help-28

[plush egret]

we are letting x be the number of cases of 16 oz cups that the factory produces in (timeframe)

what time frame do you want to use

[tardy ruin]

Ok I get it

So it’s

Let x be 15 cases of 16 oz that the factory produces in one hour

[plush egret]

15 cases 👀

you are measuring cups in 15's of cases?

[tardy ruin]

No one case

[plush egret]

so whats up with the 15

[tardy ruin]

I was reading 15 at the bottom

But realized I don’t worry about it rn

[plush egret]

there is a 15 in the problem, but why is it in your variable 😄

ah ok

[tardy ruin]

15 should be after =

Wait so

let x be 1 case of 16 oz cups that the factory produces in one hour

[plush egret]

no

i mean

i think youre close

this still doesnt sound variable to me

you want it to be able to change

Let x be the number of ...

i know it probably seems really nitpicky

you dont want it to always be 1

or 15

[tardy ruin]

Let x be the number of cases

[plush egret]

that what 👀

[tardy ruin]

Ohhhh

So

Let x be the number of cases of 16oz cups that the factory produces in 1 hour

[plush egret]

thats one variable done

[tardy ruin]

Let’s goooo

[plush egret]

whats y

[tardy ruin]

Let y be the number of cases for 20oz cups that the factory produces in one hour

[plush egret]

honestly im not sure if 1 hour or workday is right

but

you can always go up

i feel like its harder to go down

if that makes sense

[tardy ruin]

Kind of

[plush egret]

its easy to decrease resolution because it makes things simpler

[tardy ruin]

So do I change it

[plush egret]

nah

do you get how to use these variables?

i mean can you start making relationships now

[tardy ruin]

Wait so y is correct too

[plush egret]

yea 😄

[tardy ruin]

Ok

[plush egret]

so idk try one

[tardy ruin]

I’m going to write them down

[plush egret]

you said youre okay with this part

o k

[tardy ruin]

Wait ill try to see if I’m good

I’m good once I get the equations

[tardy ruin]

Wait

So for 8 hours can you guide me through it

Then I’m good from there

[plush egret]

try

[tardy ruin]

Ok

[plush egret]

i mean dont uhh

just try for 5 minutes=

[tardy ruin]

Ok

[plush egret]

we identified these 4 ish pieces of important relationship info

[tardy ruin]

Ok

Wait so

Do I use the amount of money for each one

At the end of equation

Like other word problems

[plush egret]

I'm not seeing any suggestion that the money information is important

maybe its on another page or something

every word problem is different though

and throwing in extraneous information is very common

[tardy ruin]

Ye

So for the first one

Would I throw 15 and times it by 8?

[plush egret]

your equation for 1 is 15*8?

[tardy ruin]

No

It’s 16x + 20y so far

So how do I implement 15 and 8 in

[plush egret]

here

start here

make an equation and it needs to use your variables

dont worry about the full day yet

whats an hour look like

remember you want an equation with one degree of freedom right?

[tardy ruin]

16x + 20y = 15

[plush egret]

say the factory was running for one hour, and you made 1 case of 16oz cups

16 👀

i dont know why you are using these numbers

16 and 20

why

[tardy ruin]

Wait

It’s x+ y =15

No numbers

[plush egret]

you gotta remember like

i mean all the worry about 16 and 20oz

thats baked into defining the variables

now were playing the job of translators

yea x+y=15

[tardy ruin]

Ye

[plush egret]

this is how you translate "we can only make 15 cases an hour"

using our variables

so this is true 8 times in a row

yea?

[tardy ruin]

I remembered with equations u need to do x+y= number

First

Then other equation u put the numbers in right

[plush egret]

thats not necessarily true i mean

[tardy ruin]

But for this one it is

Certain problems

[plush egret]

yea

i mean the important part is x+y=15 defines a relationship between the important variables yea?

[tardy ruin]

Ye

[plush egret]

we can choose x and y

but theyre related in ways defined by the problem

these equations dont necessarily have to take any form just by uhm

[tardy ruin]

So X + y= 15 is first equation

[plush egret]

just by virtue of being in a word problem

well, this is for 1 hour

the problem is not asking for 1 hour

[tardy ruin]

Ye it’s asking for 8

So do I do another equation below it?

[plush egret]

this is where i think

i think we may change the variables a little bit

to working day

instead of hour

because looking at these problems like

...in 8 hours

...used per day

i dont see a lot of mention of things changing per hour

so maybe we dont need that much resolution

per day (or per 8 hours) should be fine

make sense?

[tardy ruin]

Kind of

So I change the variables coefficients or..

[plush egret]

let x be the number of cases of 16oz cups that the factory produces in 1 hour

change this to not for 1 hour, but for 8 hours

or you may say in a working day

[tardy ruin]

So let x be the # of cases of 16oz Cups that the factory produces in 8 hours

[plush egret]

yea

this makes it way more straightforward yea

[tardy ruin]

So would I multiply 15 by 8

[plush egret]

you would 😄

[tardy ruin]

To get the 8 hours

[plush egret]

exactly, yea

[tardy ruin]

So it’s x+y = 120

[plush egret]

,calc 15*8

[glossy valve]

Result:

120

[plush egret]

woo

[tardy ruin]

Ohhh

So the equation would be for that first question

[plush egret]

yea

[tardy ruin]

X+y = 120

[plush egret]

i think so, yea

[tardy ruin]

Ohhh that makes sense

So onto the next question

For resin

I know 2 different measurements

Units*

18lbs and 14 lbs

[plush egret]

so this is another case where like

i think instead of just writing 18lbs

i mean even if its only for yourself

it may help to be clear

18lbs of what? for what? per what?

might help decipher what role its gonna play

in the equation

[tardy ruin]

18 lbs of plastic resin per case of 20 oz

Cups

[plush egret]

so we use 18lbs of plastic resin per case 20oz cups we make

[tardy ruin]

Yup

[plush egret]

and Y is the number of cases of 20oz cups we made in one working day

[tardy ruin]

Ye

[plush egret]

so how many lbs of plastic resin do we use making 20oz cups in one working day?

[tardy ruin]

So it would be 18lbs x 120

Since 120 is cases in a day

[plush egret]

120?

We use 18lbs of resin for each case of 20oz cups right

[tardy ruin]

Ye

[plush egret]

how do you know were making 120 cases of 20 oz cups

in a day

[tardy ruin]

Because 15 x 8 = 120

Since it’s 15 per hour

[plush egret]

how do you know its 15 cases of 20oz cups each hour

[tardy ruin]

It says it in the problem

[plush egret]

Where?

"About 15 cases of either product can be produced per hour"

[tardy ruin]

Oh

So wait can you rephrase that

[plush egret]

rephrase what?

[tardy ruin]

So 15 case of either product per hour

[plush egret]

yup

each hour, the factory, working at full steam

pops out 15 cases of cups

the factory doesnt care which kind of cup ('either product')

[tardy ruin]

Ye

[plush egret]

but you arent getting more than 15 cases out each hour

[tardy ruin]

Ohhhhh

I get it

We don’t know how many cases of 20oz cups are being produced each our

And that’s what we need to find

[plush egret]

well we dont need to find it

this problem is weird like

we can get a number

you actually almost accidentally got the right answer

but youre cheating yourself if you get it by accident 😄

[tardy ruin]

Yen

I wanna learn how

[plush egret]

so

[tardy ruin]

Cause cheating it would help on test

[plush egret]

haha

[tardy ruin]

Lol

So how do I put it in equation

Like another hint lol

[plush egret]

15 cases an hour, yea

[tardy ruin]

Ye

[plush egret]

you have that previous equation

x+y=120

[tardy ruin]

Yea

[plush egret]

so we got sidetracked actually, i was askin this one question

we use 18 lbs of resin to make each case of 20oz cups

[tardy ruin]

So would it be X + y = 15

[plush egret]

and Y is the number of cases of 20oz cups we make in one day

[tardy ruin]

Oh wait

[plush egret]

so how many pounds of resin do we use each day in making 20 oz cups

in terms of y

[tardy ruin]

18lbs

[plush egret]

in terms of y

we dont only use 18 lbs a day

it changes with many cases of 20 oz cups we make

[tardy ruin]

18y

[plush egret]

yea

how about for the 16oz cups?

each case uses 14lbs, right?

[tardy ruin]

So it would be 14x + 18y = 15

[plush egret]

why 15

[tardy ruin]

15 cases per hour

[plush egret]

that side of the equation is very far off

x and y are per working day right

[tardy ruin]

Ye

[plush egret]

so even if that was right itd be off by a factor of 8

but its not right

[tardy ruin]

Wait so do I times them all by 8

[plush egret]

no

[tardy ruin]

I’m confused

[plush egret]

explain to me what is 14x

what is representing

what physical quantity

[tardy ruin]

It represents the lbs needed per case

[plush egret]

thats just the 14

14lbs needed per case of 16oz cups

what is 14*x

[tardy ruin]

Ye

[plush egret]

we take 14

[tardy ruin]

Times by x

[plush egret]

multiply it by how many cases of 16oz cups we made in a day

what physical quantity are we talking about

[tardy ruin]

Wait is it

1800

[plush egret]

like if i make x dollars an hour, and i work 5 hours, then 5x represents the physical quantity of how much money im making

is what 1800

[tardy ruin]

After the =

1800

[plush egret]

lol type out the equation

[tardy ruin]

18x + 14y = 1800

[plush egret]

yea, with one uhh

[tardy ruin]

One what?

[plush egret]

youve done a switcheroo

[tardy ruin]

Wait

So do I switch one of them around with another

[plush egret]

what is x?

cases of 16oz cups right

per day

[tardy ruin]

Ye

[plush egret]

and y is the same but 20oz cups

[tardy ruin]

Ye

[plush egret]

so why do you have 14 with y

[tardy ruin]

Ohhhh

It’s 14x + 18y = 1800

Right?

[plush egret]

and yea

i did wanna say like

[tardy ruin]

Ohhh

[plush egret]

so theproblem implies that 14x+18y <= 1800

right?

"at most 1800 lbs per day"

[tardy ruin]

My mind jumped and paired variables without wrong numbers

[plush egret]

but the answer to that question

is equals

because thats the most

does that make sense?

[tardy ruin]

Ye

[plush egret]

its a similar thing with the 120 part

the problem implies a range but

hopefully that part is pretty straightforward

but really the equations the problem implies are actually inequalities

[tardy ruin]

Wait so do I keep it as is and don’t add <

[plush egret]

but the prompts are asking for equations so

yup

[tardy ruin]

Ok

[plush egret]

well the prompt is asking for maximum

[tardy ruin]

But I understand 1800 is maximum per day

[plush egret]

yup

so we wanna be equal

we wanna use all 1800

however we use it

20oz or 16oz

[tardy ruin]

Ok

Ok

[haughty lotus]

Question: compute the total differential of f(x,y,z) = x^2yz
My answer: 2xyzdx+x^2zdy+x^2ydz

is this correct

[tardy ruin]

This chat is occupied

Wait @plush egret sorry for tag but for part c

[haughty lotus]

Can I be next?

[plush egret]

#❓how-to-get-help

[tardy ruin]

Go to available chat

Type in there

[plush egret]

theres so many askers tonight

not enough helpers ever

[tardy ruin]

Ye lol

[plush egret]

but still

better chance of success here than other servers

you ever try to ask on like

reddit or something

youre lucky if someone farts in your general direction

[tardy ruin]

Ye but no one helps

[plush egret]

lol

[tardy ruin]

Lol

[haughty lotus]

so you cannot help me?

[plush egret]

you need to read #❓how-to-get-help

it will tell you what to do

[tardy ruin]

Anyways lol

[plush egret]

ye

[haughty lotus]

I did but no one responded

[plush egret]

you waited literally 5 seconds

[tardy ruin]

I have to wait

😂

[plush egret]

part c makes no sense to me

man

its like

we got two variables right

2 equations

[tardy ruin]

Ye

[plush egret]

whats the problem lol

this is enough to solve

what do they mean versus

[tardy ruin]

Wait so I use both equations

To solve and get 3rd equation for that one

[plush egret]

i dont get what this prompt is asking for or why we need it

you should ask your teacher

2 variables and 2 equations is enough to love a system

solve*

you can solve from here im guessing?

[tardy ruin]

Nah I think it’s a 3 variable question

[plush egret]

its not

[tardy ruin]

Oh

[plush egret]

but convince me i mean

they only give you 2 spaces for variables

i think it might be there to help nudge you towards substitution

[tardy ruin]

But it says 3 equations to write

[plush egret]

yea, ask your teacher

either way, solve the system

you have enough info

[tardy ruin]

But wouldn’t it be wrong if I don’t have 3rd equation

[plush egret]

whats your reasoning for believing this

[tardy ruin]

It says right an equation 3 times

Wait unless

[plush egret]

it also gave you information about money :p

[tardy ruin]

Ye lol

[plush egret]

if the problem also told you for every case of 16oz cups we make, a kitten gets to go outside

would you believe that kittens were important

[tardy ruin]

No

[plush egret]

i think what theyre saying is like

write y in terms of x or x in terms of y like

manipulate an equation to isolate for some variable or another

i think is what its asking?

to sorta prompt you into using substitution to solve

since elimination is sort of strange and not immediately motivated by the equations

[tardy ruin]

Wait so I’m confused lol

[plush egret]

like elimination right

you want a+b=20

and a-b=10

[tardy ruin]

Ye

[plush egret]

if you had equations like this

elimination is really motivated

just add them together, b goes away

our equations have like

plusses

[tardy ruin]

Oh I know that

[plush egret]

and nothing looks immediately like its gonna cancel

[tardy ruin]

But I don’t know what to do for that part tho

[plush egret]

idk

my guess is somehow write x = (something something y)

but im not sure

[tardy ruin]

Oh

Wait

What if I solve them both

Like solve the equations

And then put the answer in part c

[plush egret]

idk exactly what you mean

you can only solve both 1 and 2 at the same time

as a system

[tardy ruin]

Ye that’s what I mean

Solve them as a system

And put the coordinates in c

However it asks for an equation

[plush egret]

idk what to tell you

the solution is straightforward from here

im not sure what 16 oz vs 20oz means

[light sonnet]

FYI user opened a second channel

[plush egret]

but its unnecessary to complete the rest of the problem

[tardy ruin]

Mb

Thought u didn’t know what to do for part c

[plush egret]

its nonsensical

ask your teacher

its also extraneous

solve the system with what you have now

i gotta go to bed

[tardy ruin]

I solve it

[plush egret]

complete the problem then ask your teacher whats the deal with this third part did i miss something

[tardy ruin]

Ok

[plush egret]

anyways

have a good night

[tardy ruin]

I’ll ask around for part c too

Ye u too

Gn

Thx again

Really appreciate it

Good bye 👋

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[tacit swift]

<@&286206848099549185>

[gritty rose]

Chill

• After 15 minutes, feel free to ping @Helpers.

[tacit swift]

ok

sorry sir

[drowsy viper]

recognize that at 10 am the angle sunrays make at the ground is 45 degrees

[tacit swift]

how is that so?

[drowsy viper]

that is because the shadow length is equal to the stick

sticks's length*

stick's

[tacit swift]

oh!

got it

[drowsy viper]

yep

[tacit swift]

tanx = 1

[drowsy viper]

exactly

[tacit swift]

so now the length will be 46tan(120)

right?

which gives me 79.7 cm in the opposite direction?

@drowsy viper

[drowsy viper]

hold on

[tacit swift]

sure

[drowsy viper]

45+75= 120
so the sunrays are 30 degrees (120-90) in the opposite direction
tan(30)=46/x
x=46/tan(30)
x=79.6 cm

[drowsy viper]

yep

correct

[tacit swift]

thanks mate 🙂 💗

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[torn jolt]

solve the system of equations

[full forum]

@torn jolt Has your question been resolved?

[dense oriole]

what have you done?

[torn jolt]

give me a sec

[brisk nexus]

what is the quesiton

[torn jolt]

solve the system of equations

[torn jolt]

I don't know what am I doing

[brisk nexus]

is that a minus or multiplcation

[torn jolt]

minus

[brisk nexus]

from this we can say that bc-ac-ab=0

[torn jolt]

so how to solve the system of equation?

[brisk nexus]

give me 5 minutes

[torn jolt]

<=> 0=ac+ab-bc

[torn jolt]

ok

[brisk nexus]

maybethatisyourname

[brisk nexus]

you are on path until this

[torn jolt]

what's wrong?

[brisk nexus]

you got the two equations already

add them together

you will get $\frac{2}{y}+\frac{1}{x}+\frac{1}{z}=\frac{1}{a}+\frac{1}{b}$

oh no

sorry

i got the variables mixed up

😅

[torn jolt]

no no

I knew it

[brisk nexus]

did i?

[torn jolt]

nope

wait

[brisk nexus]

nah

i did

it supposd to be 2/y

[torn jolt]

yeah

[glossy valve]

alephcomputer

[brisk nexus]

and you already have $1/c=1/x+1/z$

[glossy valve]

alephcomputer

[brisk nexus]

take this

[brisk nexus]

and subtract by this

[brisk nexus]

which goes to this part

is $1/a+1/b-1/c=2/y$

[glossy valve]

alephcomputer

[brisk nexus]

so $2/y = \frac{bc+ac-ab}{abc}$

[glossy valve]

alephcomputer

[brisk nexus]

now im sure you can do the rest 😄

[torn jolt]

nope, i can't

could you do it, pls?

[brisk nexus]

it'd be better to spend 10-15 minutes to try playing around with what we did so far first

[torn jolt]

ok

thanks btw

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[viral zenith]

Hello!

[viral zenith]

Is a = 8, r = 1/3 and S = 12?

[vast fossil]

First term is 8 and common ratio is 1/3 yeah

And the sum is therefore 12

[gritty rose]

,wolf sum n=1 to infinity 8/(3^(n-1))

[glossy valve]

Results provided by WolframAlpha

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

Requested by riemann#2529

[hollow herald]

@viral zenith

[viral zenith]

Yay

I’m not dumb

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[vast fossil]

The angles of both triangles are the same

[last sparrow]

so this is a bit of similarity, basically the question makes it so that the triangle formed by Shiva and the lighthouse are similar

^ and then because of similarity, the sides are in proportion

and so they are in equal ratios

[vast fossil]

Set ratios of the corresponding side lengths equal

h/1.6 = 75/4.8

[last sparrow]

like, find h

which is what the question is asking for

[vast fossil]

Multiply both sides of the equation by 1.6 and notice that 1.6 cancels with 4.8 (4.8 = 3*1.6)

Yes

So h = 75/3

h = 25, that's it

I do not see any way that could help but sure
$\frac{h}{1.6} = \frac{75}{4.8} \ h = \frac{75}{3\cdot{1.6}}\cdot{1.6} = \frac{75}{3} = 25$

[glossy valve]

Beans

[vast fossil]

Found the mistake in LaTeX

This is the solution

Yes

[full forum]

@torn jolt Has your question been resolved?

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[ocean thunder]

I have to connect these curves together. There are three pairs of sine curves and their respective spectrum. Sine curves are marked as follows: Red, green, and blue curves are individual, pure sines, while the black curve is the sum of the three aforementioned. I don't know how I can connect the sine curves with their respective spectrums. Please help me to understand the assignment.

[ocean thunder]

<@&286206848099549185>

<@&286206848099549185>

[full forum]

@ocean thunder Has your question been resolved?

[ocean thunder]

<@&286206848099549185>

<@&286206848099549185>

[slender onyx]

chill with the pings

[torn jolt]

I'm not really sure how to do the calculation, but this requires merging the different frequencies of the wave into one, meaning doing a fourier transform.

If I understood the question correctly

[fading steeple]

if i understand the question right that's also the black line

op needs to convert time to frequency

offhand i can't remember how to do that though

[full forum]

@ocean thunder Has your question been resolved?

[ocean thunder]

Thank you guys ❤️

[torn jolt]

Np

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[torn jolt]

Hello

[torn jolt]

For the problem number 6, do we need exact answer like given on the book? Or we can simplify it our own way.

[vast fossil]

Well I mean yeah as long as your answer is equivalent to the answer in the book

[torn jolt]

Got it.

And sorry for one stupid question:

In problem number 11, I got the answer like a book.

But why can't we multiply x with cos x?

[vast fossil]

Wdym by that

[torn jolt]

For the 11th question, we have answer:

xcosx + sinx

Now for further simplification, can we multiply x and cosx?

[vast fossil]

Still can't see what you mean, x and cosx are being multiplied here

[torn jolt]

Ohh. I realized what mistake I was doing.

Sorry

Thank you for being patient with me.

.close

[full forum]

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[vagrant ravine]

how would i show this?

[vagrant ravine]

using these properties

i know it should apply the telescoping property, but i don't know how i owuld split x^k

[vast fossil]

You could either factor 1 - x^(n + 1)

Or prove it by induction

[vagrant ravine]

hm? could you show me how that would work?

i don't think ive seen factoring like that

[vast fossil]

1 - x^(n + 1) = (1 - x)(x^n + x^(n - 1) + x^(n - 2) + ... + x + 1)

[vagrant ravine]

how does the n get into the exponent? is there a property of sums im missing?

[vast fossil]

Pretty famous factoring trick

But I think you'd need to use induction

In order to use the properties

[vagrant ravine]

alright

ill try using mathematical induction rn

[vagrant ravine]

ive never seen it before

im assuming that's what they meant by the hint?

[vast fossil]

Oh yeah

That's the factoring I mentioned

[vagrant ravine]

hmm i looked at the solution to see whether that was the method used, and this is what it said

i don't really see what happened though

is there some formula for changing the k = 0 to k = 1

[vast fossil]

Which step is confusing you?

[vast fossil]

That's just shifting

All they did was write

$-\sum_{k=1}^n(x^{k+1}-x^k)$ as $-\sum_{k=1}^nx^{k+1}+\sum_{k=1}^nx^k$

[glossy valve]

Beans

[vast fossil]

$x^{k + 1}$ is just $x^k\cdot{x}$

[glossy valve]

Beans

[vast fossil]

And they just factored out the x

So that it'd be $-x\sum_{k=1}^nx^{k}+\sum_{k=1}^nx^k$

[glossy valve]

Beans

[vast fossil]

Which is just $(1 - x)\sum_{k=1}^nx^k$

[glossy valve]

Beans

[vagrant ravine]

i understand that part, but what i'm confused about is how $\sum_{k=0}^{n} x^k = -\sum _{k=1}^{n} (x^{k+1} - x^k)$

[glossy valve]

sean

[vast fossil]

They simply solved for the sum of x^k from 2nd line

[vagrant ravine]

i understand what happened after

[vast fossil]

Divided both sides by (1 - x) and then x

So they had $\sum_{k=1}^nx^{k - 1}$ which is the same as $\sum_{k=0}^nx^k$

If you don't see why this is true, consider writing out the sum without the sum notation

[glossy valve]

Beans

[vagrant ravine]

right lemme take a second to try and understand this, ill try write everything down and work it out like that myself

okay

i got mostly everything

but

im still confused on how to change the k=1 to k=0

i got to $\sum_{k=1}^n x^k = \frac{x(1-x^n)}{1-x}$

[glossy valve]

sean

[vagrant ravine]

now all i need to do is change that k=1 to k=0

oh wait

[hollow herald]

btw, the last problem you asked about... the "non-rigor" way was to go:

$$\sum_{k=1}^n (2k-1) = \sum_{k=1}^n [k^2 - (k-1)^2] = \sum_{k=1}^n k^2 - \sum_{k=1}^n (k-1)^2 = \sum_{k=1}^n k^2 - \sum_{k=1}^{n-1} k^2$$

$$= n^2$$

[glossy valve]

Ansh

[vagrant ravine]

oh yeah i got that problem

i just used the telescoping property

turns out that was very easy to do

alright i found out how everything works now

but i have one last confusion (sorry haha, thanks for being patient)

[hollow herald]

np

[vagrant ravine]

so i found that $\sum_{k=0}^n x^k = 1 + \sum_{k=1}^n x^k$, now I need to put the 1 into the sum to change $1+ \sum_{k=1}^n x^k \implies \sum_{k=1}^n x^k - x^{k+1}$

[glossy valve]

sean

[vagrant ravine]

and i don't understand how to put the 1 back into the sum

[full forum]

@vagrant ravine Has your question been resolved?

[hollow herald]

that makes zero sense to me tbh

[tulip marlin]

Notice $x^0=1$

[glossy valve]

Shuri2060

[vagrant ravine]

how would i use this though?

[hollow herald]

You don't

You use sum of geometric series

[tulip marlin]

huh?

i thought they wanted to stick it into the sum

[vagrant ravine]

uhh i haven't learned that yet

[hollow herald]

Okay?

[vagrant ravine]

yeah

[tulip marlin]

oh nvm they took it out the sum...

[hollow herald]

(1 - x)*(1 + x + x^2 + x^3) = (1 - x^4) is something you need to learn?

even if it is... the hint is given in your textbook

Just try taking the product of (1 - x) and the sum you need to simplify

[vagrant ravine]

i don't understand, why does this come out here?

never mind

i found it

alright thanks, i didn't know about this formula

[river ivy]

Are bro

What about my question

Find c

AB-10

[full forum]

@vagrant ravine Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
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[torn jolt]

Dr. Gorgonzola has a bank account that has an annual interest rate of 6 percent, but it compounds monthly. If this is equivalent to a bank account that compounds annually at a rate of $r$ percent, then what is $r$? (Give your answer to the nearest hundredth.)

[glossy valve]

crabbo

[torn jolt]

is the answer 0.06*12=0.72?

[hot herald]

no

[torn jolt]

hmmm

why not?

should it be 0.06/12?

[hot herald]

no

[hollow geode]

#❓how-to-get-help

[hearty latch]

So u guys know how to do this 😭

[hot herald]

your work should resemble an application of equations related to compound interest

currently it just looks like your randomly choosing values given in the question and multiplying or dividing them
with no idea what it'll actually give you

[torn jolt]

P(1+c)^n

fir compound interest

c in this case is

0.06

[hot herald]

no

[torn jolt]

P(1+0.06)^n

[torn jolt]

the percent

[hot herald]

0.06 is the nominal rate

you interested in what happens if

annual interest rate of 6 percent, but it compounds monthly

[torn jolt]

you would divide by 12 i believe

[hot herald]

for that part yes.
what about your n

[torn jolt]

divide by 12 aas well

but we only care about the percent, r, @hot herald

[hot herald]

r represents the effective rate after 1 year of compounding monthly

dividing 0.06 by 12 only gets you the monthly compounded rate

[torn jolt]

Dr. Gorgonzola has a bank account that has an annual interest rate of 6 percent, but it compounds monthly.

i dont really understand this

[hot herald]

6% is the nominal rate (doesn't account for stuff like compounding)

dividing that by 12 gives you the monthly rate and if compounded monthly that's how much you're investment will increase by every month

i.e. each month the investment increases by 6%/12

[torn jolt]

ok

If this is equivalent to a bank account that compounds annually at a rate of $r$ percent, then what is $r$?

[glossy valve]

crabbo

[torn jolt]

how can we find r

[hot herald]

after finding the monthly compound rate the question pretty much reduces to finding the % gain after a year if your investment is compounded monthly at a rate of $\frac{6}{12}$% per month

[glossy valve]

ℝamonov

[hot herald]

(you can find r using the compound interest formula, applying the appropriate values)

you should expect a result to be a little higher than 6%

[torn jolt]

hmmm

P(1+c*12)^(n*12)

[hot herald]

no

[torn jolt]

hmm

[hot herald]

start with searching/writing up the compound interest formula along with all the things the variables in that formula represent

[torn jolt]

Compounded monthly:
P(1+6/12%)^n/12

[hot herald]

start with searching/writing up the compound interest formula along with all the things the variables in that formula represent

(instead of jumping ahead doing some hidden stuff behind the scenes and ultimately give something wrong)

[torn jolt]

P(1+6/12)^(n*12)

[hot herald]

where's n/12 coming from

[torn jolt]

i meant n*12

[hot herald]

is also wrong

try identifying the values represented by
r
n
t
in the image you posted

[torn jolt]

r=6/12?

[hot herald]

no

[torn jolt]

r=6/12%

[hot herald]

no

[torn jolt]

what happened to what we came up with

[hot herald]

wdym

[torn jolt]

this

[hot herald]

that isn't the same as what r represents in the image you posted

forget about how the variables were previously used

focus on how they defined them in the formula

[torn jolt]

is it just 6%

[hot herald]

yes

and then identify your
n
and
t

[torn jolt]

i believe n is 12

and we dont know t in this problem

[hot herald]

n is 12,

t is known

you're interested in what happens after 1 year

[torn jolt]

ah right

so t is 1

[hot herald]

yes

[torn jolt]

if we plug this in we get
$P(1+\frac{6%}{12})^{12*1}$

[hot herald]

\%

[torn jolt]

ah

[glossy valve]

crabbo

[torn jolt]

what is r in this expression?

[hot herald]

evaluate

[torn jolt]

evaluate what

we dont know P

[hot herald]

evaluate the stuff after P

[exotic wave]

Any helpers here?

Im new to the server

Does anyone here know discrete math/proofs

[hollow geode]

#❓how-to-get-help

[full forum]

@torn jolt Has your question been resolved?

[onyx glen]

@torn jolt are you still here

[torn jolt]

sorry

im here

i was doing something

im going to evaluate now

[onyx glen]

hopefully you're not doing it by hand

and instead running it through a calculator

which should not take you longer than the amount of time to key in all the numbers

[torn jolt]

i would never

[onyx glen]

ok great

are you able to answer the question posed by the problem now?

[torn jolt]

1.06 is the answer i assume

[onyx glen]

no

If this is equivalent to a bank account that compounds annually at a rate of r percent, then what is r?

right now what you're saying is that 6% p.a. compounded once a month is almost six times worse than compounding once a year, i.e. that it's as if you had only had a 1ish% annual interest rate

[torn jolt]

106%

[onyx glen]

oh, so now you're saying a 6% rate turns into a "double your money in 1 year" scheme?

[torn jolt]

i just turned it into a percent

did i mess up my math or something?

[onyx glen]

i think you messed up your conceptual understanding of how interest works

or how percentages work

or the relationship between multiplication by <number> and increase by <number>%

[torn jolt]

what is the result representing

[onyx glen]

that's the question i should be asking you

what does the result of that calculation represent?

[torn jolt]

the total amount of interest

rate

idk

[onyx glen]

do you know how compound interest works conceptually

[torn jolt]

yes

[onyx glen]

okay, explain it in your own words then

[torn jolt]

bank gives a an interest rate

every years, you add to your initial amount

the interest percent of that amount

for the next year, you do the same, but to the new amount

thats it

[onyx glen]

every year, the bank adds into your account a certain percentage of the money already in the account

or to put it another way, the bank multiplies the money in your account by a certain factor

for compounding more frequent than annual, this happens once every compounding period as opposed to once every year

if you look at the ccompound interest formula, you can see that the principal is multiplied by a factor that depends on the rate, time and compounding freq

and in your case you have computed this factor to be 1.061677812

multiplication by 1.061677812 is equivalent to a ___ percent increase

fill in the blank

[torn jolt]

i dont know how to fill it in

106% was wrong

wait

is it a 6% increae?

[onyx glen]

you're rounding too crudely

reread the problem, look again how you're asked to round your answer (if at all), and round it appropriately.

[torn jolt]

nearest hundred

[onyx glen]

no

you are not asked to round r to the nearest 100.

[torn jolt]

so 0?

[onyx glen]

???

are you even reading what i am saying?

[torn jolt]

nearest hundreth

1.06

[hot herald]

multiplication by 1.061677812 is equivalent to a ___ percent increase
fill in the blank

[torn jolt]

106%

idk

[hot herald]

lets try something else,
lets say i wanted to increase something by 50%,
what decimal value would you multiply by?

[torn jolt]

1.5

[hot herald]

and if something was multiplied by 1.5, what will be the % increase

[torn jolt]

150%

[hot herald]

no

reread what's being asked carefully

your last two responses are contradictory

you said that to increase something by 50% you'd multiply by 1.5
and then subsequently implied that multiplying something by 1.5 increases it by 150%

which also implies that multiplying by 1 increases something by 100%, (i.e. doubles its value)
(which is clearly wrong)

[torn jolt]

50%

[hot herald]

yes

[torn jolt]

so the answer for the original is 6% increase

[hot herald]

no

[torn jolt]

why not

[hot herald]

you're rounding too crudely

[torn jolt]

how am i rounding too crudely

what does it mean to round crudely

[hot herald]

they want you to round the % to the nearest hundredth

NOT round 1.061677812 to the nearest hundredth and the convert to the % increase

and in your case you have computed this factor to be 1.061677812
multiplication by 1.061677812 is equivalent to a ___ percent increase
fill in the blank
and don't do any rounding

would you be able to do that

[torn jolt]

6.1677812%

[hot herald]

and then round that value to the nearest hundredth

[torn jolt]

6.17

[hot herald]

%

yes

[torn jolt]

cool that worked

[onyx glen]

yeah

see how it works when you actually listen to what people tell you to do

[torn jolt]

more like i wasnt understanding what people were telling me

[gritty rose]

clearly ann meant round to the nearest 100 decimal places

[torn jolt]

lol

Sue can either borrow $10,!000$ dollars for $5$ years with a simple interest of $7%$ annually or an interest which compounds annually for $6%$. How much more money, rounded to the nearest dollar, would she have to pay back for the more expensive interest than the less expensive interest?

did i do this correctly?

[glossy valve]

crabbo

[gritty rose]

what's n and t in your question, for the "compounds annually" formula

[torn jolt]

n is 1

t is 5

[gritty rose]

looks good

[torn jolt]

When Lauren was born on January 1, 1990, her grandparents put $$1000$ in a savings account in her name. The account earned $7.5%$ annual interest compounded quarterly every three months. To the nearest dollar, how much money was in her account when she turned two?

[glossy valve]

crabbo

[torn jolt]

what does

The account earned $7.5%$ annual interest compounded quarterly every three months.
mean?

[glossy valve]

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

[hot herald]

the idea is the same as the previous questions

instead of being compounded monthly or yearly, its compounding every 3 months

[torn jolt]

i see

so

1160 is the answer then

right?

.close

[full forum]

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• 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>.
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[grave crescent]

I am not sure how to do this. When using a trial function to get the particular integral the unknowns all cancel out and when I try get the particular solution with just the complementary function I get 0?

[full forum]

@grave crescent Has your question been resolved?

[grave crescent]

<@&286206848099549185>

[gritty rose]

what have you tried?

[grave crescent]

i can send my workings

i tried using psin5x + q cos5x as the trial function

but the ps and qs all cancelled out so i got 0 = 0.5sin5t

[gritty rose]

guessing and checking sometimes works

you should review this if you haven't seen ODEs in a while
https://math24.net/second-order-linear-nonhomogeneous-differential-equations-constant-coefficients.html

you have this

[grave crescent]

yeh

[gritty rose]

you want to apply this theorem

[grave crescent]

yeh

[gritty rose]

Using 2. here

[grave crescent]

the issue was when i was trying to get the particular solution

this was my workings

[gritty rose]

separation of variables yea?

uh i'm not gonna open files

just screen shot it

[grave crescent]

ok wait

it is shm though so the general solution is different right

[gritty rose]

your mistake

[grave crescent]

whats wrong with it?

[gritty rose]

oh wait i couldn't read your handwriting

that's a 25 not a 2h

[grave crescent]

oh sorry my bad

[gritty rose]

the rest looks good

[grave crescent]

u reckon its like a prank

and A is meant to be 0

[gritty rose]

intuitively makes sense to me

[grave crescent]

and B is 0

[gritty rose]

if you don't provide a force, then a spring doesn't move from rest

the force is the right hand side

[grave crescent]

yeh

[gritty rose]

probably could have reasoned that without math but you did it already

[grave crescent]

i did think that

but idk if they exam people are that big balled enough to do that for a question

thats why i thought i did something wrong

[hollow herald]

,w solve y'' + 25y = 0.5 sin 5x

:|

[grave crescent]

yo what is this

[hollow herald]

what is this behaviour >_<

[grave crescent]

btw its sin5x

[glossy valve]

Results provided by WolframAlpha

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

Requested by Ansh#3502

[hollow herald]

y(0) = 0 => c1=0

lol

[grave crescent]

@hollow herald ngl, u lost me

[gritty rose]

handwriting for the loss

[hollow herald]

(@_@;) Is this the wrong solution?

[grave crescent]

err idk at this point

it might be right tbh

i just dont know how u get there

[hollow herald]

bruhhhh mathlamar is the best site for ODE afaik

this one won't even explain how to deal with p and q

;-;

[gritty rose]

never heard of it 🤔

[hollow herald]

https://tutorial.math.lamar.edu/Classes/DE/ComplexRoots.aspx =_=

[gritty rose]

oh ok that i know

more examples for you to review
https://tutorial.math.lamar.edu/classes/de/UndeterminedCoefficients.aspx

[gritty rose]

what makes you think wolf is wrong?

[hollow herald]

your comment -_-

and my ineptness

[gritty rose]

which one? i did make a mistake earlier since i read something wrong

[hollow herald]

Alright I got the gist of it

[hollow herald]

Oiiiiiiiii

$x_c = A \sin 5t + B \cos 5t$ is only a general solution

[glossy valve]

Ansh

[grave crescent]

wait

wdym

[hollow herald]

Since your differential equation is of the form:

$$y'' + p(t)y' +q(t)y = g(t)$$

[glossy valve]

Ansh

[hollow herald]

and not just the usual, $y'' + p(t)y' +q(t)y=0$

[gritty rose]

"general" is the same as "particular"

[glossy valve]

Ansh

[hollow herald]

the solution of y( ) you found is only the general solution to the equation

[hollow herald]

no it's not -_- particular solution is esp. introduced for the g(t)

[gritty rose]

substitute $ Q_m(x) = 0.5$ and $\sin(\beta x) = \sin(5 t)$

[glossy valve]

riemann

[grave crescent]

yeh i have the general solution

[gritty rose]

you're right! i'll delete

[hollow herald]

Yes

[grave crescent]

its the particular integral

[hollow herald]

Now find the particular solution to the differential equation

[grave crescent]

the issue is

when i put the conditions in

i get a and b as 0

[hollow herald]

what is your expression for "x(t)"?

[gritty rose]

i think he found it in his image already

[hollow herald]

Lemme check -,- wolfy isn't wrong

[grave crescent]

this was my workings btw @hollow herald

[hollow herald]

So you couldn't find any p and q for which your trial function existed, and you decided to ignore that part? (@_@;)

[grave crescent]

well the p and q cancelled out

so i didnt know what to do

[hollow herald]

so you at least know what you're missing right?

[grave crescent]

yeh kinda

the particular integral

but idk how to get it now

[hollow herald]

how about checking trial function px sin5x + qsin 5x?

[grave crescent]

cause usually u can compare coefficients

[grave crescent]

only px?

[hollow herald]

nope px(sin 5x) + q sin5x

[grave crescent]

ah ok