help-23

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[small plume]

I actually don't even know how to begin solving this, I tried splitting the middle term but codulnt find any that gave the power -14. It's part of the calculation for a derivation. The required answer is 0.95 x 10^-7

[lean chasm]

complete the square

[safe radish]

@small plume Has your question been resolved?

[small plume]

Damn

it worke

Holy crap lol thanks ❤️

There's some binomial approximation in there

But I got the required final result

Thanks a lot ❤️

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[timid relic]

I have f(x) = x(x+1)(x-1) can I convert it into f(x) = x * x^2 - 1^2 ?

[pulsar condor]

no

cause x isn't a factor of x^3-1

[timid relic]

but its the binomial formula right

[pulsar condor]

wdym

(a+b)(a-b)=a^2-b**^2**, yes

[timid relic]

yes

[pulsar condor]

that's difference of squares, not binomial theorem

[timid relic]

so i cant use it here?

[pulsar condor]

you can

You just did it incorrectly

[timid relic]

how can i do it ?

[pulsar condor]

you apply it

$x(x-1)(x+1)=x(x^2-1)$

[flat frigate]

Mosh

[timid relic]

oh

okay I get it

thanks

[timid relic]

@pulsar condor wouldnt -1^2 get converted into +1 tho ?

[pulsar condor]

no.

cause you don't have +(-1)^2

you have -1^2

[timid relic]

oh right

thanks for helping me out

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[plush dagger]

How to solve this problem? I don't know if this even possible?

[slender coral]

Are you sure that there isnt anything more on the right side of the equation? Or that the $>$ isnt a $\geq$?

[flat frigate]

opfromthestart

[bronze prism]

The right hand side, at it stands, has at most two distinct roots

[zinc crown]

Hence there would be repeat roots in its square.

[plush dagger]

Yep that's what it gives

[zinc crown]

First factor the right side completely, then you would probably see what the answer would be

Oh wait

Strict inequality on the question

So the question can’t be answered actually

[slender coral]

if it were $(x^2-12x+27)^2-1$, it would be solveable and I think actually have integer solutions.

[flat frigate]

opfromthestart

[slender coral]

Not integer solutions but it would have 4 distinct solutions.

[plush dagger]

So that's confirmed as unsolvable right?

[slender coral]

Yes

since the best you can do is $9\geq 9>3\geq 3$.

[flat frigate]

opfromthestart

[plush dagger]

Oh

So thanks for help!

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[grave flint]

@final loom #help-14 message What's not good about these?
and why would it be fine if I traced my steps back a bit confused here.
Also doesn't seem to make sense if I use <=> when they aren't equal.

[safe radish]

@grave flint Has your question been resolved?

[grave flint]

Anyone could help here, I'm wondering what is wrong with the proofs I did

[stoic dune]

They are backwards.

For the first, you're assuming the result, and then implying that 0 < (x - y)^2

Why should that matter? Does it prove the result?

Consider switching the order of the proof. That is, start with 0 < (x - y)^2, go back to the original proposition

[grave flint]

How does the less than or equal sign imply they are only equal? Also what result am I assuming? If I switched the order of the proof how would I show how I got to the (x-y)^2 in the first place

[safe radish]

@grave flint Has your question been resolved?

[stoic dune]

"Also what result am I assuming?"
The first line. Why start with this? You want to prove it true, so it should be the last thing.

"If I switched the order of the proof how would I show how I got to the (x-y)^2 in the first place?"
Why do you need to?

Sorry, I kept typing = when I meant <. Edited.

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[grave flint]

.reopen

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✅

[grave flint]

right but how do i show how i got to 0 <= (x-y)^2in the first place

[stoic dune]

You don't need to!

0 <= (x-y)^2 is always true. So if you start there, anything you arrive at will also always be true

On the other hand, it is possible to start with something false, and arrive at something true

[grave flint]

i understand that but i dont want it to seem that i just picked this arbitrary statement to start off with, especially where i have z

[stoic dune]

Well, everybody reading will know exactly how you got to it. Just, the order of your proof won't be the same as the order of the search

[grave flint]

alright

thanks!

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[violet cobalt]

can i get some help pls, a bit stuck

[safe radish]

@violet cobalt Has your question been resolved?

[violet cobalt]

<@&286206848099549185> help pls

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@violet cobalt Has your question been resolved?

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[twilit rose]

I need help finding the equation to write

This is what I wrote down but it's wrong. What did I do wrong?

Srry it's sideways

<@&286206848099549185>

[royal kiln]

@twilit rose idk, rounding? Fat-fingered it?

answer should be 239.3

wait until the end to round

[twilit rose]

K

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[snow minnow]

In this particular question, Im struggling to shift the summation form to explicit sum

what is the best way of going about this

[blissful gate]

Can you show the above examplle

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[snow minnow]

I had to leave for some work but Im back to get this resovled

[snow minnow]

this is the example

I would like to figure out how to get the first one into explicit form then solve

[marsh walrus]

like how to prove it with induction?

[snow minnow]

precisely

[marsh walrus]

i guess i never tried it but given the formula it cant be that bad

or maybe i have done ths

whats your base step?

almost not even worth doing but

[snow minnow]

well r can't be 1, so i was wanting to make r = 2

[marsh walrus]

i dont think you can make r anything

just cant make it 1

it has to be general

the thing you fix in the base step is n

you fix it to be whatever the initial case is

[snow minnow]

oh

n = 1 then

[marsh walrus]

so you want to show $\sum _{i=0} ^0 r ^i = \frac{1-r^{0+1}}{1-r}$

[flat frigate]

jan Niku

[snow minnow]

yes

[marsh walrus]

is it?

[snow minnow]

are we sure the base case is 0 in this scenerio

[marsh walrus]

i think so

a single term

r^0

[snow minnow]

ok

we'll try it

[marsh walrus]

theres not a lot to show

maybe more of a 'convince yourself' sort of scenario

[snow minnow]

oh

[marsh walrus]

maybe something like

r^0 = 1

[snow minnow]

im workin it on paper to see

[marsh walrus]

sure

dont let me stop u

[snow minnow]

base works with n = 0

just proving it inductively seems to be weirder since it wants it in explicit form, and I'm not very good at it

[marsh walrus]

have you done inductive proofs before?

what do you mean explicit+

[snow minnow]

i have done them before

im not good at going from summation to explicit

it wants to follow the example from the 2nd picture

[marsh walrus]

lemme see if i can sketch the start

[snow minnow]

something like this?
1 + r + r^2 + ... + r ^ i + 1 ; r =! 1

[marsh walrus]

so heres not a bad clue

ill have to check that this does work out

but id start at the bottom here

see if you can make use of the inductive hypothesis

[snow minnow]

uhm

[marsh walrus]

it works out

[snow minnow]

the one i wrote above or the one you wrote?

[marsh walrus]

the one i wrote

i dont really get what you mean with yours

[snow minnow]

well i was thinking term after term, but it doesn't really get me much

yours is more distinct

and makes more sense

[marsh walrus]

sorry my comp just crashed

gimme a sec

but

[snow minnow]

take ur time

[marsh walrus]

try subbing in your inductive hypothesis

[snow minnow]

uh

[marsh walrus]

here

can u vc?

[snow minnow]

yes

[marsh walrus]

one sec

its glitchy

my comp is dying 😭

[safe radish]

@snow minnow Has your question been resolved?

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[final loom]

@normal grove

[normal grove]

I guess I am just lost on the fundamental concepts here.

[final loom]

Q. Find a bijection from $\mbb{R} \mapsto (\sqrt{2}, \infty)$

[normal grove]

Im not really understanding what $\mathbb{R}$ is mapping to

[flat frigate]

MillsMade

[final loom]

I can walk you through if you're willing-

[normal grove]

And a bijection means it is both injective and surjective

Injective means that for every $x,y \in A, x\neq y \implies f(x)\neq f(y)$

[flat frigate]

MillsMade

[normal grove]

Surjective means that for every $b\in B$ there exists $a in A$ where $f(a)=f(b)$

[flat frigate]

MillsMade

[normal grove]

So "mapping" $\mathbb{R}$ and $(sqrt{2},\infty) meets both these criteria.

[flat frigate]

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

[normal grove]

shit

So "mapping" $\mathbb{R}$ and $(sqrt{2},\infty)$ meets both these criteria.

[flat frigate]

MillsMade

[normal grove]

What does it mean to map $\mathbb{R}$ to $(sqrt{2},\infty)$ ?

[flat frigate]

MillsMade

[normal grove]

Is $(\sqrt{2},\infty)$ an ordered pair?

[flat frigate]

MillsMade

[normal grove]

Cant be because of infinity right?

But it is not an interval...

[normal grove]

Yes, please

[final loom]

Let's go

First.

what is meant by a function creating a "mapping between two sets"?

@normal grove

very trivial question, I'm asking just honest opinions abt it

[normal grove]

creating a function that when you input the values from set A, the output is the values from set B

[final loom]

precisely

so suppose 3 is in the domain of f(x)

and 4 is in the range such that f(3) = 4

this implies

a map was made from domain to range that joined 3 to 4

okay?

[normal grove]

understood

[final loom]

Let's go

Now,

what is the domain of the function $f(x) = e^x$

[normal grove]

$\mathbb{R}$

[flat frigate]

MillsMade

[final loom]

the set of values of "x" for which this function is well defined

Yes!

Absolutely

The Domain of $f(x) = e^x$ is $\mbb{R}$

[final loom]

and.. if I may ask, what is the range of $f(x) = e^x$ given domain $\mbb{R}$?

[final loom]

range is the set of values which have a pre-image of themselves in the domain

[normal grove]

$\infty$

[flat frigate]

MillsMade

[normal grove]

no

[final loom]

Yep, the range is a "set"

[normal grove]

The range would be $\mathbb{R}>0$

[flat frigate]

MillsMade

[final loom]

$\mbb R_{>0}$

[final loom]

Yeah!

so you see

you're almostttttttttt there

$f(x) = e^x$ maps $\mbb R \mapsto (0, \infty)$

[final loom]

and you need a function that maps $\mbb R \mapsto (\sqrt{2}, \infty)$

[final loom]

Do you think you can take it from here?

[normal grove]

Yeah, you would just need to add $\sqrt{2}$ to the exp function

[flat frigate]

MillsMade

[final loom]

perfect!

$f(x) = e^x + \sqrt{2}$ maps $\mbb R \mapsto (\sqrt{2}, \infty)$

[final loom]

You can see this yourself if you consider this graph

,w plot y = e^x + sqrt(2) and y = \sqrt(2)

it's just the graph of f(x) = e^x shifted √2 upwards

[normal grove]

Understood

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by Ansh#3502

[final loom]

so now, do you have the bijection?

[nocturne lion]

brr brr

more calculus

[final loom]

spadeXD more like, Joker2xD

[nocturne lion]

bruh

not funny

[final loom]

that's the point

[nocturne lion]

stupid keyboard is set to german

[normal grove]

So for the proof I would still need to show how this is injective and surjective...

Thats where Im at now

[final loom]

well, that's trivial though

e^x is bijective, so the rest follows by construction

[normal grove]

ah, right

thanks for the help

[final loom]

.close

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[fading raft]

what's the q

they want u to select which graph is right?

(a)

np

calculate $\sqrt{9^2-2(9)+1}$ and that's the answer

[flat frigate]

azeem321

[fading raft]

What is $9\times9$

[flat frigate]

azeem321

[fading raft]

now subtract 18

good

now add 1

$\sqrt{64}=?$

[flat frigate]

azeem321

[fading raft]

$\sqrt{64}=(64)^{\frac{1}{2}}$

[flat frigate]

azeem321

[fading raft]

What number equals 64 when you multiply it by itself?

$3\times3 = 9$

[flat frigate]

azeem321

[fading raft]

$4\times4 = 16$

[flat frigate]

azeem321

[fading raft]

So what two numbers multiplied by itself gives 64?

[light shoal]

$-8$

[flat frigate]

OurBelovedBungo

[fading raft]

good

8

yes

any more questions?

Do you know what this notation means? $f(x)$

[flat frigate]

azeem321

[fading raft]

Let's say I did $f(x) = x^2$

[flat frigate]

azeem321

[fading raft]

So $f(1) = 1^2$

[flat frigate]

azeem321

[fading raft]

$f(2)=2^2$

[flat frigate]

azeem321

[fading raft]

Now try this

If i let $g(x) = 3x+4$

[flat frigate]

azeem321

[fading raft]

What is $g(4)$

[flat frigate]

azeem321

[fading raft]

yes

Wherever you see an $x$ in the expression for $g(x)$ you replace with $4$

[flat frigate]

azeem321

[fading raft]

4

find g(4)

ok so look our expression is

$g(x) = 3x+4$

[flat frigate]

azeem321

[fading raft]

To find g(4), we replace 'x' with '4'

So g(4) = 3(4)+4

You see what i did?

now calculate g(4)

good

good

Now let's try one more

$p(x) = x^2+3x$

[flat frigate]

azeem321

[fading raft]

find p(2)

yes

6+4=12

?

lmao

ok final one $p(x) = \sqrt{x^2+3x}$ find p(1)

[flat frigate]

azeem321

[fading raft]

$1^2=2?$

[flat frigate]

azeem321

[fading raft]

What does $a^2$ mean?

[flat frigate]

azeem321

[fading raft]

It means $a \times a$

[flat frigate]

azeem321

[fading raft]

$a^3 = a \times a \times a$

[flat frigate]

azeem321

[fading raft]

good

Now could you solve this by yourself now with your new knowledge?

good

yes

good

Do you understand what this notation means $\sqrt{x}$

[flat frigate]

azeem321

[fading raft]

$\sqrt{}$

[flat frigate]

azeem321

[fading raft]

What does it mean?

So basically it means we want to find a number such that $y \times y = x$

[flat frigate]

azeem321

[fading raft]

We want to find a number when you multiply it by itself, it gives the number under bracket

ok

np

bro

this is easy

i gave you the knowledge for this

solve it

doesn't matter

could be f,g,k,l

etc

just apply the same rule

[light shoal]

Someone typed \mathbb [?

[fading raft]

I think for your purposes this means nothing

[light shoal]

It's a tex command that displays something using "math blackboard" font, which is what those [ and ] look like

Looks nonstandard, could mean "round to nearest integer" or something like that, but you would have to check with your instructor

ah good

[fading raft]

Are you sure

because your stuff is very basic

have u been taught

that's what it means?

ok good

then carry out the normal procedure i give u earlier

dw

we solve it before then

ok first think of

u(x) = 2x-1

without the bars

what is (-2.1)

[thin bridge]

<@&268886789983436800>

[light shoal]

wtf, you are taking an exam right now?

not cool

[fading raft]

im confused? you are not allowed to give help to people in exams?

[cerulean canyon]

no, it isn't

.close

[safe radish]

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[light shoal]

See #rules "Do not cheat on tests or exams. Do not be academically dishonest. Do not offer money for doing homework assignments, and vice versa."

[safe radish]

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[mint plume]

Hi can you help me with homework, i from russia and doing English better than math

[safe radish]

@mint plume Has your question been resolved?

[mortal meteor]

I suggest that you translate your problem to english then, that increases the probability to get help

[jagged snow]

#❓how-to-get-help

You simply don't need to post whole homework, just post where you get doubt

[mint plume]

First number

[mortal meteor]

...

[safe radish]

@mint plume Has your question been resolved?

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[calm crater]

Hey guys, how do i turn this equation into x =.....

[calm crater]

This is the answer key

[royal kiln]

assuming you started correctly, you're just a few steps away?

is this one of those statistics calculus probs?

[calm crater]

I'm not sure if it's statistics but it's calculus, yes

[royal kiln]

you made it this far, just mult both sides by the denominator and distribute

then collect like terms with x in them

[calm crater]

by 2500 - x?

[royal kiln]

yes. That is the denominator

[calm crater]

ah okay let me try

owh it works

thank you very much for the help!

.close

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[tropic cipher]

hello, I don't know where to start in this equation.

[royal kiln]

f(3) means everywhere you see an x, write 3 instead and do all the operations.

oh...that's uglier than I've seen though

because the input they are showing isn't x, it's that

[lean otter]

change of variable ?

[quasi bison]

or you could just find the value of x that satisfies (x+1)/2 = 3, and then plug that in

[royal kiln]

set it equal to t?

the input?

Ann's right

[lean otter]

why just =3

where did the -4 go

[royal kiln]

b.c. that's the input, the RHS is saying the input should equal 3

[lean otter]

oh

[royal kiln]

even when the input is a formula

[tropic cipher]

can you re-explain why did we just did =3?

[royal kiln]

@quasi bison would you say this is transitive property?

[quasi bison]

no, the transitive property has precious little to do with this

you are told that a certain function f satisfies (presumably for all real x) the equation f( (x+1)/2 ) = 3x - 4

[lean otter]

isnt this the intersection of two functions

[quasi bison]

composition, not intersection.

[lean otter]

f(g(x))=h(x) such that g(x)=(x+1)/2 and h(x)= 3x-4

[tropic cipher]

so in this case f(3) = 5?

[quasi bison]

where are you getting 5 from?

are you impatient to just get the answer?

[tropic cipher]

not really i am trying to do what i was told

[quasi bison]

read this carefully then

[tropic cipher]

i found what satisfies x

5 satisfies x

[quasi bison]

misusing the word "satisfy" there

you found that x = 5

[tropic cipher]

yes

[lean otter]

can you please explain why "f(g(x))=h(x) such that g(x)=(x+1)/2 and h(x)= 3x-4" isnt correct

[quasi bison]

i never claimed it wasn't correct

[tropic cipher]

after i found the value of x

what should i do

[quasi bison]

and then plug that in

i.e. plug in that value of x into the equation

f( (5+1)/2 ) = 3*5 - 4

[tropic cipher]

f(3)=11

this is considered solved right?

[quasi bison]

what do you mean by "considered solved" as opposed to "solved"

[tropic cipher]

english isn't my first language, yeah i meant it is solved

n = 1 ?

i know that x = 2

[quasi bison]

where are you getting n=1?

[tropic cipher]

i found that x = 2 from the same way i found x in the last equation, then i didn't know what to do

[quasi bison]

you found that x = 2, so what is the value of f(4)?

[tropic cipher]

i can't know, because i dont know what is n

[quasi bison]

f(3x-2) = 4x+7

replace x with 2 here and tell me what you get

[tropic cipher]

6

[quasi bison]

no

[tropic cipher]

n = 6

[quasi bison]

...

okay so you jumped ahead

[tropic cipher]

yes my bad

im getting the hang of it

thank you

i will close this ticket, thank you guys for the help.

.close

[safe radish]

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[tropic cipher]

how do i start with this?

[tropic cipher]

after some calculations, answer is 18

can someone tell me if this is correct

[feral linden]

Yes

[final loom]

,calc 7/7

[tropic cipher]

thanks

[flat frigate]

Result:

1

[final loom]

Yeah it's correct (@_@;)

[tropic cipher]

alright, thanks guys i will close this channel

.close

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[tall bough]

so the domain of f(x,y)=sqrt((x²+y²-a²)(2a²-x²-y²))

[tall bough]

i said that the domain is x²+y²>=a² and x²+y²<=2a² or it can be x²+y²<a² and x²+y²<=2a² and other way

is it correct

the first is that both are positive and the other is that both are negative

[quasi bison]

x^2 + y^2 ≤ 2a^2 is not equivalent to 2a^2 - x^2 - y^2 being negative.

[tall bough]

i see so only the first 'condition' is correct?

[quasi bison]

it is impossible for both of these factors to be negative anyway

the domain is {(x,y) ∈ R^2 | a^2 ≤ x^2 + y^2 ≤ 2a^2}

or, geometrically, an annulus centered at the origin with inner radius a and outer radius sqrt(2)a

[tall bough]

sketching the domain is hard 😦 a^2 ≤ x^2 + y^2 ≤ 2a^2 is a combination of or a shorter version of x²+y²>=a² and x²+y²<=2a² right?

[quasi bison]

.

i gave you a geometric description

which should not be hard to sketch at all

if you wish to view it as the intersection of a disk and the exterior of another disk then so be it

[tall bough]

i mean sketching it without knowing the description

[safe radish]

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[golden lance]

Can someone help me with this?

[thin token]

i can't see anything the question is asking for

[safe radish]

@golden lance Has your question been resolved?

[feral linden]

(x+3)^2/4-y^2/12=1

You set the equation (x+3)^2/a^2-y^2/b^2=1 then use the fact that

a^2+b^2=16 and (-1,0) (0, sqrt(15)) are on it

Just a bad joke my bad

[thin token]

no dude it's fine

no offence taken

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[opaque raptor]

"What's the chance of getting a sum of 6 with 4 dice or getting quadruples with them"

[opaque raptor]

i've been trying to figure out how to do this question without doing the tedious diagram

[feral linden]

What do you mean “getting quadruples with them”?

[opaque raptor]

all 4 dice having the same number

[feral linden]

(C(4,1)+C(4,2)+ 6)/6^4

16/6^4

[pulsar condor]

Don't just give answers.

[feral linden]

Oh . If you want the sum of four dices to be 6, what are the possible combinations?

[opaque raptor]

there is a bunch

[feral linden]

Ignoring the order of 4 dices

[opaque raptor]

oh

leme write this out

alright there would only be 1,1,2,2 and 1,1,1,3

if i ignore the order

[feral linden]

Yeah and how many combinations are of the form 1122 and 1113 respectively?

you are considering order now

[opaque raptor]

for 1122 there would also be 2112, 1212, 2211 and 2121

for 1131 there would be 3111, 1311 and 1113

[feral linden]

Something is missing

Select 2 from 4

Select 2 dices to be 2 other two to be 1, so select 2 dices from 4 dices

[opaque raptor]

oh 1221

[feral linden]

Yeah so 10 in total

[opaque raptor]

okay

[feral linden]

And how many situations you have 4 equal numbers

(And you don’t need to worry about intersection of two cases since 4 doesn’t divide 6)

[opaque raptor]

there would be 6 ways

[feral linden]

16 in total so you get the answer

[opaque raptor]

yeah

so now i need to figure out how many total ways you can roll 4 dice

[feral linden]

Yeah

[safe radish]

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[pulsar condor]

dont ping random users

[lean otter]

oh

im sorry

[lean otter]

The radius of a circular hat is 3.7 inches. Find the circumference. Use 3.14 for π.
A. 1.85 in.
B. 11.618 in.
C. 23.236 in.
D. 22.2 in.

Use 3.14 for π to estimate the area of a circle. The diameter is given. Round your answer to the nearest hundredth if necessary.

A circle is shown. A dashed line extends across the circle through a point at the center connecting points on opposite sides of the circle. This dashed line segment is labeled 28.2 meters.
A. 44.27 m2
B. 177.1 m2
C. 624.26 m2
D. 2,497.05 m2
5 / 23

Find the length of the side of a square with an area of 169 inches squared.
A. 338 in
B. 106 in
C. 26 in
D. 13 in

Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and integer.
0.62478916532…

A.    rational number
B.    irrational number
C.    integer, rational number
D.    whole number, integer, rational number

Find the missing length. Round to the nearest tenth, if necessary.

A right triangle is shown. The horizontal leg is labeled x, the vertical leg is labeled 7, and the hypotenuse is labeled 19.
A. 12
B. 17.7
C. 19
D. 22.45
8 / 23

A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.

A diagram is shown of a triangular prism. The triangular base has two sides of length 10.25 millimeters and a third side of length 12.3 millimeters. A dashed line segment is drawn perpendicular to the 12.3 millimeter length side to the opposite vertex. This dashed line segment is labeled 8.2 millimeters. The height of the prism is 20.5 millimeters.

Which estimate is closest to the volume in cubic millimeters of the part?

A.    306
B.    768
C.    1,008
D.    2,016

The figure below shows two half-circles at the ends of a rectangle with the dimensions shown.

A figure is shown with two half-circles at the ends of a rectangle. The rectangle at the center has a width of 20 inches and a height of 4 inches. The 4 inch ends of the rectangle are diameters of the two half-circles.
Which is closest to the area of the figure in square inches?
A. 93
B. 130
C. 86
D. 105

Name the geometric solid suggested by a beach ball.
A. sphere
B. rectangular prism
C. pyramid
D. cylinder

A soup company packages its soup in cans shaped like right circular cylinders. A diagram for the net of the cylinder is shown.

A diagram is shown with a central bright green horizontally oriented rectangle of height 5 inches at the center. At the upper left, touching the rectangle is a lighter green circle with radius drawn and labeled 1.5 inches. An identical circle is drawn at the lower right, touching the side of the rectangle.

Which is closest to the surface area of the cylinder?

A.    38 in2
B.    61 in2
C.    113 in2
D.    160 in2

Use a net to find the surface area of the prism.

A rectangular prism is shown with a length of 14 inches, width of 5 inches, and height of 7 inches.
A. 203 in.2
B. 406 in.2
C. 476 in.2
D. 540 in.2

Find the surface area of the triangular prism.
The lower triangular face shows a width of 11 inches and a perpendicular dashed segment measuring 7 inches.
The right vertical edge of the prism measures 14 inches between the triangles.
The upper triangular face has a left side measuring 8 inches and a right side measuring 9 inches.

A.    315 in.2
B.    539 in.2
C.    469 in.2
D.    784 in.2

Use the diagram to answer the question.
Find the surface area of the cylinder to the nearest tenth of a square unit. Use 3.14 for π.
The circular face of a cylinder has a radius of 3 centimeters. The height of the cylinder is 18.2 centimeters.
A. 228 cm2
B. 399.4 cm2
C. 165.7 cm2
D. 371.1 cm2

A gift box is 12 inches long, 8 inches wide, and 2 inches high. How much wrapping paper is needed to wrap the gift box?
A. 272 in2
B. 192 in2
C. 384 in2
D. 184 in2

Alex needs to buy compressed air to fill empty cylindrical tanks for his tire store. Each tank is 12 feet deep and has a radius of 6 feet. What is the volume of compressed air needed to fill 5 tanks? (Use 3.14 for π.)
A. 565.2 ft3
B. 1,356.5 ft3
C. 3,452.6 ft3
D. 6,782.4 ft3

Find the volume of a triangular prism with the following dimensions. Round to the nearest whole number.

triangle base: 9 ft
triangle height: 4 ft
prism height: 9.5 ft
A. 23 ft3
B. 86 ft3
C. 171 ft3
D. 342 ft3

A triangle is shown. The base of the triangle is labeled 28 yards. At approximately the center of this base, a vertical dashed line segment is drawn to the opposite vertex. A small square is located at the intersection of the dashed line with the side of the triangle. The dashed line segment is labeled 7.1 yards.
A. 198 yd2
B. 106 yd2
C. 99.4 yd2
D. 32.2 yd2

<@&286206848099549185>

[safe radish]

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[sour lagoon]

i don't really know what to do

[queen parcel]

Congruent triangles?

[sour lagoon]

yes

[spice grove]

Can you try proving CGF nd CDE congruent?

[sour lagoon]

no not really

[spice grove]

Do you know the criteria for congruency?

Name a bunch.

[safe radish]

@sour lagoon Has your question been resolved?

[safe radish]

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[tight moss]

where may i have went wrong?

[plucky elk]

are you supposed to use gauss's law or something

where's your dA?

[tight moss]

^

[plucky elk]

why $A\cos(\theta)$?

[flat frigate]

riemann

[tight moss]

cause its dot product

just taking that away

[plucky elk]

what's your domain of integral?

[tight moss]

range?

wym

why would you need one

[plucky elk]

what contour integral are you doing then?

$\oint$

[flat frigate]

riemann

[tight moss]

i dont understand that question

[plucky elk]

$\oint$ is called a contour integral. you used that in your calculation. it implies a domain

[flat frigate]

riemann

[plucky elk]

what's your surface?

[tight moss]

circle

[plucky elk]

surface is usually 2 dimensional

is your just a line integral of a circle?

[tight moss]

a circle is 2 dimensional

its in the xz plane

[plucky elk]

a circle is one dimensional

[tight moss]

a line is 1d

a circle has width and height

[plucky elk]

[tight moss]

you mean 3d?

like a sphere?

[plucky elk]

anyway, you need to calculate a perpendicular vector to dot your electric field

[tight moss]

yes so the cos0 = 1

and i continued along

[plucky elk]

your perpendicular is wrong

what's the vector perpendicular to a circle?

[tight moss]

j

[plucky elk]

wrong

[tight moss]

explain

[plucky elk]

draw a circle

and draw two different normals

they're not always $\hat{j}$

[flat frigate]

riemann

[tight moss]

the circle is in the xz plane, the y dir can only be perpendicular though

[plucky elk]

wrong

[plucky elk]

.

[tight moss]

okay

continue

[plucky elk]

the normals should be in the xz plane

[tight moss]

but how if the normals are supposed to be 90 to the surface of the circle

and that would be straight up or down

in the y or -y dir

[plucky elk]

"flux through the circle"

[plucky elk]

it's neither of these

[tight moss]

but if we use the x or z directions then cos 90 would be 0

and it cancels it out

[plucky elk]

you're jumping ahead

[tight moss]

okay

[plucky elk]

share your drawing once you've done this

your drawing should only be in the xz plane

[tight moss]

?

like im not getting the normals on the edge of the circle part

if you mean another way

[plucky elk]

.

[tight moss]

other than this

[plucky elk]

your perpendicular should have 0 y-component

[tight moss]

it would be a dot facing you if i drew it

[plucky elk]

.

just draw a vector perpendicular to a circle in two dimensions

forget the problem

and start all over

[tight moss]

can you draw what youre saying

because i dont think i know what you mean by draw normals other than in that way

[plucky elk]

https://www.google.com/search?q=circle+normal+vector

[tight moss]

perpendicular to the surface

?

?

[plucky elk]

yes

[tight moss]

odd

sure

[plucky elk]

there is not "surface" a circle is one dimensional

[tight moss]

do we have different dimensions?

[plucky elk]

what's the height of a circle

[tight moss]

the height is going into the third dimension

it has 0 value in the third dimension

of course

[plucky elk]

what's the area of a circle?

ah we are talking about two different things

[tight moss]

?

[plucky elk]

i'm talking about the perimeter

you're talking about the disk

[tight moss]

yes

its a circle

lets restart

[plucky elk]

the perimeter is what you're integrating

[tight moss]

A is area tho

why would it be anything else

@plucky elk ?

anyone? lol

[plucky elk]

ok i had this wrong the whole time

yours looks right

Example 17.1.1
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/17%3A_Gauss_Law/17.01%3A_Flux_of_the_Electric_Field

rectangle instead of circle, but same idea

[tight moss]

so how come none of the answers match mine

was my original question

something must be incorrect

[plucky elk]

i guess try this

[tight moss]

what you sent or what youre about to send

[plucky elk]

i mean you try it

[tight moss]

@plucky elk something other than this?

just dont make sense. it would be specified as a wire with radius r rather than a circle

[plucky elk]

oh

the diameter is 0.05

[tight moss]

yes

[plucky elk]

you treated it like a radius

[tight moss]

oh

rip

[plucky elk]

well that was fun

[tight moss]

lmao

[plucky elk]

feel free to .close

[tight moss]

thanks .close

rip

.close

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[unborn wedge]

could i have help with c

[elfin yew]

Just estimate the y coordinate for

(-1.5, ?)

[unborn wedge]

would it be 4

[elfin yew]

About 4 ish

I would say like

4.25 maybe

[unborn wedge]

i will check the answer

The answer is wrong

[elfin yew]

oh

its 4.2 then

prolly

[unborn wedge]

i wrote (-1.5,4.2)

and it appeares wrong

[elfin yew]

You don't have to write that

just write 4.2

[unborn wedge]

oh ok

Thank you a lot

.close

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[native kiln]

help moi

i need to find x's value

I NEED HELP

[lean otter]

you want to get x/6 on the left-hand side of the equation by itself first

so how can you get rid of the 0.55

[native kiln]

subtract by itself ig

[lean otter]

exactly

and once you've done that you just need to somehow get rid of the fraction, and then simplify the rhs

[native kiln]

how do i get rid of the fraction

[lean otter]

so x/6 is the same as dividing x by 6, right

[native kiln]

ye

[lean otter]

what's the opposite of dividing by 6

[native kiln]

x

times

[lean otter]

yes

times by what

[native kiln]

6x?

[lean otter]

yeah times by 6

[native kiln]

so 6x6

36

[lean otter]

so basically $\frac{x}{6} \times 6 = x$

[flat frigate]

rustyy

[lean otter]

that's the idea

to get rid of the fraction you times by the bottom

so in this case once you get rid of the 0.55, you times by 6 and you are just left with the x on the lhs

[native kiln]

so x=36

?

wait

[flat frigate]

rustyy

rustyy

[lean otter]

do you see how that works

we are just doing times 6 on both sides

[native kiln]

so 6 times whatever is in that bracket

[lean otter]

Yep!

[native kiln]

because u isolate the x

[lean otter]

yeah thats right

[native kiln]

wow

thx bro

.close

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[low nest]

I need help with B i'm still stuck on it

[safe radish]

@low nest Has your question been resolved?

[low nest]

.close

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[narrow kraken]

Hi

[narrow kraken]

why is the point at (-1, 3) closed if it's on the horizontal asymptote?

actually, how is there a point at (-1, 3) if it's on the horizontal asymptote

isn't that not allowed

[drowsy moss]

horizontal asymptotes are not like vertical ones. The function can cross the horizontal asymptote any number of times, but the limit as x goes to infinity is that number.

[narrow kraken]

what about a vertical asymptote

if they said f(2)=2

[drowsy moss]

you can do that in a piecewise function. or if x=2 is not a vertical asymptote

$f(x) = \begin{cases} 1/x, & x\neq 0\ 0, & x=0\end{cases}$ is a function where one part has a vertical asymptote at x=0, but the point (0,0) is defined.

[flat frigate]

Zybikron

[narrow kraken]

oh

im so confused by these types of problems

do the lines matter where they're going

at the ends?

[drowsy moss]

yes

[narrow kraken]

or can you just draw them wherever

[drowsy moss]

$\lim_{x\to\infty}f(x) = -2$ means that as $x$ gets large, your function should approach -2. Basically, -2 is a horizontal asymptote.

[flat frigate]

Zybikron

[drowsy moss]

f(x) can cross y=-2 any number of times. but as x goes towards infinity, it should eventually approach -2.

[narrow kraken]

oh ok

thank you

nice pfp

have a good day

.close

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[winged sigil]

How do I simplify this? I can't get the answer

[queen parcel]

Solve for b?

[winged sigil]

Yes

[queen parcel]

First solve for sin b

Then you can use arcsin or sin^-1

[winged sigil]

Oh sin^-1

[queen parcel]

Inverse sin

Or sine inverse

[winged sigil]

So my solution earlier was:
B = 54sin37/49sin

I got confused because this time sin came after the number

[queen parcel]

Inverse sin of (54 sin 37 / 49)

You can’t have sin by itself or arcsin by itself

It needs to be sin or arcsin of something

[winged sigil]

So I'm still missing something?

Oh wait so is the answer 41.55? (Rounded off to nearest hundredths)

[queen parcel]

$\sin^{-1} \left(\frac{54 \sin 37°}{49}\right)$

[flat frigate]

Shen

[queen parcel]

Make sure you’re in the appropriate units

Degrees or radian s

[winged sigil]

Oh now I get it

Thank you very much kind sir/ma'am

[queen parcel]

I am male - but don’t worry about my pronouns too much 🙂

Thank you for thinking of them though 👌

Cool shit

Take care! Close the channel if you’re done

[winged sigil]

Take care too

.close

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[fading raft]

dont understand the boxed part. what does t-x/v represent?

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[fading raft]

.close

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[left temple]

given a matrix m by n, why is the column space in R^m and not in R^n?

[plucky elk]

Do the matrix vector multiplication

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[simple herald]

Is the slant height of a triangular prism the same height as the height from the apex to the center of the base

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[jagged snow]

nope

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[clear lynx]

guys i need help

[clear lynx]

so i rember a formula

but i'm not sure

[plucky elk]

Was it $e^{i\pi} + 1 = 0$?

[flat frigate]

riemann

[clear lynx]

in which you multiply a prime number for 3 and the result should be added to a number and the final result is a multiple of 4

can someone help me about this?

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@clear lynx Has your question been resolved?

[opal stump]

Petra y Billy tienen colecciones de estampillas.Petra tiene tres grupos de cien estampillas, más nueve más.Billy tiene tres grupos de cien estampillas.Escribe expresiones numéricas para mostrar cuántas estampillas tienen Petra y Billy. ¿Cómo se comparan las expresiones?

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[quick kestrel]

For part b, are there any hints on how I can change 6X into X? (third congruence)

[feral linden]

Divide them all by 3 first

2x=5 mod 9

(2,9)=1 you can complete the rest now

[quick kestrel]

Ok, thanks. I also found another way, which is taking the inverse.

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@pastel briar Has your question been resolved?

[feral linden]

When you said interval, like (a,b) could a be negative infinity? Or could b be positive infinity?

( if both are not allowed then you are right, it’s not a sigma algebra

Yeah countable union like countable union of (n-2,n+2) can give you the whole R

Yeah

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[quiet shard]

110

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[drowsy parcel]

You are doing a significance test with null hypothesis μ = 20 against one of the alternative hypotheses below. If your z-statistic is 1.47, find the corresponding P-value.

Give your answers as decimals between 0 and 1, rounded to two decimal places.

If the alternative hypothesis is μ > 20, then the P-value is

If the alternative hypothesis is μ ≠ 20, then the P-value is

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[shut flare]

How can I prove this?

[pulsar condor]

do you know calc?

[shut flare]

I'm in calc 2 rn

I know some calc

[pulsar condor]

ok, so let $f(x)=\arcsin(x)+\arccos(x)$

[flat frigate]

Mosh

[pulsar condor]

show it's a constant function

[shut flare]

derivative?

[pulsar condor]

what would the derivative be of f(x)?

[shut flare]

1/(sqrt(1-x^2) + 1/(sqrt(1-x^2)

I think

We covered this today

So I'm a bit new

[lyric vine]

i will argue that there is a solution which requires zero calc

[broken yew]

You can prove this with geometry yes...

but uh the range of x

[shut flare]

I'm terrible at geometry

[broken yew]

I doubt it is beyond you

[shut flare]

I should do some khan academy

[broken yew]

draw a right triangle

[shut flare]

Okay

[shut flare]

I started with that but I got stuck

[pulsar condor]

no

[lyric vine]

nah i was thinking playing with the identity

$\sin\theta=\cos(\frac{\pi}{2}-\theta)$

[flat frigate]

A Fellow Human

[pulsar condor]

arccos(x) differentiates to -1/sqrt(1-x^2)

[broken yew]

ah that would be smarter than what i said lul

[shut flare]

oh I thougght it was a difference in the original equation

I'm dumb

Thats why I ate the negative sign

[broken yew]

but either work

[shut flare]

ooh

[broken yew]

you can draw a right angle

so that the sin ratio is x

for one of the angles

[shut flare]

uhu

[broken yew]

then check what cos of the other angle is

And what they must add up to...

[shut flare]

ok let me do that rn

[broken yew]

its exactly what this identity tells you

[shut flare]

I kinda did that and stopped halfway thru cuz I felt like it was going nowhere

i'll get back in a bit, trying it now

[lyric vine]

yeah

tbf the other answer about differentiation s the way to go if you've defined sin and cos as series and not as unit circle/right triangle ratios

[shut flare]

Idk about series yet

We haven't covered it

[lyric vine]

ignore the message above then, ig you'd probably want to go by your geometric definitions

[shut flare]

do I only need one triangle for this?

[broken yew]

1

[shut flare]

ok thanks

I'm pretty sure I'm doing it wrong

(ignore the second triangle)

[broken yew]

There are 4 possible sin or cos relations to obtain from 1 triangle

[shut flare]

Hmmm

Using the same triangle