help-0

[alpine sable]

so if she wins W times, she gets 3*W points

[upbeat stone]

Ok

[alpine sable]

for every loss, she loses 2 points

[upbeat stone]

Ok

[alpine sable]

if she loses L times, she loses 2*L points

[upbeat stone]

Ok

[alpine sable]

so the total points she is left with after winning W times and losing L times is points won - points lost

[upbeat stone]

Ok

[alpine sable]

3*W-2*L

and we know that at the end she earned 25 points

[upbeat stone]

Yes

[alpine sable]

so 3W-2L=25

[upbeat stone]

Ok

So now I just solve?

[alpine sable]

yes solve the system

[upbeat stone]

Ok

[alpine sable]

the question asks for the number of wins

find W and you're good

[upbeat stone]

Ok

[noble sinew]

Arguably faster to just guess than doing this (but knowing how to solve this without guessing is very important)
(took around 20 sec to guess the solution)

[rare bough]

yes

[upbeat stone]

I got 13

Wins

[noble sinew]

Yep

[rare bough]

right now I am doing 1 + sin(theta)

[upbeat stone]

Lets goooooooo

[rare bough]

I dont see how any value can become negative

But on the graphing calc

[upbeat stone]

@noble sinew @alpine sable thx for the help

[rare bough]

it shows as negative

[harsh silo]

how would i figure out the piece wise function to this

[upbeat stone]

That looks weird weird what grade is that for

[rare bough]

10th

[noble sinew]

Find when 2x-5 is positive aka for what values of x
|2x-5|=2x-5 and same for the other abs value

[rare bough]

uhh im trying to plot points below 0 but I can't find any

[noble sinew]

Then you can make a piecewise function without abs value using the intervals you find

[pearl wraith]

how do you find UV i tried so many times but cant figure it out

[upbeat stone]

2 grades

[noble sinew]

Find angle T in triangle SRT then you know a line is 180 and we have angle T (from SRT) and 93, so T(SRT)+93+T(UTV)=180, so

T(UTV)=180-93-T(SRT)

Then you have 2 angles and a side in triangle UTV and can find UV from there

[harsh silo]

wdym

[noble sinew]

You want your piecewise function to be without |...| stuff

So eg if x=100 then|2* 100-5|=2* 100-5

So if we find all values of x where 2x-5>=0 then we know for those values that |2x-5|=2x-5

[harsh silo]

i got to this

[noble sinew]

You have 2 abs value so you end up with 4 different expressions

But solve them 1 at a time

So solve when is |2x-5|=2x-5

And then do the same with the the other abs value term

[noble sinew]

(So solve 2x-5>=0)

[stray prism]

I can go up, down, or right.
this grid:
e f
⬛⬛⬛⬛... ⬛⬛⬛⬛
S

how many ways can I go from S, go to E, or F?

[upbeat gorge]

Seems vague

[stray prism]

meaning I can go
⬆️ , ➡️ , then 🔽

[stray prism]

oop

[noble sinew]

You need to clarify what is allowed. Can you go up then down (so same spot twice)? Is it 3 tall and x long (so you want the answer in terms of x?)

[proven basin]

I got a equation here: 4x^2 -3x-7 and I am stuck on how to solve it. Factoring it ofc

[thorn kindle]

up right down

but not left?

@proven basin factors of ac, add to equal b

[proven basin]

thats what i did i ran into the problem of 4x not being able to factor with 7

[ruby current]

an equation usually has an equals sign

oh you just need to factor it

[flat gust]

It's possible

[thorn kindle]

why are you taking 4x

[proven basin]

let me show u a pic

[thorn kindle]

i said factors of ac that add to equal b

what is a times c?

[flat gust]

That just seems really wrong

You can't take anything out

[proven basin]

no shit thats why im askin help tf

[thorn kindle]

no you did it right

[proven basin]

then wat

[thorn kindle]

you're just missing a step at the end there

[proven basin]

do i do

[thorn kindle]

$4x^2+4x-7x-7$

[ocean seal]

AMD

[thorn kindle]

do you know how to factor by grouping?

[proven basin]

yes

[thorn kindle]

do it

[proven basin]

i thought it was only work with (x-3) (x-3)?

ya know stuff like dat

[thorn kindle]

that's not what factoring by grouping is

[proven basin]

o

[thorn kindle]

basically, split the expression into two parts. let's look at the first half for now

4x^2 + 4x

can you factor that

?

[proven basin]

let me try

2x(x+2)?

[thorn kindle]

not even close

[proven basin]

oof

[thorn kindle]

what are the common factors that 4x^2 and 4x share?

[proven basin]

2?

[thorn kindle]

ok. you can divide through by 2.

then what do you get?

[proven basin]

wait wat am i dividin?

4x^2 wit 2 right?

[thorn kindle]

the expression 4x^2+4x

divide that by 2

see what happens

[proven basin]

dood idk

give me a min

[thorn kindle]

ok let's try this a different way.

4x^2 = 4 times x times x

4x = 4 times x

what factors do they share?

[proven basin]

4?

[thorn kindle]

is that it?

just 4?

[proven basin]

4x

[thorn kindle]

yes.

[proven basin]

ok ok wats next

[thorn kindle]

so that means you can factor 4x from the expression

4x^2 + 4x = 4x(x+1)

[proven basin]

ok

this ties into solvin the problem how?

[thorn kindle]

right.

now look at the other half.

-7x-7

factor it

[proven basin]

-x+7?

wait wait -7(x+1)

[thorn kindle]

yes

right

so now we have

4x(x+1) -7(x+1)

[proven basin]

whoa

ok ok

(x-1)(4x-7) = answer?

[thorn kindle]

yes that's it

you've factored it

[proven basin]

ok thanks man

srry for being brainded

[thorn kindle]

did you need to actually solve it? or just factor

[proven basin]

just factor it

[thorn kindle]

ok then you're done

[proven basin]

real quick wat if there is only 1 variable with 1 real number ? or like if theres like 3 variable?

do i do the same thing?

[thorn kindle]

huh?

[proven basin]

like 3x^2 - 300 or 9x^2-13xy+4^2

same thing right!

*?

[thorn kindle]

ok that second expression is multivariable so you might not be able to factor it as easily

have you done multivariable equations?

[proven basin]

dood this is my first time ever touchin this stuff

i have no idea

[thorn kindle]

ok then don't worry about that for now

but that first equation is simple

if you have ax^2-c then x = +-sqrt(c/a)

[proven basin]

its still factoring it right?

[ashen wave]

is anyone good with chemistry? I really need the help

[sly mantle]

[ashen wave]

ok thanks your a life savor

Which group of elements would group 2 elements bond well with and why?

[ashen wave]

Are you still here rip

[alpine sable]

Can someone help me pls

Trying to figure out how many combinations of discord invites there can be

[sly mantle]

i meant this server isn't where you ask to ask, just ask and wait for a helper

[alpine sable]

there's 8 spaces, 27 lowercase letters, 27 uppercase, and 10 digits

How would this be calculated?

[ashen wave]

alright I understand

:T

[sly mantle]

@ashen wave i'll also say this server primarily helps with math. there's a chem server in #old-network, and remember to just, don't ask to ask (but don't ask on top of a convo)

[waxen lichen]

Can someone help me with this?

[stray prism]

You cannot go in same vertex twice, you can go up, down, or right. it's 2x20 long in terms of squares, and the line passes on the lines.

[white stump]

does physics count as mathmatics if it has a formula

idk what specific type of physics it is

but i can post the equations and question

[normal lagoon]

at step n, there are n rows and n +1 columns of tiny squares

[white stump]

uh here

18. Chris is playing baseball and pops the ball straight up into the air. It has a hang-time of 5.2 s. What is the initial velocity in mph of the ball off his bat?

here are the equations

[waxen lichen]

Thank you

[gleaming granite]

This is physics?

well

I guess it doesn't really matter

[white stump]

wha

uhhh

[gleaming granite]

What variables are given to you?

[white stump]

so t= 5.2

the want v0

[white stump]

this the question

well thats all the varibles i could idenify

[gleaming granite]

what about the acceleration?

[white stump]

i couldnt for anything else

[gleaming granite]

You can assume that this takes place on earth so what would the acceleration be?

@white stump

[white stump]

ig its 9.8

yes earth

9.8 is the free fall on

so ig 9.8

[gleaming granite]

okay

so you have:
t = 5.2
a = 9.8
v0 = ?
change in y
vf

does it say anywhere in the problem how much it travels vertically?

[white stump]

no

well these are the eautions our teacher gave to us

so

t=5.2
a = 9.8
vi= ?

vi =v0

i is initial

f is final

[gleaming granite]

yes I know

[white stump]

yep

[gleaming granite]

can you predict the final velocity?

[white stump]

its prob when it hits the ground

so 0?

[gleaming granite]

exactly

so now you have 3 variables and are solving for 1

[white stump]

t=5.2
a = 9.8
vf=0

so the bottom left equation

[gleaming granite]

yep

[ocean seal]

keto11

[white stump]

0= vi + 9.8*5.2

[gleaming granite]

,w 9.8*5.2

[ocean seal]

Results provided by WolframAlpha

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

Requested by keto11#8349

[white stump]

i got that but the problem is

my teacher has the answers posted

18. 57.0 mph

57 mph

[gleaming granite]

hmmm

[white stump]

vi = 57

t= 5.2

[normal lagoon]

final velocity is not 0. Also hang time is not well-defined here. If hang-time means the time the ball takes to return to the same height where it started off the bat, then the final and initial velocities would be the same just opposite signs

[white stump]

18. Chris is playing baseball and pops the ball straight up into the air. It has a hang-time of 5.2 s. What is the initial velocity in mph of the ball off his bat?

hmm

[gleaming granite]

huh

I shouldn't be helping with physics

LMAO

lemme check

[white stump]

brain ded

[normal lagoon]

Let's denote by $v_i$ and $v_f$ the initial and final velocities of the ball. We have the equation $$v_f^2 = v_i^2 + 2gh $$where $g$ is the acceleration due to gravity (we are considering downward direction as positive) and $h$ is the displacement. If $v_i $ and $v_f$ are the initial and final velocities at the same level then $h = 0$ and we have $v_i^2 = v_f^2$

[ocean seal]

andreO

[white stump]

lol

well

@gleaming granite @normal lagoon r u guys still working on it or done?

[gleaming granite]

i gave up a long time ago

[white stump]

oh ok

[white stump]

lol

[gleaming granite]

i keep getting 50.96

WTFFFFFF

@white stump just ask ur teacher

[white stump]

schools over lol

i would

but yeah

i was sleeping in class

[gleaming granite]

y r you still studying

also

[white stump]

i got a quiz tom

imma just put 50.96

[gleaming granite]

I thought your school was over

aren't you on summer break

[white stump]

wdym?

no

[gleaming granite]

w8

[white stump]

still got 6 weeks

[gleaming granite]

nvm i'm brain ded

[white stump]

nice

lol

same

[normal lagoon]

well if the answer is in mph you can't be using 9.8m/s^2

[white stump]

i had a 2nd question but imma keep that to myself after seeing the struggle

[white stump]

ah shoot

[gleaming granite]

https://tenor.com/view/hol-up-brooker2x-waymen-wayment-gif-20877774

[white stump]

LOL

no

NOOO

so convert

meters to miles

1 meter = 0.000621371 mile

:/

[normal lagoon]

the standard g often used is 32 ft/s^2

[white stump]

g force

so

t= 5.2

wait lemme post again

18. Chris is playing baseball and pops the ball straight up into the air. It has a hang-time of 5.2 s. What is the initial velocity in mph of the ball off his bat?

t=5.2

vf=0

[normal lagoon]

So assuming hang-time means the time it takes the ball to return to the same level, we have $v_f = v_i + gt$ That is, $$v_f - v_i = gt$$
$$2v_f = 32\times 5.2$$
$$v_f = 83.2 ft/s = 56.7 mph$$ and $$v_i = -v_f$$

[ocean seal]

andreO

[white stump]

we need vi

i alr have the answer tho

but i need to know how to actually solve it

[normal lagoon]

v_i is the same as v_f

just opposite sign

[white stump]

put isnt vf

0

cause its still on the ground

[normal lagoon]

no, v_f here means the velocity right before colliding with the ground

what happens after collision is not out concern

[white stump]

then answer was 57 but i think thats close enough

[normal lagoon]

also by hang time I am guessing your teacher meant returning to the same level where itt started off the bat

should have been more clear

[white stump]

wait what does the 32 mean

[normal lagoon]

acceleration due to gravity

g

[sage jacinth]

in ft/s

[white stump]

oh

[sage jacinth]

i think its 32.2, which may explain why the answer is a bit off

[white stump]

ok so meter form is 9.8

feet form is 32

[sage jacinth]

yea

[normal lagoon]

yeah

[white stump]

oh my gosh...

[sage jacinth]

i still cant get over how people use ft/s^2 for acceleration

[white stump]

wait lemme think

[sage jacinth]

i always thought people used m/s^2

[white stump]

wait so since

vi is the sam as vf

[white stump]

its 2vi

[stuck plinth]

whats that symbol called?

[normal lagoon]

room in use

[stuck plinth]

ty

[white stump]

but

wait

acceleration is always positve

ok

velocity

[normal lagoon]

no

[sage jacinth]

@stuck plinth i think he meant room in use as in this room is currently being used

[white stump]

velocity

[sage jacinth]

or she

[white stump]

not acceleration

bruh my brain

[stuck plinth]

ye i got that my ty was sarcastic

[normal lagoon]

acceleration is towards the center of the earth

downwards

[white stump]

oh so even

[normal lagoon]

so if we consider that the positive direction

[white stump]

when its going up

[normal lagoon]

upwards is negative

[sage jacinth]

v = a * t

[white stump]

gravitational forces are still being applied

[sage jacinth]

since a is a constant and you are given time you can just multiply to get your answer

[normal lagoon]

the direction gravity acts is always the same whether the ball is going up or down

[white stump]

then you get 83.2

convert

and get

57

[normal lagoon]

indeed

[white stump]

nice

2vf

[alpine sable]

Pls help me

[sage jacinth]

rip vo :/

[white stump]

16.62

[sage jacinth]

i havent seen people use vi in so long

[white stump]

wait no

[alpine sable]

Those are functions

[white stump]

first one should be 62 right

[sage jacinth]

yes you just fill in for x

and solve

[white stump]

yeah

[sage jacinth]

for the variable ones you have to put everything in terms of a variable

[white stump]

ok so

wait

back to the same problem

so

the gravitational forces

on the object

is both applied going up

then when it goes down right?

@sage jacinth

thats y its 2vi?

[sage jacinth]

i think so

[white stump]

cuz

[sage jacinth]

you might want to double check with andre i havent been following along with this problem that much

[white stump]

it'll hit

oh

ok

0_0

well ty

[sage jacinth]

any time

[alpine sable]

umm i need the answers as my reviewer.. and i still can’t understand

[sage jacinth]

Let's say you have the function $f\left(x\right)=x^2$, then you would be plugging in x for the x in the $x^2$. However, if you are given more than one variable in the input, then you have to plug in that whole input for "x."

[ocean seal]

(バカ) baka

[alpine sable]

😭So what’s the answer?

[sage jacinth]

If $f\left(x\right)=x^2$ and $g\left(x\right)=5x$, then $f\left(g\left(x\right)+5\right)=\left(g\left(x\right)+5\right)^2=\left(5x+5\right)^2$

[ocean seal]

(バカ) baka

[sage jacinth]

im not telling you what your answer is

[alpine sable]

glad I deleted it

[sage jacinth]

im here to help you not do your homework

[alpine sable]

okii tysm..

[sage jacinth]

if you really want answers that bad go to symbolab or wolframalpha and plug those numbers in

[white stump]

uh i got another problem

19. If Zion Williamson has a vertical leap of 43 inches, then what is his total hang time (total time in the air) ?

ok so d=43

and a=32.2 cuz its the customary system

[sage jacinth]

32.2 if you want complete accuracy

[white stump]

we are solving for the time

[alpine sable]

Not answerss for all of that 😭 haha i only need questions one then I’ll figure it out

Tysm thoo have a great day

[sage jacinth]

f(2) means you are plugging in 2 for x. if y = 25x+15, then f(x) means y=25(2)+15 @alpine sable

[white stump]

would the initial velocity be 0

[alpine sable]

Oki oki got it thankkkssss

[sage jacinth]

i think we should put everything in the same units @white stump

43 inches would be around 3.58 feet

[white stump]

k

[sage jacinth]

i think his initial velocity would be zero

[white stump]

and final right

[sage jacinth]

what is the answer in the book?

i think i got it i just want to make sure

[white stump]

.94

sec

[sage jacinth]

oh i forgot to double

i got 0.47

but yea v-naught should be 0

[white stump]

wha

[sage jacinth]

think about it this way

[normal lagoon]

nope initial velocity is not 0. If it was he wouldn't be able to jump in the air

[sage jacinth]

when the guy jumps

[white stump]

but isnt he still b4 he jumps

[sage jacinth]

oh i put in 0 for the initial and i got the answer

[normal lagoon]

you got the answer because you used 0 for both initial and final

[white stump]

which equation did you use

[normal lagoon]

again, initial and final are the same but opposite signs but no 0

[thorny lily]

https://i.imgur.com/5c0BsEm.png

[normal lagoon]

his muscles work to impart an initial velocity to him for the jump. The initial velocity here means after that has happened, the veocity with which he left the ground

[thorny lily]

lowkey confused

[white stump]

oh you got to draw a function for that qustion

it basically

between those points

-infinity to -1 and 2, 4

its got to be abovey=0

and then vise verse for the negative

[alpine sable]

f(x) is positive on the intervals (-00, -1) and (2,4)

[thorny lily]

ik

but like I dont know how to draw it

[alpine sable]

draw a horizontal line

set integers

[thorny lily]

isnt the f(x) the y axis?

[sage jacinth]

is this wrong?

[normal lagoon]

forgot the dollars

[sage jacinth]

oh

Equation: $d=vi:\cdot :t:+:\frac{\left(a\cdot :t^2\right)}{2}$

Since when you jump you have to come down the guy is actually traveling a distance of 3.583, so the equation becomes: $3.583=\frac{1}{2}\left(32.2\cdot ::t^2\right)$

Solving for t we get: t=0.4717, and since the guy has to come down you must double that, so the final answer is 0.9434

[ocean seal]

(バカ) baka

[sage jacinth]

ignore the colons

[alpine sable]

(-00, -1) and (2,4)

this is curve positive on the line

while the others are negative

yes, you will draw both x and y axis

[normal lagoon]

you are calculating the time it would take him to fall through 3.583 ft if he jumped off a building or wall

if his v_i was 0 , since gravity works in downward direction, he would be falling

not going up

[sage jacinth]

well this is embarrassing :/

somehow the answer is right

[normal lagoon]

because the roles of the velocities were reversed

when he reaches his max height his velocity is 0

[sage jacinth]

ah i see, thanks

that clears things up

[alpine sable]

@thorny lily

this is how it would look in theory

[clever frigate]

hey, how do i solve this diff eq?

$$y'' + 3y' + 2y = 2t^2 + 4t, y(0) = 1, y'(0) = 0$$

[ocean seal]

Doukutem

[worn nimbus]

how do i properly solve this? like the formula for it

[clever frigate]

<@&286206848099549185>

[alpine sable]

i can help you with this one, but please ask in an unoccupied channel

[umbral pecan]

Can someone explain on the steps to decide if H0 should be accepted or rejected on a two tailed test?

I understand for a two tailed test using p value approach, we find the critical Z value, find the area on the left or the right depending on negative or positive z value, then multiply it by 2 (since this is two tailed) and compare it with the alpha value.

What do I do if I don’t want to use the p value approach but just the Z value approach?

Is it the same step as a one tailed z value approach?

[foggy onyx]

Quick question, does the sequence have a ellipsis on the set of numbers
or the Series has the ellipsis

[charred flint]

what

they both go on forever so you add an ellipsis on them sure

[south marsh]

how do u solve this?
How many odd 2-digit positive integers greater than 30 are there?

[charred flint]

try to write a list of those integers, including the lowest and highest one

like (4,6,8..., 36)

[south marsh]

oh i think i kinda get it

How many positive odd integers less than 10,000 can be written using the digits 3, 4, 7, 8, and 0?
my answer in here is 200, is it correct?

my sol. is
4 * 5 * 5 * 2 = 200

[charred flint]

almost

[south marsh]

ohh wait

i think the first one should be 5 too

250?

[charred flint]

er I think there's a lot of pitfalls here

[south marsh]

5 * 5 * 5 * 2 = 250

[charred flint]

wait I misread

[south marsh]

ohh okaay take ur time

[charred flint]

yea 250 looks good

[south marsh]

thanks sorry but in here i don't really get it, the easiest way i mean w/o listing it

[ancient sphinx]

はたはたはたはま

[charred flint]

oh by listing I don't mean just counting

just say the lowest is 31 and the highest is 99, and it skips by 2

so like (31,33,35,..99)

and you want to convert it to counting numbers 1 to n

[native temple]

hello

[charred flint]

so you subtract by 29 and divide by 2

31 goes to 2, 99 goes to 70

(2,4,6,...70)

and divide by 2 for
(1,2,3...35)

so there's 35 because this list has the same # of elements

[south marsh]

ohh thanks

[elder viper]

how do i simplify this thingy right here

[charred flint]

I think you have to realize it as a binomial expansion

[elder viper]

uh, i see

not dumb

ty ill try that

[tough ether]

Given 40 vertices, such that for any 3 chosen vertices, at least two of them are connected, what is the minimum number of edges such a graph can have?

[charred flint]

try to find a lower bound then build it

[alpine sable]

I need help with this

Also can relative max also be absolute max because for this it looks like two maxes

[tough ether]

The trivial lower bound is 39

[alpine sable]

yoo can someone help me with this and how you got that

[sand oak]

@alpine sable I think the result comes from applying the method of differences

[alpine sable]

thank you!

[sand oak]

np!

[small flame]

how do i find the regression coefecient

sorry for poop grammar, and can you please provide an example

[turbid kindle]

if $\sum_{i \in X} i = \sum_{i \in Y} i $ and $\prod_{i \in X} i = \prod_{i \in Y} i $ does that imply $X = Y$?

[ocean seal]

QuAnTuM

[alpine sable]

Hey anyone know what the answer for this is the answer I got is

wait let me post the question first

Give an expression for the number of different race results there are in a horse race of h horses if any ties -- up to all h horses -- are possible. Explain your reasoning

(h, h - (h+1)) x (h-1)!

any help?

casework by # of ties?

ya number of ties but there can't be multiple sets of ties basically

need to gibe an equation

oh ok then i think i know how to do it

I got (h/(h-(h-1)(h-1)!

is that off?

oh ill see if i get the same

okay let me know what you ge

get

,rotate

[alpine sable]

casework on ties

0-way tie, 2-way tie, 3-way tie, etc

for the case of 5 horses

you can generalize this pretty easily to h horses

the summation bit simplifies to this

we can check this with your formula

[alpine sable]

lmao

no the h-1 would be at the top

yours seems more correct

https://math.stackexchange.com/questions/1058978/horse-race-combinations-when-ties-are-allowed/1060236

What do you think of this?

welp

the horses are distinct right

yes

The answers for 0, 1, 2, 3, or 4 horses are 1, 1, 3, 13, and 75.

looks like we both messed up somewhere

Ya i know that sequence is ordered bell numbers

Can someone check my answers please

[alpine sable]

answer to this on stackexchange assumes that there can be multiple sets of ties

Dan can u help me

ask in an unoccupied channel

there's plenty of people here that can help

I didn’t think this was occupied

[alpine sable]

i assumed there could not be multiple sets of ties cuz of this

so my cases for h=5 were no ties, a two-way tie, a three-way tie, a four-way tie, and a five-way tie

cuz i assumed there could only be one "set" of ties

@alpine sable do you have any more questions about that combo problem or are you good?

[severe quarry]

oh nvm

[elfin matrix]

Do i multiply the exponents?

[alpine sable]

x^2 * (y^(-6) )^2

then use power to a power rule

x^2 * y^(-12)

[elfin matrix]

Thanks a lot dude

I was struggling but now i got it

[alpine sable]

np

[vagrant heart]

i dont know how to solve x and y

i know how to figure out the rest of angles

but that's about it

[small stag]

Use the tangent function

You have the opposites and adjacents of both angles

[vagrant heart]

tg (23) = y/ x+25
tg (41)= y/x

you mean that?

[small stag]

Good

Yeah

[vagrant heart]

ohhh equation system

[small stag]

It’s a system

Yeahhhh!!

Good work you got this

[vagrant heart]

that's what i get for pulling an all-nighter

thank you

<333

[small stag]

Np hope you get good sleep

[vagrant heart]

nah, got the exam in 3 hours and i have to go to school in 1

but thank you <3

[small stag]

Power naps

They help

[vagrant heart]

ill forget everything tho

gotta remember all of those

[small stag]

Derive them

And make patterns

[vagrant heart]

by deriving them?

will i see things?

[small stag]

Well just like

For half angles

It’s nasty right

[vagrant heart]

i'm in 11th and i just learnt derivation so it might get ... messy

[small stag]

Oh no no no

Not like

Take the derivatives

Just like prove the identities

Sorry about the confusion

[vagrant heart]

np, but how do i prove identities?

[small stag]

Double angle is easy you just substitute

For half angles

Basically like

Say 2x = A

And x = A/2

And change only one side of the equation

Until you get to the other

That’s proving it

Here I’ll do the first

Sin(x) = sqrt ( 1-cos(2x) / 2 )

Sin(x) = sqrt ( 1- (cos^2(x) -sin^2(x) / 2 )

Sin(x) = sqrt ( 2sin^2(x) / 2 )

Sin(x) = sin(x)

And also they all have +/- I’m just too lazy to do that

Oh yeah finally

[vagrant heart]

uhhhhhhhhhhhhhhhhhhhhh

I'd like to say that I understand

but,

uh

[small stag]

It looks stupid without latex

I’ll walk you through it

[vagrant heart]

okay, but if i disappear it's because i have to play asleep

[small stag]

Basically half angles makes use of the cos(2x) identity

So to see it clearly I’m gonna substitute a for 2x

So we have this right?

Sin(x) = sqrt ( 1-cos(2x) / 2 )

Same thing just a different variable

Okay i think yoh left

[vagrant heart]

Just got back

[small stag]

Basically just use the cos(2x) identity

All good

Which is (cos^2(x) - sin^2(x))

[vagrant heart]

In what way?

[small stag]

I’m explaining it rn

The last two things

[vagrant heart]

Oh sorry

[small stag]

It’s all good don’t worry

So plug it back in

And in the numerator of the fraction we have

1 - ( cos^2(x) - sin^2(x) )

Distribute and we get

1 - cos^2(x) + sin^2(x)

1 - cos^2(x) = sin^2(x)

So that’s 2sin^2(x)

Divide that by 2

And take the square root

Plus minus

And voila sin(x)

[vagrant heart]

Ohhhhh

[small stag]

But let’s change back into a

[vagrant heart]

Okay, I see it

[small stag]

So sin(a/2)

But remembering that process is time consuming

So what I do is

When I need cos(a/2)

I want to add cos(a)

And when I need sin(a/2)

I do the opposite

[vagrant heart]

If i dont remember that I'll use it

Wow

[small stag]

I would just use that

It’s efficient

[vagrant heart]

This could be one of those "prove that (trigonometric expression) = (trigonometric expression)" exercised

[vagrant heart]

True

But i have good memory for formulas, luckily

[small stag]

Yeah

Lucky

The sum to product and product to sum ones are inverses of eachother

But I can’t get it down ever

[vagrant heart]

Then again i dont remember Peoples names or my mom's birthday (a soul for a soul)

[small stag]

So I have to rederive them all the time

I’m bad with names

But I’ll never forget a face

[vagrant heart]

I dont remember the face of my therapist and k see her every 15 days lmao

A soul for a soul, again

Anyway

Thank you so much

Now i understand and i learnt a way to remember these wack formulas

<3

I'd give you a cookie but, yknow.

[small stag]

That’s gooddddd

[vagrant heart]

Gotta go to school but ill check this out again when I've slept

[small stag]

Too kind

[vagrant heart]

nou

Helping strangers

;)

[small stag]

Lmk know how you do on the test if you want to do something tho

Also I would learn how to derive product to sum first

[vagrant heart]

I suck at trigonometry and ill prolly make small dumb mistakes

[small stag]

Then use that to make sum to product

[vagrant heart]

And the test is more than trigonometry

But ill tell ya

Ttyl <3

[small stag]

Well I hope you drop an a+

@real ore

Fudge

Sorry bro

[vagrant heart]

Lol

[alpine sable]

If something that weighs 150 g costs 12 dollars, how do I find out how much something that weighs 1 kg costs?

[vale wigeon]

are we assuming that price is proportional to weight?

[alpine sable]

I'm not sure, it's not said

[vale wigeon]

are you rephrasing the question in any way

[alpine sable]

Not really

[vale wigeon]

okay so like, if we're buying a good that's sold by weight

like cheese or meat or homemade butter or something

and if you're not afraid of decimals and/or fractions

then this is literally just a matter of dividing 12 USD by 0.15 kg to get the price per kilogram

[alpine sable]

Thank you

That makes sense

And I get the correct answer

[vale wigeon]

notably, price need not scale with weight in general. you could have a 200ml carton of juice sell for, say, $1.20 and a 1L carton for $5.50 (instead of the 6 you would expect if price were proportional to volume)

[ocean seal]

Ann

[alpine sable]

Yeah, that makes sense

I just have a follow-up question as well

[vale wigeon]

yes?

[alpine sable]

Oh nvm I figured it out

Thanks for the help again

[balmy light]

i dont know what is going on here

any help will be great

[balmy light]

anyone?

please?

[alpine sable]

yeah i can help

[balmy light]

yes please

[alpine sable]

for problems like this you'd probably find it helpful to draw a timeline

ill send a visual

[balmy light]

sure

[balmy light]

okay yeah makes sense

[alpine sable]

so now we convert this to algebra

[balmy light]

yes

[alpine sable]

start of 2018 value is x dollars

and we have a 15% decrease

x-15%x=85%*x=0.85x

so that's the price at the start of 2019

you follow?

[balmy light]

yeah okay i see

[alpine sable]

so now let's go from 2019 to 2020

[balmy light]

increase in a%

[alpine sable]

we have an a% price increase

[balmy light]

yeah

[alpine sable]

(0.85x)+a%(0.85x)=(1+a%)(0.85x)

[balmy light]

uhm, how about we keep our starting value thats x as 100? wount that make it a bit easier?

[alpine sable]

yeah that would help

percentage increase would be the same no matter the starting value

[balmy light]

yeahh

so year 2018 we have 85

[alpine sable]

so start of 2019 it'd be 85 dollars

[balmy light]

yes

[alpine sable]

85+a%*85=(1+a%)*85=(1+a/100)*85

same thing for 2020-2021

(1+a/100)*85 + a%[(1+a/100)*85]

[balmy light]

wait but dont we have to use the new value of 2019?

[alpine sable]

that's what i did

start of 2018 you have 100

[balmy light]

yeah

[alpine sable]

start of 2019 you have 85

[balmy light]

yes

[alpine sable]

start of 2020 you have (1+a/100)*85

[balmy light]

yeah

[alpine sable]

start of 2021 you have (1+a/100)*85 + a%[(1+a/100)*85]=
(1+a/100)[(1+a/100)*85]

[balmy light]

$$(1+a/100)*85 + a%[(1+a/100)*85]=(1+a/100)[(1+a/100)*85]$$

[ocean seal]

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

[alpine sable]

so this value is 2.85% greater than the starting value

[balmy light]

is this right?

[alpine sable]

compile error, it's messed up

[balmy light]

yeah so equate it to 2.85% of 2018

which is 100

[balmy light]

lol its ayt

uhm you there?

[alpine sable]

would look like this

yeah i'm here

so (1+a/100)[(1+a/100)*85]=85+2.85%*85

[balmy light]

yeah

[alpine sable]

=87.4225

[balmy light]

uhun

[alpine sable]

wait actually first we should divide by 85

(1+a/100)[(1+a/100)*85]=85+2.85%*85
(1+a/100)[(1+a/100)]=1+2.85%*1

[balmy light]

okay so from here

[alpine sable]

(1+a/100)^2=1.0285

[balmy light]

yes

[alpine sable]

square root both sides solve for a

[balmy light]

lemme try that

i am getting 1.41

[alpine sable]

yeah that's what wolfram alpha says as well

now we check the solution

[balmy light]

uhm thats gonna be wrong

its supposed to be 10

i actually got that before

but wel doesnt add up if we put it in the equation

[alpine sable]

https://www.wolframalpha.com/input/?i=(85*(1%2Ba%2F100))(1%2Ba%2F100)%3D85%2B85*(2.85%2F100)

oh wait i see what went wrong

he paid 100 for the house at the start of 2018

https://www.wolframalpha.com/input/?i=(85*(1%2Ba%2F100))(1%2Ba%2F100)%3D100%2B100*(2.85%2F100)

so yeah you should get a=10%

@balmy light

[balmy light]

yeahh

thats the one

thanks man

[alpine sable]

Can anyone tell me why B isn't congruent to the figure shown?

[jade birch]

The answer is in the definition of congruent figures: Two figures are congruent if they have the same size and same angle (measures).

B is the not same size as the figure shown, however, it has the same angle measures, therefore it's only similar

[alpine sable]

So because the perimeter of A is the same as the perimeter of the figure, they're congruent?

[mystic crown]

Anyone here able to help me ?

[jade birch]

Not at all what I said

[alpine sable]

But they don't have the same size

Other than what the sides add up to

[jade birch]

You dont look at what the sides add up to

you look at the individual sides

[alpine sable]

What makes A different from B then?

[jade birch]

Different angles and sizes

however

you are not comparing B to A or A to B

Youre comparing A to the figure shown and B to the figure shown

[alpine sable]

I don't understand

I understand that I'm comparing to the figure shown, but I don't understand what makes A congruent and not B, when none of the sides are alike to those of the figure shown

[gray isle]

who's saying A is congruent

[alpine sable]

The answer

[jade birch]

You are not looking for the congruent figure

Please reread the question

[gray isle]

A is neither similar NOR congruent

[jade birch]

Just because one figure is similar but not congruent DOES NOT IMPLY that the other is congruent but not similar

[alpine sable]

I understand now

I didn't read it right

[alpine sable]

Thank you

[austere thorn]

Can anyone help me

To find the equation of the function and the derivative

[obsidian crane]

It's a quadratic function's graph (if im not wrong) @austere thorn

[austere thorn]

Yea

[obsidian crane]

The general equation for a quadratic is this :

x^2 - Sx + P = 0

S is sum of the roots

P is product of the roots

[austere thorn]

Ok

[obsidian crane]

You know the roots from the graph.

[austere thorn]

Nope

[obsidian crane]

Roots are the points (on x-axis) where the graph crosses the x-axis.

[austere thorn]

Ok

From left to right

[obsidian crane]

They are -8 and 4

[austere thorn]

Yes

[obsidian crane]

Now find their sum, and their product. Put it in the equation.

[austere thorn]

Can I dm you

[obsidian crane]

S = -4
P = -32

Sure

[austere thorn]

Ok

[obsidian crane]

Putting these values in x^2 - Sx + P = 0 will give you the quadratic.

[verbal ermine]

can someone help with the last part

thats what i did

but i get a quadratic when i should just get one answer?

i skipped that step btw

isnt the sum from r = n+1 to infinity the sum from 1 to infinity - the sum from 1 to n?

[sage summit]

have you tried solving the quadratic ?

[verbal ermine]

yeah i get like 0.22 and a negative

and the answer is 4

not really sure

[sage summit]

well then you got a wrong quadratic equation

[verbal ermine]

ik but i dont see anything wrong

[noble sinew]

3/2-1/(n+1)-1/(n+2)=3/2-11/30

is what you want to solve

isn't it

[verbal ermine]

wouldnt it be 3/2 - (3/2 ...

[sage summit]

a-b-c = a-d is not equivalent to b-c = d

[verbal ermine]

sum from r = n+1 to infinity the sum from 1 to infinity - the sum from 1 to n?

[noble sinew]

you want the sum to be equal to 3/2-11/30

,w 3/2-1/(n+1)-1/(n+2)=3/2-11/30

[sage summit]

actually you wrote so little stuff it's hard to tell what you are doing

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[verbal ermine]

oh right

so where does the r = n+1 to infinity come from

[noble sinew]

the sum from 1 to inf is 3/2

[verbal ermine]

yep

so its 3/2 - the sum from 1 to n

[noble sinew]

the sum from r=n+1 to inf we want to be 3/2-11/30

[sage summit]

no ?

[verbal ermine]

i dont get why the 3/2 is on the other side

wait

[mystic crown]

Anyone here free to help ?

[noble sinew]

yes?

if the sum fron 1 to n is 11/30

[sage summit]

there are like 5 other question channels that are not in use right now

[verbal ermine]

thats what we're trying to solve?

[noble sinew]

then the sum from r=n+1 to inf is then 11/30

[sage summit]

what's the question again

[mystic crown]

A two-payment stream consisting of $1750 due today and $2900 due in 18 months is to be replaced by an economically equivalent stream comprised of an undetermined payment due in 9 months and a payment of $3000 due in 19 months. Calculate the unknown replacement payment if money is worth 9% compounded monthly and focal date is in nine months from today.

[verbal ermine]

bro...

@sage summit

[noble sinew]

oh

[sage summit]

so yes you have to solve 3/2 - (3/2 - 1/(n+1) - 1/(n+2)) = 11/30

[noble sinew]

typed wrong but solution right

[verbal ermine]

i think

[sage summit]

but then you messed up the signs

that's how you got a wrong quadratic

[verbal ermine]

yeah im trying again

[mystic crown]

Can anyone help me plz.

[noble sinew]

this equivalent to what I wrote yep

[verbal ermine]

that

so now i cancel the 3/2s?

[sage summit]

yes ?

[verbal ermine]

4.1 close enough to 4?

[sage summit]

no ???

[verbal ermine]

i cant see anything wrong

[indigo jetty]

how did u get 4.1

[sage summit]

n=4.1 is wrong the rest is okay

[indigo jetty]

because i got 4 with the exact same equation

[verbal ermine]

put it in my calc wrong

thanks guys

[sage summit]

also, since you know the solution has to be an integer, it's not that difficult to solve 1/(n+1) + 1/(n+2) = 11/30

[verbal ermine]

how come?

[sage summit]

n+1 and n+2 are coprime, so (n+1+n+2) and (n+1)(n+2) are coprime, and so you must have n+1+n+2 = 11 and (n+1)(n+2) = 30

now try to factor 30

30=5*6 is the only way to get two factors that are consecutive integers

[verbal ermine]

haha im not a problem solver man

[sage summit]

and 5+6=11 so it works out

[verbal ermine]

i see

can you see what cancels here

circled is what should be left

i dont see a pattern

[sage summit]

I'm not sure what I'm looking at

[verbal ermine]

method of differences

[woeful pulsar]

did you forget to square the (n-1)

[verbal ermine]

wdym

[verbal ermine]

part ii

[woeful pulsar]

1/2-1/16?

[verbal ermine]

i didnt square

damn

in part iii

why have they done 1- 1/4 in the brackets

i did 1 + 1/4

[woeful pulsar]

wait why is there squared in the denominator?

[verbal ermine]

thats answer to part 2

[woeful pulsar]

because if 8i is true, then the things should cancel out mostley?

okay for part 8iii you just need to get rid of the r=2 and r=3 term

[verbal ermine]

sum from 1 to infinity - 1 to 3

but inside the bracket would be 1 + 1/4 no?

they did 1 - 1/4

[woeful pulsar]

substituting 1 doesn't make sense

we should be continuing from part 8ii

[verbal ermine]

the sum from 4 to infinity

is the sum from 1 to infinity - the sum from 1 to 3

right?

just like if i have the sum from 30 to 50 its the sum from 1 to 50 - the sum from 1 to 29

[woeful pulsar]

the term doesn't make sense when r=1

[verbal ermine]

but my part ii is right

[woeful pulsar]

yeah, so your part 8ii sums from r=2

[verbal ermine]

ohh right

i keep missing that 2

so how do i do it now?

@woeful pulsar

[woeful pulsar]

just remove r=2 and r=3

[verbal ermine]

like that?

[woeful pulsar]

hmm might want to use the actual terms, that might make the calculation easier

[verbal ermine]

wdym?

actual terms?

[woeful pulsar]

how did you get (5/4-1/9-1/16)?

[verbal ermine]

plugged r = 2 into

[woeful pulsar]

where did you get that from?

[verbal ermine]

the answer to part ii

[woeful pulsar]

oh,

no wonder

your answer to part to is about n if the summation ended there

if your summation went to infinity, then you need n to go to infinity

[verbal ermine]

yeah i used the answer to part ii

[acoustic bay]

Can someone please help me, I dont understand the proof for how we find the moment generating function of a gamma distribution?

[acoustic bay]

I dont understand how to show the mgf here

[verbal ermine]

thats the question sorry

bro u gotta use a free channel

[woeful pulsar]

so how did you use the answer in 8ii?

[verbal ermine]

i found the expression from r = 2