help-26

[lunar pond]

yes

[winged roost]

so you ended with

$\frac{1-x}{x^2+3x+2} \leq 0$

[thorny flame]

IntelligentCake

[winged roost]

yes?

[lunar pond]

yes

when i get x ^ 2 in a fraction or equation i get confused

[winged roost]

right

well I suggest first you start off by not expanding that denominator

it well help with the solution

$\frac{1-x}{(x+1)(x+2)} \leq 0$

[thorny flame]

IntelligentCake

[winged roost]

so this is what you have

first look at numerator

[lunar pond]

ohh

(x+1) (x+2) != 0

i should make a table

[winged roost]

you want to look at when the numerator becomes negative

and when the denominator becomes negative

[lunar pond]

i use table to make it simpler 🙂

[winged roost]

whatever works for you

[lunar pond]

microsoft math hardly disagree with :/

$\x\in (-2,-1)\cup [1,\infty)

$\ x\in (-2,-1)\cup [1,\infty)

Uh

Microsoft says x is in this

[slow sapphire]

$\ x\in (-2,-1)\cup [1,\infty)$

[thorny flame]

Toxstxr

[lunar pond]

Yes 👍👍

Ohh

I solved it correctly

It should be negative

Does microsoft round numbers?

-1.5 is a solution for me

Works

.close

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[lunar pond]

.reopen

[topaz sinew]

✅

[lunar pond]

Thx 👍👍

.close

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[regal cypress]

anyone able to help me with this question? not able to show how the radius of the smaller circle is 1.25 cm.

[elder rampart]

draw BW

[regal cypress]

BW would be 5 no?

[elder rampart]

yeah

then what would BX be

if you call the small radius r

[regal cypress]

hm?

[elder rampart]

BW = BX + XW right?

[regal cypress]

yeah

[elder rampart]

if we assume that XW (the radius of the small circle) is r

[regal cypress]

yep

[elder rampart]

then BX must be 5-r

[regal cypress]

yeah but what do we do with that info

since we know we can get anotehr equation which is 5 + r = AX or CX

[elder rampart]

what else can we say about BX in the triangle ACX

[regal cypress]

its the height

[elder rampart]

exactly

now we can use Pythagorean Theorem

[regal cypress]

eh?

(5+r)^2 = (5-r)^2 + 5^2?

AH

gotcha

thanks alot fam

[elder rampart]

[regal cypress]

👍

[elder rampart]

yw

good luck with the rest of the worksheet

[regal cypress]

yep will do

thanks alot

just got stumped on that one question

tqtq

have a good day ahead man!

[elder rampart]

u2

[regal cypress]

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[chrome forge]

I dont understand how the answer will be year 2024, I had gotten 2023 as my final answer

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[chrome forge]

<@&286206848099549185>

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[junior sand]

is this correct

[keen venture]

You're missing a solution by dividing by cos(x)

Factoring is the safer option

[junior sand]

how do I factor it

[loud dawn]

\begin{align*}
2\sin x \cos x - \cos x = 0\
\cos x (2 \sin x - 1) = 0\
\cos x = 0 \quad\text{or}\quad 2\sin x - 1 = 0
\end{align*}

[thorny flame]

a.b.s._.0.

[loud dawn]

@junior sand

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[onyx vessel]

so for this question i kinda need to exaplain

this is the formula that we used

so i intergrated it to get x(t)

which is

and now i have to get a(t)

im not sure how do i have to intergrate it again ?

[topaz sinew]

@onyx vessel Has your question been resolved?

[onyx vessel]

<@&286206848099549185>

[maiden igloo]

why do u have to integrate it

[empty sail]

Derivative of position is velocity, derivative of velocity is acceleration
Integral of acceleration is velocity, integral of velocity is position

[onyx vessel]

The question before asked me to intergrate in order to find postion as a function of time

[maiden igloo]

fair enough

[onyx vessel]

would it not be 1 - e ^ -t/tmaxspeed

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[topaz sinew]

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[granite ivy]

Do rational functions have a special feature with what they look like?

[sweet shard]

Look up the definition of rational function

There's nothing special, just definition

[granite ivy]

oh

i already know the definition

[sweet shard]

What is it

[granite ivy]

Its a function that looks like a fraction and it has two polynomials

thanks

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[young walrus]

hello! Id like some help with this example question. I can see the answer but I don’t know how they arrived to it. I dont think it makes sense to me that :
25x^2 + px + 16 = (5x + 4)^2

[young walrus]

it seems to have left px out of the answer like it just dissapeared. Is this an error of my understanding or an error in the question?

[empty sail]

Error in your understanding

[restive inlet]

probs your understanding

[empty sail]

It's saying that 25x^2 + px + 16 is a perfect square, and as it stated, polynomials in the form of (x + a)^2 are the form of perfect squares, so you take 25x^2 + px + 16 and square root the first term and the last, and that's how it got the right side

[young walrus]

sorry I still don’t understand

in the answer, there is no such px

i just

[empty sail]

Do you know what it means to be a perfect square?

[young walrus]

yes

i understand why (a+b)^2 = a^2 + 2ab + b^2

[empty sail]

So then 25x^2 + px + 16 is a perfect square polynomial, correct?

[young walrus]

25x^2 and 16 is , yes

and its telling me that px is too

my problem is that

[empty sail]

No it's not

[young walrus]

its notb

?

[empty sail]

It's not saying that px is a perfect square

[young walrus]

sorry let me explain my thought process so you’ll see where im going wrong

[empty sail]

Look at the example above that green box, is 12x a perfect square?

[young walrus]

no, i don’t think it is

[young walrus]

anyway illcontinute

so

[young walrus]

25x^2 + 16 = (5x+4)^2 , correct?

[restive inlet]

no

that is contradictory to

i understand why (a+b)^2 = a^2 + 2ab + b^2

[empty sail]

25x^2 + px + 16 = (5x+4)^2

[young walrus]

wait

[empty sail]

You're trying to find what p is

[young walrus]

25x^2 = (5x)^2 right?

[restive inlet]

yes

[young walrus]

and if 16 = (4)^2

[restive inlet]

not if

[young walrus]

then surely

[empty sail]

So because that's a perfect square, you can "simplify" the left side 25x^2 + px + 16, to be the right side, (5x+4)^2. Then you expand the right side to determine what the value of p is

[restive inlet]

16 is definitely equal to 4^2

[young walrus]

tell me one thing, is this correct ? (5x)^2 + (4)^2 = (5x+4)^2

[restive inlet]

no

that is contradictory to
i understand why (a+b)^2 = a^2 + 2ab + b^2

you wouldn't say (a+b) is a^2 + b^2 would you

[young walrus]

hmm

[restive inlet]

if you're making this mistake then you don't really see how

(a+b)^2 = a^2 + 2ab + b^2

it doesn't matter what a,b are

to potentially make it clearer for yourself

[young walrus]

oh hold on

I see

[restive inlet]

expand out (5x+4)^2
using the method they used at the top of the page

[young walrus]

I understood this but i wasn’t applying it to this equation

okay

ill try

im beginning to see where this is going

[young walrus]

okay, so I understand how 25x^2 + 40x + 16 = (5x+4)^2

but i just didn’t understand how they got to this conclusing by saying
25x^2 + px + 16 = (5x+4)^2

[empty sail]

Perfect square concept

[young walrus]

thank you for being patient with me btw

i umm

[empty sail]

p is an unknown you are looking for

So applying the perfect square concept, 25x^2 + px + 16 will became (5x+4)^2

[restive inlet]

well your binomial will need to have 5x and 4 so that when squared will give you the
25x^2 and 16 (in addition to a third term)

[empty sail]

And p is indirectly hidden in (5x+4)^2 and when you expanded (5x+4)^2, you determined what p is

[young walrus]

hmm

indirectly hidden

[restive inlet]

you really need to fully grasp

(a+b)^2 = a^2 + 2ab + b^2

[young walrus]

I swear I understand why that is the case

(a+b)^2 = (a+b)(a+b)

then expanding that gives you the answer you gave

here, 40x is the P we were looking for, i see that

p = 40 as a result

could you make up a question in this style and ill see if I can solve it?

i think i understand now

[winged roost]

,rotate

[young walrus]

okay im fairly sure I understand most of it

[winged roost]

do you still need help?

[young walrus]

could you help with questions 3?

ive only introduced myself to polynomials today, so I don’t know the exact definitions of it.

[winged roost]

polynomials must have integer exponentiation

go from there

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[neon iron]

can someone help me find the value of a, k, d ,c

[neon iron]

well i know that c=+4

idk abt a k d

[mighty epoch]

where and what the hell is a,k,d,c?

[neon iron]

It is transformation of exponential functions

like

Like this

[loud ingot]

I have no idea but just based on your example answer, imma say a=-3, k=1, d=1

[neon iron]

oh alright

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[foggy prawn]

how to find inverse tan of a degree or radian?

[foggy prawn]

the formula for the integral of e^x uis e^u * u' right?

[tulip light]

you use inverse tan on the ratio to get the angle

[foggy prawn]

so inverse tan of 0 would be 0 right?

at 0 we have (1, 0)

tan 0 is 0

since y/x = 0/1 = 0

[tulip light]

yeah

in general with $\tan^{-1}(\frac{a}{b})$ you can draw the triangle and plug the numbers

to see if it's a special triangle

or any angle you recognize

[thorny flame]

Doggo

[tulip light]

for inverse tan of 0, the denom can be anything but the opposite side being 0 should be your clue here

[foggy prawn]

<@&286206848099549185>

[topaz sinew]

@foggy prawn Has your question been resolved?

[celest glade]

no

$\int e^{f(x)}dx$ doesn't have a general formula

[thorny flame]

illuminator3

[foggy prawn]

/close

.close

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[chrome hinge]

@tiny sapphire

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[chrome hinge]

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[mild oasis]

Are you trying to check you answer or ask how to solve this?

[bitter pumice]

Check

[mild oasis]

,w (x)/(49 - 14) = 8/14

[thorny flame]

Results provided by WolframAlpha

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

Requested by Pluton#6301

[mild oasis]

Its correct

[bitter pumice]

May I ask another question?

[mild oasis]

Yes

[bitter pumice]

Im pretty sure im correct or its median

[bitter pumice]

^

[mild oasis]

Yey its correct

[bitter pumice]

Am I correct?

[mild oasis]

What is m?

[bitter pumice]

measure

it doesnt mean

anything

just forget it

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[bitter pumice]

<@&286206848099549185>

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[lapis oxide]

if someone could check my working out pls idk why im getting 5

[topaz sinew]

@lapis oxide Has your question been resolved?

[modest quest]

86 ≠ 2x35 + 17

should be +16 not +17

[topaz sinew]

@lapis oxide Has your question been resolved?

[lapis oxide]

oooooooohh my god

[lapis oxide]

thank you so much i cant believe i made such a stupid mistake

[modest quest]

nah dude a few min ago i wrote that 3x8 = 33

i don't even know how i got this far with my brain

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[jovial shoal]

What have you tried?

Did you tried applying what the sum means and using properties of sum?

[vast bluff]

I didnt know how to solve this

Please guide me

47. 45?

[jovial shoal]

$$\sum_{k=0}^95$$ means?

[vast bluff]

48. 4970?

[thorny flame]

BenJr

[vast bluff]

I dont get it

[jovial shoal]

What does the symbol mean?

[vast bluff]

Sigma

[jovial shoal]

Which means?

[vast bluff]

I dont know what

What is 49 and 50?

[jovial shoal]

I will not tell your the answer. Read this for better understanding. https://www.mathsisfun.com/algebra/sigma-notation.html

Me telling you the answer which not help you learn.

[vast bluff]

Give me the formula😭

In a simple way

[vast bluff]

45

[jovial shoal]

It’s not 45 which means the problem is wrong. It’s should start from k = 1.

[vast bluff]

40?

[jovial shoal]

If you understood sums you be able to tell this. Please read the link and use other online resources to understand sums.

[vast bluff]

Whats the formula for 47?

.close

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[neon iron]

804.2477 is what i got but its not an answer choice?

[neon iron]

these are the answer choices

.close

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[knotty ledge]

what have you tried?

[simple orchid]

I'm not sure how to approach this problem

[knotty ledge]

have you learnt implicit differentiation?

[simple orchid]

No

I did watch a video related to it, but I didn't understand

Do you just like go around and ask people if they had tried anything?

[sweet shard]

i mean you're supposed to do that

and there's no point in explaining to you something you don't know

so that's why people helping ask for a baseline of your knowledge

[jovial shoal]

What don’t you understand about implicit differentiation?

[simple orchid]

Well I am supposed to solve these problems

When I have learned until chain rules

[sweet shard]

how would anyone besides you know whether or not you understand implicit differentiation

[simple orchid]

Like how

Where is dy/dx coming from

[jovial shoal]

I give you a better video. Not even sure what that is.

[simple orchid]

Please, thank you

[sweet shard]

chain rule / power rule

[simple orchid]

?

[sweet shard]

a question mark is not useful in explaining where you're confused

[jovial shoal]

Oh I see it now.

I read it wrong.

[simple orchid]

Writing the names of two rules isn't really helpful on what your trying to say

[sweet shard]

it answers your question

[sweet shard]

if you'd bother to remember your question

[simple orchid]

I don't see the relevance

[simple orchid]

How should I do with it?

[jovial shoal]

What was your question again?

[sweet shard]

the exponent is 2

[simple orchid]

All I know about chain rules and power rules didn't went through dy/dx

[sweet shard]

and chain rule comes in because y is a function of x, so dy/dx is just dy/dx

[sweet shard]

didn't went through dy/dx
what does this mean

[simple orchid]

Means that I have never seen dy/dx b4

[sweet shard]

y is a function of x

you don't know what that is yet, so dy/dx = derivative of y with respect to x

[simple orchid]

I'm not sure how to do implicit differentiation

[sweet shard]

https://math.stackexchange.com/questions/340744/what-do-the-symbols-d-dx-and-dy-dx-mean

[simple orchid]

Okay

[jovial shoal]

Try doing what Riemann is saying.

[sweet shard]

and
https://www.math.stonybrook.edu/~tony/archive/calc/97calc1/handouts/dydx.html

[jovial shoal]

Here’s another reference https://youtu.be/xbviQHhU1rA

[simple orchid]

Then should I start by factoring this equation?

[topaz sinew]

@simple orchid Has your question been resolved?

[knotty ledge]

last time I tried to help you, you said this

not sure what you want from people here

[simple orchid]

When I look at other channels, you've only asked them if they have tried, and you sort of go AWOL

[jovial shoal]

y is a function of x, finding derivative of y^2 is done using chain rule.

[simple orchid]

Correct me if I'm wrong, and I'm not here to cause a dissension

[knotty ledge]

bc i have a life outside of this server, and go and do other things, them saying what they have tried will help other people that come along and help them

[jovial shoal]

You differentiate both side of the equation with respect to x.

[simple orchid]

I think I understood that part

[jovial shoal]

Ok so what you stuck on?

[simple orchid]

6y + 2x - 1 = 1

Like this?

[jovial shoal]

No. Your not applying chain rule properly. First What is the derivative of y^2?

When y is a function of x.

[simple orchid]

2y d/dx(y)?

[jovial shoal]

Yep.

[simple orchid]

Reuploading for reference

So this becomes

3y d/dx(2y) + 2x - 1?

How can I apply chain rule here?

There are no inner and outer functions

[jovial shoal]

y^2 is the composite of f(x) = x^2 and the function y. That is (f o y)(x) = f(y(x)) = y^2.

[jovial shoal]

You need to find the derivative of xy

Also there should not be a constant.

[simple orchid]

Isn't it the same like this?

[jovial shoal]

D(3y^2) = 3D(y^2). Where D mean derivative wrt to x.

So no it’s not.

Nvm it is.

[simple orchid]

Huh I'm confused

[jovial shoal]

Let’s backtrack. 3yd/dx(2y) + 2x part is right.

It’s just your missing the derivative of xy.

[simple orchid]

d/dx of xy is d/dx(x) + d/dx(y)?

Which I thought it was equal to 1

[jovial shoal]

Are you applying product rule here properly?

You have to remember y is a function of x.

Product rule says (fg)’ = fg’ + f’g.

[simple orchid]

y + x d/dx(y) maybe?

[jovial shoal]

Yep.

[loud ingot]

d/dx (3y^2) = 6y dy/dx

d/dx (x^2) = 2x

d/dx (xy) = (x * dy/dx) + (y)

d/dx (1) = 0

[jovial shoal]

Second part is wrong, it’s 2x.

[loud ingot]

Oh sorry

Fixed it

So you get: (6y dy/dx) + 2x - (x dy/dx) - y = 0

Solve for dy/dx

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[livid shell]

Prepare 2000 kg of diet from corn (9% CP), SBM (46% CP), fish meal (60% CP) and vitamin/mineral premix (0% CP) of the diet. The fish meal is to be fixed at 5% of the diet and vitamin/mineral premix fixed at 10% of the diet. The final diet should contain 20 % crude protein.

1. How much KG of vitamin/mineral premix will be in the diet?

2. How much fish meal will be in the diet?

3. How much kg of CP will the diet contain?

4. How much kg of CP will fish meal contribute?

5. How much CP will the SBM and corn contribute collectively?

6. Determine the quantity of corn and SBM in the diet and the CP contribution of each?

[icy sky]

There you go

[livid shell]

Do you mind adding me?

[icy sky]

I dont really add people

[livid shell]

Ok, no problem

[icy sky]

Anyway do you meed help with all problems or specific ones?

[livid shell]

With all of them

[icy sky]

Hold on ill be right back

[livid shell]

Ok, no problem!

Do you know how to do the Pearson Square for it?

[icy sky]

Im back

Never heard of a pearson square

Anyway the first 4 are sorta given in the problem

@livid shell

Lets starts with the first one

I want you to take a guess before i guide you through the problem

[livid shell]

Is it 200kg?

[icy sky]

Yup

Im sure you got the second problem too

[livid shell]

They require a pearson square though

[icy sky]

They don't?

[livid shell]

It's 100kg

[icy sky]

Yes

And for the third problem?

Im looking up what a pearson square is

[livid shell]

That part is giving me trouble

[livid shell]

Ok, cool

I learnt this in my Animal Nutrition class for University

[icy sky]

Oh interesting

[livid shell]

I am trying to properly understand this in preparation for an upcoming test.

[icy sky]

The last sentence in the problem states

The final diet should contain 20% crude protein

We know how big the the diet is so how much kg of CP is there?

[livid shell]

2,000kg?

[icy sky]

Thats the total diet

We are looking for just the CP part

I found out what a pearson square is and you only need it for p6

Ah excuse me for getting interrupted again brb

[livid shell]

Ok

20% of 2,000?

=400kg

[topaz sinew]

@livid shell Has your question been resolved?

[icy sky]

Ok sorry

Im back

Yes that is correct

Try number 4 now

[livid shell]

Ok

60% of 100 = 60kg?

[icy sky]

Yup!

[livid shell]

Number 5 is hard

[icy sky]

What about p5?

It shouldnt be too bad

Let me explain

You know the amount of CP already required and the amount that the fish contributes

So you just need to find the remaining amount of CP

[livid shell]

400 - 60 = 340kg CP?

[icy sky]

Yup!

Side question, what percent of the total mass is that

[livid shell]

60%

???

[icy sky]

340 is what percent of 2000?

Is what im asking

[livid shell]

17%

?

[icy sky]

Alright

So now its time to set up the pearson square

[livid shell]

And the table

[icy sky]

Table?

[livid shell]

Yeah

[icy sky]

Ok lets statt with the pearson square tho

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[icy sky]

??

.reopen

Eel can you say .reopen pls

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[icy sky]

Retaking the channel

[livid shell]

Reopen

[icy sky]

False you have a help channel already

So the pearson square looks like this right?

[terse parrot]

yea

[livid shell]

Yes

[icy sky]

What parts do you know how to fill out?

[livid shell]

9% Corn and 46% SBM

[icy sky]

Ok, whats the center box?

[livid shell]

I am not sure

[icy sky]

Oh crap hold up

Lemme figure that out

Ah ok

So we know that the fish and veg take up 300 kg total right?

[livid shell]

20%?

[icy sky]

Yes!

[livid shell]

340/1,700 x 100 = 20%

[icy sky]

Yup

[livid shell]

20 - 9 = 11 parts sbm

[icy sky]

I got this, but 37 seems like an odd number

[livid shell]

46 - 20 = 26 parts corn

[icy sky]

Yes

[livid shell]

Are you a man or a woman?

[icy sky]

Why does that matter?

[livid shell]

Because I was going to say that you're really smart

[icy sky]

Ok anyway

Continuing on

[livid shell]

Ok

[icy sky]

You know how to finish off the problem or do you need my help

[livid shell]

The table is to fill in the missing parts

[icy sky]

Ah ok

[livid shell]

I need help

[livid shell]

In kg

[livid shell]

And CP Contribution

[icy sky]

Oh ok

So im assuming the first thing you want to find is kg per part

[livid shell]

Yes

Corn = 26/37 x 1,700 = 1194.5kg

SBM = 11/37 x 1,700 = 505.4kg

[icy sky]

Yup

[livid shell]

Protein check = 1194.6 x .09 = 107.5kg CP

505.4 x .46 = 232.5 kg CP

[icy sky]

Sums to the 340 we need

[livid shell]

107.5 + 232.5 = 340kg CP

Thank you so much for your assistance!

[icy sky]

No problem

[livid shell]

I hope that I can be assisted by you again soon, because I still need practice with more Ration Formulation questions

Can I be connected with you through Instagram?

[icy sky]

You can ping me here

If you ever need help

Just be sure to use an available help channel

[livid shell]

How may I do that?

[icy sky]

@icy sky

Just do @garl by that point my name should just pop up

[livid shell]

Ok, thanks!

[icy sky]

Click on it then send the message

[livid shell]

I will send you a message now, so I don't lose your username

[icy sky]

.close

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[grim laurel]

im unsure on how they created the equation highlighted- could someone explain?

[wary tulip]

well it's kinda weird they use h twice for two different things, but the first line says that the formula is accurate within 4 cm, and |h - 164.2| <= 4 is supposed to say that the difference between the actual height and the predicted heigh, 164.2, is less than or equal to 4

h represents the estimated height but then they reuse the letter h for the actual height too

[grim laurel]

why less than or equal to four:?

[wary tulip]

so the first line says that the formula estimates the height h, and that it's not perfect but it will be within 4 of the real height

that's something given

so if the formula predicts 164.2 for a given femur length, then the real height will be between 160.2 and 168.2

[grim laurel]

like atleast 4cm correct of the estimated height?

[wary tulip]

ahh I'm not sure what you mean

[grim laurel]

okay liek

im confused what "it will be within 4 of the real height" means

[wary tulip]

so following the example in the image, let's say a woman's femur is 45 cm

her height is unknown

but the formula predicts it is 164.2

her actual height being within 4 of her estimated height means that her actual height is greater than (or equal to) 164.2 - 4, and less than (or equal to) 164.2 + 4

so it's between 160.4 and 168.4

[grim laurel]

so the four means

it could be four off or four more\

?

[wary tulip]

yea, the actual height could be

[grim laurel]

okay

wait i have another one

why is it 7.5 and 4.7

[wary tulip]

being within 1.4 of 6.1 means it's between 6.1 - 1.4 and 6.1 + 1.4

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[neon iron]

x^2+18=0

=>x^2=-18

now u need to take the pm sqrt of both sides

ya

now

$\sqrt{-18}=i\sqrt{18}=3i\sqrt{2}$

[thorny flame]

∆y/∆x=πy+π^2x

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[mild fractal]

is this a perfect square?
A^2 + 2AB + B^2

[mild fractal]

(pls ping)

[digital vale]

yes

[remote basin]

@mild fractal

Yes, it is (A+B)^2

[mild fractal]

ok ty

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[candid dove]

can we say that the average velocity is basically the average of the sum of all possible instantaneous velocities

[candid dove]

ik its a physics question but it can also be mathematically interpreted

[sturdy oracle]

yes

pretty much

theres a formula for that

$$\frac{1}{b-a}\int_a^bv(t)dt$$

[thorny flame]

Umbraleviathan

[candid dove]

ooo thx mate

.close

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[misty lodge]

The equation shows what a machine is worth after x years. 160,000 · 0.95x = 50,000

[misty lodge]

After how many years is it worth 50000?

[sturdy oracle]

you mean $160000+0.95x = 50000$?

[thorny flame]

Umbraleviathan

[sturdy oracle]

Or $160000(0.95x) = 50000$?

[thorny flame]

Umbraleviathan

[misty lodge]

well in my book here it the same as i wrote

) The equation shows what a machine is worth after x years. 160,000 · 0.95x = 50,000
a) How much is the purchase price of the machine?
b) What is the annual percentage reduction?
c) After how many years is the machine worth SEK 50,000?

thats copy and pasted

[sturdy oracle]

why would they seperate the 160000 from the 0.95

do they mean $160000\cdot 0.95^x=50000$

[thorny flame]

Umbraleviathan

[misty lodge]

yeah i think so

[sturdy oracle]

In which the price of the time machine depreciates by 5%

What have you tried

[misty lodge]

I went with the process that they mean 0.95^x

[sturdy oracle]

show me what youve tried

[misty lodge]

well A) i put 160000 B)5% And on c) i have not really done anythin

[sturdy oracle]

just solve for x

try something

the dot means multiplication

@misty lodge

[misty lodge]

yeah im not really getting the right answer here

[sturdy oracle]

$$160000\cdot 0.95^x=50000$$
$$0.95^x=0.3125$$
$$x=\log_{0.95}{(0.3125)}$$

[thorny flame]

Umbraleviathan

[misty lodge]

what was the process?

I dont really get it

im not sure thats the right answer, or how do i check if it is?

am i allowed to ping you while we talk or is that still a no?

<@&286206848099549185>

[loud ingot]

What part you not understand?

[misty lodge]

how did he get 0.3. How can i check so its correct?

[loud ingot]

You mean 0.3125?

You divide both sides by 160000

Simply algebra

,calc 50000/160000

[thorny flame]

Result:

0.3125

[misty lodge]

alright i hear u, so ur saying if i take the buy in pice divide it with the questioned amount, in this case 50000, i get the years it takes for the amount to reach 50000?

[loud ingot]

0.3125 is not the final answer bro

You are solving for x

,calc log0.95 (0.3125)

[thorny flame]

The following error occured while calculating:
Error: Undefined symbol log0

[misty lodge]

yeah, so that leaves it at 0,95^x=0,3125?

[loud ingot]

Yes bro

,w = 0.95^x=0.3125

[thorny flame]

Results provided by WolframAlpha

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

Requested by Diegoro#7896

[loud ingot]

After like 22 years

[misty lodge]

my goodness

this is so easy when Its all infront

thanks man

can i ask a different question while ur here?

[loud ingot]

Jag sover snart så

[misty lodge]

Alright, tack ändå

dröm sött

.close

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[elfin spruce]

Good morning mate

[elfin spruce]

I don’t understand the #40 question

Is it (2w-1)(w-1)

?

[twilit yew]

@elfin spruce it is saying 2w*w = 70

[elfin spruce]

Oh but what is that 1 foot about?

[twilit yew]

Here is some insight. square feet describes area (ft^2). I'm guessing the 1 foot boarder is just a way to describe it

[elfin spruce]

70ft^2 is the area of the rectangle and the area=L*W so it 70=3w or 23 1/3 ft?

But the answer sheet is 11 ft by 22 ft

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[elfin spruce]

.close

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[grim jacinth]

• Show your work, and if possible, explain where you are stuck.

[marsh tartan]

Got it

I’m stuck on getting the component forms of lines PQ and QT

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@marsh tartan Has your question been resolved?

[marsh tartan]

<@&286206848099549185>

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@marsh tartan Has your question been resolved?

[sweet shard]

,rotate

[urban grove]

Try using this formula, magnitude of torque = |r||F|sin theta where theta is the angle in between r and F

this is one way to compute the magnitude of the cross product

[marsh tartan]

ok

So the vector would be (79cos(40), 79sin(40), 0)

[urban grove]

Don't worry about the vector

all you need is the magnitude of the vector

but if we were to compute it with vectors, the force vector should be 79 newtons straight down

[marsh tartan]

= (67)(79) sin(50)

is this right?

got it

Thanks!

.close

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[frosty pagoda]

Hello can someone help me with a trigonometry question?

[jolly stump]

Don’t just ask basic things, post the problem and we can help right away.

[jolly stump]

You clearly didn’t read this.

[frosty pagoda]

It’s was loading

[jolly stump]

It’s been a while since I did stuff like this but wouldn’t the 35 degree angle and the 90 and then unknown angle in the very small triangle to the far right need to add up to 180 since it’s a straight line?

90+35 = 125
180 - 125 = 55

I’m going to continue finding the angles hold on

[timber vault]

It’s nothing that complicated

Using sin=opp/adj, you can find the vertical height

[frosty pagoda]

Isn’t it like cah soh toa

[timber vault]

With that length, you can use both angles to find the length of the bottom

Yes exactly

[jolly stump]

oh yeah

Sorry I do more calc

Then geo

I’m wayyy more algebraic

[timber vault]

opp/hyp***

sorry

💀

Is that clear?

[frosty pagoda]

Yea

But for a don’t I like have to find hyp,adj or opposite

I think

[timber vault]

Consider the left-hand triangle, with the 40 degree angle and 6m hypotenuse

[frosty pagoda]

Yea

[timber vault]

Its a right angled triangle, so you can calculate the opposite length of the angle, which is the vertical height

[frosty pagoda]

The dotted line?

[timber vault]

Yeah

[frosty pagoda]

Ok that

I am guessing using sin tan or cos

[timber vault]

Use sohcahtoa to figure out which one to use

[frosty pagoda]

Ok

sin=opposite/hyp cos=ap/hyp tan=opposite/ap

[timber vault]

whats ap?

[frosty pagoda]

Ap is adjacent

[timber vault]

Weird abbreviation but alright

Use those formulas to find the length of the dotted line

[frosty pagoda]

Adj

[timber vault]

More@conventional yeah

[frosty pagoda]

Since hyp is 6

Sin

[timber vault]

Yea

[median spade]

lol ive never heard that being used before

[timber vault]

ikr

[frosty pagoda]

HEY

x/6=sin(40)

??

[timber vault]

Yep!

[frosty pagoda]

So know

[timber vault]

Find x, thats the solution to part A

[frosty pagoda]

Ok

which mode

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[safe nymph]

I have a doubt

[safe nymph]

.close

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[quick gorge]

as far as I understand your question.. anything can be substituted for y

a line like that isn't restricted at all

sure if you want

wait but what is the question?

yes, y can be a number.. it is a number

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[quick gorge]

uh okay

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[normal oar]

hi guys

[urban pulsar]

hola

[strange whale]

hi

[rich void]

hows it going

[normal oar]

good how about you guys

is my answer correct?

wait

[rich void]

ayo

[rich void]

u forgor about the second part?

[normal oar]

w>3 is the second part

im not familiar with the notation tbf

ive had math in dutch all my life thats why

how'd i notate this?

[rich void]

i see

[normal oar]

like this?

[rich void]

so the first inequality states that $w \geq -2$

[thorny flame]

FructosePear

[rich void]

the second one states that $w > 3$

[thorny flame]

FructosePear

[rich void]

this is technically correct

but can you simplify it?

anything that satisfies the second equation will definitely satisfy the first

[normal oar]

simplify the second part?

idk how

[rich void]

it has to satisfy BOTH of these equations

anything that satisfies the second will definitely satsify the first

[normal oar]

like this?

[quick gorge]

looks right to me

[topaz sinew]

@normal oar Has your question been resolved?

[topaz sinew]

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[topaz sinew]

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[patent flame]

can someone explain real quick why

[patent flame]

1.5t^2+216

[patent flame]

has a range of y>=10

how can i explain the range

[steady cloud]

I'm afraid this isn't correct. The range of y = 1.5t^2 + 216 is y >= 216

The reason why is as follows

[celest shuttle]

*216

[steady cloud]

Haha let me correct that typo

Firstly, note that t^2 is never negative. In fact, it can be any value >= 0

Similarly, 1.5t^2 can be any value >= 0

[patent flame]

oh wait

yeah i typed it wrong

[steady cloud]

So all together, 1.5t^2 + 216 can be any value >= 216

OK, try again

[patent flame]

lolol its 1.5t^2+36t+216

[steady cloud]

Good stuff

[sturdy oracle]

Bruhg

[steady cloud]

Do you know the method of completing the square?

This is a very helpful method of solving this kind of problem.

[sturdy oracle]

Find the y-value of the vertex

You can use -b/2a to find the x-value of the vertex

[patent flame]

i already have the zeros and i know the range is y>=0

i just need to explain why

and thats where my struggle is

[steady cloud]

OK, that's fine, but we're not looking for the zeros

Do you know how to turn something of the form x^2 + ax + b into the form (x - p)^2 + q?

This is what it means to complete the square

I think you'll find that putting the function in this form will be helpful.

[patent flame]

i forgot actually

[steady cloud]

OK, you should take a moment to remind yourself of how to do that

Once you've done so, try putting 1.5t^2+36t+216 into that form.

[sturdy oracle]

You don't need to put it into that form

If $(h, k)$ is the vertex of parabola $ax^2 + bx + c$, then $h = -\frac{b}{2a}$

[thorny flame]

Umbraleviathan

[sturdy oracle]

@patent flame This way is a lot easier

[patent flame]

ok i can try that maybe

other than finding the range tho how do i explain why the function outputs only y>=0

im not too worried abt finding the range itself i can review that later im mainly trying to focus on explaining why the range is y>=0

but i just realized i might not need to

[sturdy oracle]

Range is not that

[patent flame]

what?

1.5t^2+36t+216 i graphed it and the vertex of the parabola is at x=0 so y>=0

but i feel like that explanation doesn't work idk?

ig it'll suffice

[topaz sinew]

@patent flame Has your question been resolved?

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• Ask your math question in a clear, concise manner.
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• Be polite and have a nice day!

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

[crisp surge]

Could somebody please walk me through how my prof factored this?

[sweet shard]

which line exactly

[crisp surge]

The arrow

[sweet shard]

is the question mark yours?

[crisp surge]

line 2-3

yes

[sweet shard]

are you able to factor out the exponential and put the remaining over a common denominator?

[crisp surge]

I believe so, I am just curious as to how he factoring out 4/(x-3)^4 leaves (4-8(x-2)) remaining

[sweet shard]

multiply these two and see what you get

oh there's an error

should be -2 and not -8

[crisp surge]

I got -8(x-5) / (x-3)^4

[sweet shard]

no idea how you'd get 5

[crisp surge]

I replaced (4-8(x-3)) w/ (4-2(x-3)) = (4-2x+6) = (-2x+10) Distributed 4 and factored

[sweet shard]

i already said the 8 was wrong

after factoring out the exponential and the common denominator, you're left with

$4^2 - 8(x-3) = 16 - 8x + 24 = -8x+40$

[thorny flame]

riemann

[sweet shard]

oh that's how you get 5

ok our answer's the same after factoring out 4

[crisp surge]

Ok so it was just an error from my prof?

[topaz sinew]

@crisp surge Has your question been resolved?

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