]

ok

[weak abyss]

you substract 200 times the minutes

remember how multiplication goes

[prime pecan]

soo

its

[weak abyss]

3x = x + x + x

[prime pecan]

yeh

[weak abyss]

or 5z = z + z + z + z + z

[prime pecan]

2000x - 200 - 200 - 200 -200

bruh

thats not it

lol

[weak abyss]

almost

[prime pecan]

h9ow

[weak abyss]

you substract 200 an arbitrary amount of times

[prime pecan]

yes

so

we do...

[weak abyss]

you choose how many times you do it

[prime pecan]

.-.

6

[weak abyss]

given by the minutes that have passed

if times is 2

200 - 200

if times 4

[prime pecan]

so we are writing the equation relating the time T with the volume V

so i need like a

[weak abyss]

200 - 200 - 200 - 200

[prime pecan]

V = T x 6

[weak abyss]

something like that

[prime pecan]

V = T x 6 - 200

?

[weak abyss]

close

whats the number that gets multiplied?

[prime pecan]

2000 = T x 6 - 200

[prime pecan]

2000?

[weak abyss]

no, you got 2000 just once

but the 200 becomes bigger

[prime pecan]

ye

2000 becomes less

per minute

so its like 2000 - 200 x 6

bc its 6 mins

Right>?

is that the equation

@weak abyss !?

[weak abyss]

almost

[prime pecan]

bruh

[weak abyss]

it could be 6

[prime pecan]

what am i missing

[weak abyss]

or could be not

[prime pecan]

i said its 6 just bc in the top bit

[weak abyss]

instead of 6 it could be 2

[prime pecan]

6 is the amount of time

[weak abyss]

or 3

or 8

[prime pecan]

what does itmena

the 6 or the 2 or the 8 or the 3

[weak abyss]

so the 6 is the time variable

[prime pecan]

2000 - 200 x T

HOW ABOUT THAT

surely

[weak abyss]

YOU DID IT

[prime pecan]

BRUH

FR

so its

V = 2000 - 200 x T

??!?

[weak abyss]

ur gonna be top of ur class

yes

[prime pecan]

les GO

BUT NANO

WE NOT DONE YET

U KNOWWHY

[weak abyss]

tell me

[prime pecan]

calculate the volume of remiining water in the bucket after 8.5 mins

so

2000 - 200 x 8.5

?

[weak abyss]

YES

[prime pecan]

omfg

[weak abyss]

good job

[prime pecan]

thanks bor

bro

ur a legend for helping me man

just know that 🙂

[weak abyss]

no worries it was all your own effort

good luck in your classes 👍

[prime pecan]

thanks bro

gl w ur class coming u

p

close this ticket up

[weak abyss]

.close

you got to do it

[prime pecan]

07

oh

.close

[amber wasp]

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[weak abyss]

o7

[amber wasp]

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[normal patio]

here u see, i will convert the dimensions into a rectangular box, the problem is i already tried it but it didn't turn into a rectangular box bcs of the length and its width, the length is bigger than its width and is insufficient bcs of the 3 inch h for the corner .What/how shall i do?

[stark bay]

You are only meant to ping helpers after 15 minutes has passed

[vestal hatch]

It's not insufficient

what does it matter if the length is bigger than the width?

[amber wasp]

@normal patio Has your question been resolved?

[amber wasp]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[fierce edge]

I found this question randomly

Am i going dumb or is something wrong with the question lol

let's say the total price is 60 and the average is then 10

if each of them only contribute between 5 to 10 then how can they ever meet the total price

since there isn't a friend who's "overshooting" to compensate for the other person who's paying below average?

[amber wasp]

@fierce edge Has your question been resolved?

[marsh nest]

Yeah that’s right. My guess is it was supposed to say not more than half the bill amount. Eg: 4x5 + 2x20 since if one 20 became a 5 the last would be more than half the bill

[coral wigeon]

[amber wasp]

@fierce edge Has your question been resolved?

[amber wasp]

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[plain bane]

anyone know where ive went wrong here?? cant figure it out

[plain bane]

i meant 2x+50=180 on the second line btw

ok nah ive just answered my own question bruh

.close

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[lucid plume]

Is $20/H a lot?

[lucid plume]

Not sure if I should be employed as a teenager.

[honest bobcat]

That's not really a question for the help channels

lol

[pallid canopy]

.close

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[coral wigeon]

hi lily ily

[honest bobcat]

hi laylaaaa

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[toxic sierra]

The answer that i got is wrong, im not sure what i done wrong. Can anyone help me spot the error in my working

[lucid tendon]

i mean the numbers are just the wrong way around how did you get that b^4 equation to begin with

did you expand (a+bi)^2

[normal patio]

read "I'm supposed to create a box"

[toxic sierra]

yeah, i realized what i done wrong, its meant to be b^4+16b^2-225.

i done -16b^2

[lucid tendon]

yeah i always make those kind of mistakes

[amber wasp]

@toxic sierra Has your question been resolved?

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[lofty dagger]

So I was able to find the derivative right

[pallid canopy]

what's the whole question

[lofty dagger]

Which 4/3(x-3)^-2/3 -1/3

How the hell do they translate it into what came after that

Nvm im slow ik what they did

Mb

.close

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[hot spade]

if im given a unit circle and am given tangent, how do i calculate secant?

[pallid canopy]

can you draw a picture of what you're asking

[amber wasp]

@hot spade Has your question been resolved?

[zealous oriole]

mmm a secant is a line that cuts in two different points. Point 1 => replace the equation of a tangent into the circles eq (x^2+y^2=1)

then you have your point 1

then chose any other point in the circle

There you have 2 points. Afterwards take the equation of a line that goes through 2 different points

and there you have your secant

i'm not sure I understand the need

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[high moon]

Two die are thrown. What is the probability that
a) At least one of the two die is a 4

[high moon]

this is 1/3 right

[robust willow]

How'd you get 1/3?

[high moon]

i counted the sums of the 4th row and 4th column

i got 12

and there r 36 total sums

so 12/36

[cedar plaza]

you double counted

[robust willow]

There's a lotta double counting happening there

[cedar plaza]

over counted*

[high moon]

how come?

[cedar plaza]

when counting the number of cells in the column or row, put a dot on the cell you count

[high moon]

oh

11/36?

[cedar plaza]

yes

[high moon]

.close

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[robust willow]

Is it 11/36?

[cedar plaza]

what do you think it is

[robust willow]

Nvm

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[spare galleon]

It asks for the parallelpiped that these OA, OB, and OC span out

The area of the parallelpiped for sure

I took the determinant of them and failed to operate it properly

I’m going to show my process

.close

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[sour schooner]

without differentiation how do you get the minimum value of H ?

[crimson cloak]

What have you tried

[lost star]

acosx+bsinx=csin(x+Φ)

[crimson cloak]

😮

[lost star]

where a, b, c, and Φ are constants

[sour schooner]

since the minum value is the smallest value of a function, and the ranges of cos(t/2) and 4sin(t/2) is -1<cos(t/2) <1 and -4 < 4sin(t/2) < 4 respectively, i just tried substituting values from the ends of these domains to get the lowest possible values

since the question was just a 2 mark question

[crimson cloak]

But remember minimizing H is maximizing the denominator

[sour schooner]

yep

[lost star]

is f(x) has minima at L, g(x) has minima at H then it is not necessarily true that f(x)+g(x) will have a minima at L or H

[crimson cloak]

So you want the highest posdible values

[sour schooner]

ah alr
lemme try it out and see

[lost star]

if you know the process, this should be more than enough of a hint

[crimson cloak]

Does it relate to one of these

[lost star]

sum difference Identity 1

[crimson cloak]

But is that not different

[sour schooner]

ahhh it worked

after getting it into tht form and equalling csin(x+Φ) to 1, the min value is reached

thanks a lot guys

appreciate the help

.close

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[verbal lark]

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[verbal lark]

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[quick ridge]

ok well it’s best to define the range of the parameter so that the path is traversed only once

[verbal lark]

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[quick ridge]

and yea you’d start at t = 0

[quick ridge]

…

you mean traversed?

[verbal lark]

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[quick ridge]

consider the unit circle

[quick ridge]

yea

[verbal lark]

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[quick ridge]

we wouldn’t want to define t for 0<=t<=5pi for instance

because the whole circle is traversed just for the first 2pi

[verbal lark]

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[quick ridge]

well we don’t even need the equality on 2pi but yea

since 2pi is the same point as 0

[verbal lark]

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[grizzled pagoda]

knief

[verbal lark]

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[verbal lark]

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[quick ridge]

so for this ellipse you’d do x = 2cost and y = sint

just take the sqrt of the coefficient

[verbal lark]

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[quick ridge]

hmm they gave a different parametric form

so use theirs actually

god i need to sleep

[verbal lark]

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[quick ridge]

guess what time i went to bed

[verbal lark]

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[quick ridge]

nope

7 am

[verbal lark]

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[quick ridge]

like 11

am

[verbal lark]

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[quick ridge]

homework

[verbal lark]

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[quick ridge]

lol

[verbal lark]

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[quick ridge]

i’ll help you with this last one

[verbal lark]

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[quick ridge]

yea

[verbal lark]

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[quick ridge]

so

$\langle -2\cos(t), 4\sin(t)\rangle$

[grizzled pagoda]

knief

[verbal lark]

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[quick ridge]

start at t = 0

when t = 0 we start at the point (-2,0)

[verbal lark]

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[quick ridge]

so we’re on the left of the ellipse

[verbal lark]

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[quick ridge]

as t increases cos decreases and so -cos increases

and as t increases sin increases so we’re going to the right and up from -2,0 so yea clockwise rotation

[verbal lark]

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[quick ridge]

to get back to the same point we just come back at 2pi

so 0<= t <2pi

the period of the two functions given is 2pi

[quick ridge]

^

[verbal lark]

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[quick ridge]

goodnight sir

[verbal lark]

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[signal hull]

yo I just have a question in regards to solving this question

[signal hull]

are you supposed to use the trig function identities to solve this?

such as tant = sint/cost?

or do you solve it in a different way

[winged quest]

you can do this for tan, and then use reciprocals for the others.

You could also draw a picture and then read your answers off the picture.

[signal hull]

csc and sec and cot are just the inverse of the answers no?

so csct =8/5

[winged quest]

yes

in English, "inverse" has a ton of meanings, so I'd always use the word reciprocal here

[signal hull]

sect = 7/2sqr10 which when rationalized is 7* square root of 10 / 20?

[winged quest]

(like cosecant is the inverse of sine, but arcsine is also the inverse of sine)

[signal hull]

cause you multiply both numerator and denominator by square root of 10

[winged quest]

it looks like you just gave one answer for a part of (a) and then another answre for a part of (b). I'm not sure if that was intentional or if you misread (a).

[signal hull]

oh yeah mb I def did

[split sail]

Hi

[signal hull]

I was just losing my mind over rationalization for some reason

[signal hull]

quick question

I know that question 8

is telling me that we are in the 3rd quadrant

cause its inbetween pi and 3pi/2

why is that important again?

is it just that it determines whether the answer is negative or positive?

sint = 12 cost = 5 but since we are in 3rd quadrant its -12 and -5?

so sect = 1/cost which is 1/5 but its -1/5 because t is inbetween pi and 3pi/2?

[winged quest]

you have the right ratio between sine and cosine, but sin(t) can't be 12

sin(t) is always at most 1

[signal hull]

really?

I thought since tant = sint/cost 12/5 means sint is 12

[signal hull]

wouldn't that also make cost at most 1?

[winged quest]

yes, cos(t) is always at most 1 also

remember that sine is opposite/hypotenuse, but the hypotenuse is the longest side in the triangle

the opposite can't be larger than the hypotenuse, so the fraction can never be greater than 1

[signal hull]

oh wait yeah im stupid

nvm

so sect is equal to 1 + tant^2 right?

12/5 squared gives us 144/25 + 1 which would be 25/25 so we get 169/50?

and then you square root this no?

oh wait no

144/25 +25/25 is 169/25 not 169/50

so

13/5

negative cause we are in 3rd quadrant

so -13/5?

here I also realised hypotenuse is square root of 65

I don't believe that can be simplified can it?

[pallid canopy]

Nope

[signal hull]

okay whelp

all I needed

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[split sail]

can someone show me how to do pt 2

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[olive blaze]

I don't study in English, so I would like to know what it's called in English so I could research more about it.
I was told that if this condition holds true for some function f(x,y) then its exact differential is called "whole" (the whole part is a translation from the language I study in, google doesn't recognize the term "whole differential" so I believe it's called in some other name).

[worldly locust]

this is the condition that a differential equation has to satisfy to be classified as an exact differential equation, as you mentioned

basically we require that the symmetry of the second partial derivatives to hold true

[limpid sun]

https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives

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@olive blaze Has your question been resolved?

[olive blaze]

by exact differential I meant this

[olive blaze]

Thanks!

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[olive blaze]

I don't get it, so what does it imply if a function satisfies the symmetry of second derivatives?

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[mint nacelle]

I think that means your function is continuous

https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives

yes I know this as Clairaut's theorem

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[olive blaze]

Are there functions that do not satisfy this symmetry but are continuous?

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[split sail]

you get a ln on the left also also

cosu du / sinu = dx/x
t = sinx
dt/t= dx/x

[modern marsh]

Aah darn

Thx

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[split sail]

how would i go about solving pt 2?

[robust bane]

Remember that the minimum value of $\sin(\text{something})$ is -1 and the maximum is 1

[grizzled pagoda]

cristorenzo99

[split sail]

okay, so when trying to solve it would I just plug it in to 90 + 10 times 1 and 90 +10 times -1

[robust bane]

Yes

[split sail]

okay so the max would be 100 an the min would be 80

so the blood pressure reading would be 100 over 80?

[robust bane]

I believe so

[split sail]

the last part of this equation states this

how would I go about solving this last part

nervermind i figured it out!

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[split sail]

my professor told us this is a limit that is solved using a specific lemma but didnt had time to tell us which lemma

i tried to do some tricks and bring 1/n² out of the sum and use cezaro stolz but didnt work oit

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@split sail Has your question been resolved?

[pallid canopy]

anything can be a lemma. i'd just ignore it and try solving it without the lemma

did you try any tangent identities

what does "bring 1/n^2" out of the sum even mean

[split sail]

tangent identities such as what

i dont really know any lol

[pallid canopy]

https://en.wikipedia.org/wiki/List_of_trigonometric_identities

[split sail]

which ones should i even be interested in? there are so many

[pallid canopy]

stolz-cesaro only tells you if it converges. is the question to find the sum or show convergence?

[split sail]

lim n -> infinity of 1/n² sum from k = 1 to n of tg k

[pallid canopy]

$\tan(a/b) \neq 1/b \tan(a)$

[grizzled pagoda]

riemann

[pallid canopy]

did you change the problem?

[split sail]

no

thats the exact problem

as it states it

[split sail]

it says calculate the following limit

[pallid canopy]

yea then this is incorrect

[split sail]

why

[pallid canopy]

.

[split sail]

i see alright

so what can we do here

[pallid canopy]

actually i was wrong stolz-cesaro does tell you the limit if you can find a comparable sequence

[split sail]

right

yea

but it doesnt work here

[pallid canopy]

why

[split sail]

bcz in the end you end up with tg n+1/polinomial expression which doesnt have a limit

bcz tg infinity is undeterminate

[pallid canopy]

why do you think b_n has to be polynomial

[split sail]

i dont lol thats what it gives me

think about it

wait

[pallid canopy]

what is "it"

[split sail]

wait

do we take 1/n² as b_n?

or tg(1/n²) as b_n

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[signal hull]

just a quick question

[signal hull]

for this do you use radius of 1

[pallid canopy]

it won't matter what radius you use, but yes you can use r=1

[signal hull]

and do y/r x/r y/x r/y r/x x/y

[signal hull]

well what im asking is

for questions that regard the terminal side

you actually have to find r

through finding the square root of x^2 + y^2

[pallid canopy]

any ray from the origin that passes through the given point will have the same values for the six trig function

[signal hull]

mhm

but in order to find sin for example

its y/r not just the y point of p

correct?

well I mean technically y value remains the same cause its divided by 1

[pallid canopy]

when r=1 those are the same

[signal hull]

but

you get what I mean

[signal hull]

cool

just trying to remember all these goofy identities

[signal hull]

also by the way

could you create a random radical fraction for me

like 3/2 * square root of 3

im trying to make sure I don't mess up on rationalizing a radical

[pallid canopy]

,w random number

[grizzled pagoda]

Results provided by WolframAlpha

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Requested by rie.mann

[signal hull]

nvm

[signal hull]

just one final question, I know that if you were to graph y = 3sin4x

you would have 2pi/4 which is pi/2 which is the period

you would then divide this by 4 which is pi/8

then you multiply pi/8 by 0 1 2 3 and 4 to get your total amount of x values the final one being pi/2

then since its sin you have to find the v values associated with those values and then mulitply it by 3 since its 3sin and thats how you graph it

how do you approach it though if its something like y = 3sin(pi/3)

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@signal hull Has your question been resolved?

[signal hull]

.close

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[frosty geode]

How do I do this

[frosty geode]

My brain can’t even grasp the question

So it has 5 sides since it’s an open box?

How do I even know which sides are 16inch and which are 12inch

[opaque maple]

these aren't the right measurements, but i have a visual from a previous question that might help
https://www.geogebra.org/classic/byk3ebn6

slide h and b to see how the box is being made

[frosty geode]

I’m confused

Where does it show the box? Haha

[opaque maple]

oh lmao

is there a 3d view button? i haven't use this on mobile before

[frosty geode]

Oh hold on I’ll pull it up on my pc

[untold shoal]

Click menu bar - view, and there must be options there

[frosty geode]

Oh so ye 5 sides

[opaque maple]

oh perf yayyy 🥳

[frosty geode]

What do I do with it haha

Is b 12 or h

[opaque maple]

well that's just the visual

you'll want to set up your own equation

[frosty geode]

Does this use the volume formula

Idek where to begin tbh🤣

[opaque maple]

well we're making a rectangular prism

so V = lwh

[frosty geode]

What’s a prism?

[frosty geode]

Oh yea!

Length width height

How do I know what’s 12 and what’s 16

[opaque maple]

https://telgurus.co.uk/srcgurus/uploads/2021/11/Prism-in-Maths.jpg

[frosty geode]

Ohh

Oh god I’ll have to do all of these?🥲

[opaque maple]

nonono

just examples

we have the rectangular one

[frosty geode]

I mean in calc 2

🥲🥲

So h is height, what’s b?

[opaque maple]

b isn't relevant, just for the visual. you should ignore it

[frosty geode]

I see

[opaque maple]

try to sketch a rectangle where we'll cut out the squares

[frosty geode]

How can it be a square if it’s 16 by 12

Aren’t all sides of the square supposed to be equal

[opaque maple]

we're cutting out corners

so we can fold it up

we're starting with a rectangle

[opaque maple]

first pic here is after we cut out squares from the corners

[frosty geode]

Ohhh holy shit that’s difficult

[opaque maple]

it's not so bad

dw

[frosty geode]

So we need to cut 4 squares out of the rectangle so we can make a box

[opaque maple]

yep!

but we only care about the volume

which makes it a lot easier

we can express V = lwh with x, 12, and 16.

[frosty geode]

How does that solve the height

Wouldn’t that only solve the width and length of the squares

[opaque maple]

and when we fold it up?

[frosty geode]

Then we get the height of the box

[opaque maple]

yeeee

[frosty geode]

Haha, I see

So x is 12 and y is 16?

[opaque maple]

no x is our square side length

[frosty geode]

How do I connect it to the formula

Why did you choose 12 and not 16?

Wait if you need to cut out equal squares wouldn’t the length be half and half

No wait

It would be like 4x4

Like 4 by 4

[opaque maple]

hold up

start with the rectangle

that's 12*16

[frosty geode]

The rectangle is 12 by 16 right?

[opaque maple]

yees

[frosty geode]

So if you cut a 12 inch you’d just remove a whole piece

You need to cut just a corner

So maybe like a 4 by 4

From each corner

[opaque maple]

yes and that corner is a square with sidelengths x

it's variable

since we want to optimize volume

[frosty geode]

So basically that corner has an adjacent x and that adjacent’s length is the total length of 12?

[opaque maple]

not sure what you mean

[frosty geode]

Why do we use 12 to find the corner size