help-36

[warm elbow]

How do I show my work like the typing sent by texit?

I want to verify if it’s correct with you

This thing

And what about the x^2+y^2=0 part?

[proud jolt]

$\forall z\in \mathbb{Q} : : : xyz \leq 0$

[soft zealot]

tales

[proud jolt]

whats of the negation of being equal

[warm elbow]

Ohhh not equal

Like /=

So negating statements is just changing “there exist” to “for all” and then just change whatever condition they have to the opposite?

We keep the “being an element of what set” constant? That’s the only thing we don’t change?

[proud jolt]

yes

[warm elbow]

Does the imply symbol need to change or is this good?

[final saddle]

@warm elbow Has your question been resolved?

[warm elbow]

.close

[final saddle]

Channel closed

Closed by @warm elbow

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[hoary nacelle]

what would then be the Standard deviation of lead time ??? (considering months as time unit for calculations)

[final saddle]

@hoary nacelle Has your question been resolved?

[hoary nacelle]

<@&286206848099549185>

[final saddle]

@hoary nacelle Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[dapper canopy]

how do I solve |x^2 - 8x +6| < 6

[spark anchor]

compute the roots first of all

[dapper canopy]

wdym

[spark anchor]

find the roots.

[stone wagon]

consider two cases
x^2 - 8x + 6 < 6
or
x^2 - 8x + 6 < -6

[dapper canopy]

what like ( x - 8 )( x + 0 ) < 0

and ( x - 6 )( x - 2 ) <0

[dapper canopy]

alright

[final saddle]

@dapper canopy Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[reef granite]

Hello, can someone help me confirm my proof is correct?

[hoary kelp]

what proof?

[reef granite]

the proof states: ax+b is even if x is odd or b is even

[hoary kelp]

how about a?

[reef granite]

doesnt say

[hoary kelp]

then I don't think it fully correct

[reef granite]

I just flipped the argument around and said: if x is even and b is odd then ax+b is odd

and then I set x = 2k and b = 2k+1

[hoary kelp]

$3*1+4$

[soft zealot]

Jon

[hoary kelp]

if you try that it will equals to 7

[reef granite]

damn

[hoary kelp]

which x is odd and b is even

by the way, this is a way to disprove something, just try to use some random numbers or special numbers to see if it works

[reef granite]

okay ill try it

.close

[final saddle]

Channel closed

Closed by @reef granite

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[crude ravine]

Hello! I need help with a combination problem
There are 8 points drawn on a piece of paper such that no three of the points are collinear
a. How many distinct lines joining these points can be drawn
b. How many distinct triangles whose vertices are among the 8 points can be drawn

[ivory vessel]

if you draw a line on any of the given 8 points

how many points do you use

[crude ravine]

2?

[ivory vessel]

yes

so the number of lines you can draw out of 8 points is...?

[crude ravine]

Do I multiply or divide?? 4 or 16??

[ivory vessel]

have you learned choose

[crude ravine]

4?

[rich tide]

does the first question ask for the maximum lines that can be drawn?

hop into #discussion

[crude ravine]

Honestly idk but the question is just written like that I didn't change anything

The question says no three of the points are collinear I'm not sure what that means tho

What does that mean

[rich tide]

two points may lie on the same line

which they always do

but no three points can lie on the same line

I misinterpreted it

the question is completely right

[crude ravine]

So what do I do?

[rich tide]

consider one point out of the 8

[crude ravine]

Then?

[rich tide]

how may lines can you draw to the remaining points

[crude ravine]

I'm sorry I'm stil confused TT

[rich tide]

like mark 8 points on any piece of paper

consider one point

and count how many lines can you draw so that the lines passes through that point and any other point

[crude ravine]

wdym by consider one point?? I'm rlly slow sorryyyy TT

[rich tide]

Okay let's go by a different method

if you draw a line on any of the given 8 points how many points do you use

[crude ravine]

2

[rich tide]

and how many points are available?

[crude ravine]

8

[rich tide]

can you conclude that each pair of points determines a distinct line

like if you chose any two points at random, they form a distinct line

[crude ravine]

Is it 4?? There's 4 pairs in 8

[rich tide]

no

[rich tide]

there are 4 distinct pairs in 8 and we're not looking for distinct pairs

what we're doing here is basically choosing two points out of eight

can you write that in combination notation?

[crude ravine]

N=8 r= 2 right??

[rich tide]

yes

[crude ravine]

It's 28

[rich tide]

yes

[crude ravine]

Is that it for part a??

[rich tide]

yes

[crude ravine]

Can you also explain part b??

[rich tide]

now how many points you need to form a triangle?

[crude ravine]

3

[rich tide]

can you again conclude that any 3 points would form a distinct triangle?

[crude ravine]

I do the combination notation again??

[rich tide]

ye3s

yes

[crude ravine]

56

[rich tide]

yes

[crude ravine]

Thank youuu

.close

[final saddle]

Channel closed

Closed by @crude ravine

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[quaint scarab]

i dont rly know where to start

[neon slate]

do you remember any trig formulas that might be relevant here?

hint: double angle

[quaint scarab]

ok lm check and think

so then a=15

or?

its 15sin6x

[neon slate]

what trig identity did you use?

[quaint scarab]

sin2(theta)=2sin(theta)*cos(theta)

i havent done much trig before so i dont come up with them on the spot, the hint was usefull!

[neon slate]

yes that's it, , sin(2theta)

[quaint scarab]

ok thank u!

.close

[final saddle]

Channel closed

Closed by @quaint scarab

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[warm elbow]

Hi! Could someone help with this?

[warm elbow]

I have no idea what to do here🥲

<@&286206848099549185>

.close

[final saddle]

Channel closed

Closed by @warm elbow

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[nova iron]

Hi, how would i do this?

Sorry you guys have to read this essay lol

4 facilities: 2x
[2,4] facilities: 3x
0 facilities: 4x
i think

[wet warren]

Let the people who use 4 facilities be F4, who uses 3 be F3, who uses 2 be F2, who uses 1 be F1. People who don't use any be F0
So
F0 = 2xF4
F0+F1+F2+F3+F4=1160
There is also the line that says for every person who use F facilities, there are exactly 3 persons who use AT LEAST F-1 facilities
Which I don't know how to take advantage of mathematically

[nova iron]

right

[wet warren]

Let's say that for every person of F4 people there are exactly 3 people who use at least 3 facilities
Meaning they may use 3 or 4

[nova iron]

yeah i think that's what i wrote out

for every other person you have three so if we use n as a counting index

2n is the 4 facilities

and 3n is the [2,4] facilities

cuz for every 2 in 4 faciities you have 3 in the [2,4] faciities, no?

maybe i should ping helpers too? idk

could someone help

[final saddle]

@nova iron Has your question been resolved?

[nova iron]

<@&286206848099549185> could someone help?

[final saddle]

@nova iron Has your question been resolved?

[nova iron]

<@&286206848099549185> 😭 could someone help please

[tranquil pine]

no

[final saddle]

@nova iron Has your question been resolved?

[nova iron]

don't worry, i think you need help yourself too lol

.close

[final saddle]

Channel closed

Closed by @nova iron

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[tawny ivy]

How can I show that?

[final saddle]

@tawny ivy Has your question been resolved?

[tawny ivy]

Nope <@&286206848099549185>

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

@tawny ivy Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[teal crescent]

With the formulas KA = 0.24x + 55 and KG = 0.32x + 49 you can calculate how much you have to pay at the car sharing companies AutoShare and GreenCars if you rent a car for one day and drive x kilometers. Here the costs are K in euros.

a Investigate by solving an inequality how many kilometers of driving GreenCars is cheaper than AutoShare.

b For how many kilometers is AutoShare at least 10 euros cheaper than GreenCars?

(0.24x+55<0.32x+49-10

0.24x-0.32x<49-10-55

-0.08x<-16

x>200

AutoShare is at least 10 euros cheaper than GreenCar when driving more than 200 km.)-> answer from school

Why do they do -10 at greencars formula when autoshare is supposed to be 10 cheaper

[teal crescent]

Please ping me when someone replies!

[final saddle]

@teal crescent Has your question been resolved?

[final saddle]

@teal crescent Has your question been resolved?

[final saddle]

@teal crescent Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[verbal basalt]

Let $\Delta:X \rightarrow X\times X$ be diagonal map where $X$ is manifold. It's derivative at point $p$ is $d \Delta_p(v) = (v,v) $ for $v \in T_pX$.

My question is, why is pullback $d \Delta^_p (\eta,\zeta) $ equal to $\eta +\zeta$ where $\eta ,\zeta \in T^_p X$?

[soft zealot]

Gigrise

[final saddle]

@verbal basalt Has your question been resolved?

[final saddle]

@verbal basalt Has your question been resolved?

Channel closed

Closed by @verbal basalt

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[bitter glacier]

is the answer 4.5 im just asking because its really annoying to get questions wrong on ixl

[fathom walrus]

well howd u do the problem

[bitter glacier]

ok so first i figured out that i needed to use tan so i just did tan(27)=square root of 5/TU

and then i multiplied by tu

on both sides

then i just put tan(27) into the calculator

gave me 0.509

[fathom walrus]

howd you figure out that u needed to use tan

[bitter glacier]

tbh idk how to explain i kinda just used instincts because tu is adjacent to angle t and square root of 5 is opposite to angle t

[fathom walrus]

ok so heres the thing

theres an angle, theres a side opposite the angle, a side adjacent to the angle, and the hypotenuse

TU is the hypotenuse

the hypotenuse is the side opposite the right angle

always.

[bitter glacier]

oh yeah

so i wouldnt be able to use tan

[fathom walrus]

correct

[bitter glacier]

so then id have to do sin

[fathom walrus]

yea

[bitter glacier]

alr hold up imma redo my work and then give an update of what i get

[fathom walrus]

ping when done

[bitter glacier]

@fathom walrus alr so i got 4.9555556, ixl is asking me to round it to nearest tenth so would it be 5?

[fathom walrus]

yea

if thats the right value then yea

[bitter glacier]

alr i got it right this can be closed now

.close

[final saddle]

Channel closed

Closed by @bitter glacier

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[silent heron]

im confused how to graph this bedcause i always end up with the asypmtote being above the graph

[final saddle]

@silent heron Has your question been resolved?

[silent heron]

<@&286206848099549185>

[white tiger]

shouldnt your hor asymptote be y = -5

[silent heron]

yeah which is why im confused that my y was -8

[white tiger]

how did you even get that

[silent heron]

cuz i did 1-4*2

-5

to get -8

for x bgeing 3

[white tiger]

if x is 3 then 4^(x-3) is 1 no?

3-3 = 0

4^0 = 1

2(1) - 5 = -3

[silent heron]

i just transalated the previpous one down 5 and right 3 and then multiplied the y values by 2

[white tiger]

the original asymptote for 4^x-3 is y=0

shift it down 5 units

so your new asymptote is y = -5

[silent heron]

oh wait for the original equation i used 4^x and not 4^x-3

does that change it

[white tiger]

not really

4^x and 4^x-3 has the same asymptote

y = 0

[silent heron]

i need to find the points for x=0 and x=1 to make a graph and i thinkthats where i messed up

i plugged them into to get 1 and 4 and just used ther tranformations to get -4 and -1

then i multiplied those by 2

to get -8 and -2

but i messed up because it cant be below -5

[white tiger]

eh idk i think its easier if you work with the original equation itself

seems like x = 3 and x = 4 will give you a whole number

[silent heron]

does x have to be above 3

oh wait nvbm

it doesntg

does this seem right

[white tiger]

,rccw

[white tiger]

yeah seems about right

[silent heron]

alr ty

[white tiger]

then you just draw it flatter as x goes to the left

just like the normal exponential graphs

[silent heron]

o yeah

[final saddle]

@silent heron Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[woven harness]

Need help on the other 3 questions on conditional probability

[woven harness]

same is the probability and republican is the given right?

[marsh temple]

for the first one, yes

you're computing the probability that someone believes the economy is the same given that you know they're republican

[woven harness]

yeah I simply did the sum of republicans divided by the total of those people

but besides that for the P(same | Republican) I have to divide same and republican by something right?

[final saddle]

@woven harness Has your question been resolved?

[final saddle]

@woven harness Has your question been resolved?

[tall mantle]

For P(same|Republican) you are only considering the adults who chose "Republican", so the denominator is the sum of Republican
The numerator is the adults who chose "same" among those who chose "Republican" so it's 104

Besides did you calculate the second question correctly? Seems it didn't match mine

[woven harness]

ah ok

[woven harness]

yeah went to fast on a too easy question with that

[woven harness]

and I'm guessing the Republican | same is 186/104

[tall mantle]

Noooo the probability cannot exceed 1

[woven harness]

yeah just caculated earlier

its a whole number

so what should I do in its place?

[final saddle]

@woven harness Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[violet bramble]

what's a mean of variable change?... How do I solve part (a) and use it to solve (b)... Additionally, in the reduction formula question. I don't understand what he means by "Establish" like should i prove the formula given or what?

[floral nova]

That is a typo, it should say "means" and yes you should prove the reduction formula.

[final saddle]

@violet bramble Has your question been resolved?

[violet bramble]

okay byt i still don't understand how to answer part a

but*

[lyric summit]

in point a) you have to derive the given formula using appropriate substitution, because the change of the integration variable can be obtained by substitution

[violet bramble]

so sorry but can you like show me a working cuz i don't understand

[lyric summit]

Have you ever integrated using substitution?

[violet bramble]

yea i did but never came across a question like this

I just don't understand how we should do it

[lyric summit]

take the integral on the right-hand side, and use the substitution u = a + b - x

and try to obtain the integral in the simplest form possible

[violet bramble]

ah okayy i think i get it

thank uu

[lyric summit]

yw)

[final saddle]

@violet bramble Has your question been resolved?

Channel closed

Closed by @violet bramble

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[boreal spruce]

\textbf{\textit{\textcolor{blue}{Question:}}}
An absentminded worker does not remember which of his 12 keys will open his office
door. If he tries them at random and with replacement:
\begin{enumerate}
\item On average, how many keys should he try before his door opens?
\item What is the probability that he opens his office door after only three tries?
\end{enumerate}

\textbf{\textit{\textcolor{red}{My answer:}}}
\begin{enumerate}
\item The worker is trying the keys with replacement, which means after each try, he puts the key back, and each key has an equal chance of being picked again. This is a geometric distribution problem. The expected value (average) of a geometric distribution is 1/p, where p is the probability of success on each trial. In this case, the probability of success (picking the right key) is 1/12 (since there are 12 keys and only 1 will open the door). So, on average, he should expect to try keys $1/(1/12) = 12$ times before the door opens.

\item The probability that he opens the door on the third try (which means the first two tries were unsuccessful, and the third try is successful) can be calculated using the formula for the probability mass function of a geometric distribution: $p*(1-p)^{n-1}$ where p is the probability of success on each trial, and n is the number of trials. Here, p = 1/12 and n = 3. So, the probability is $(1/12)(1 - 1/12)^{3-1} = (1/12)(11/12)^2 \approx 0.071$ or about 7.1%.
\end{enumerate}

[soft zealot]

Trenton

[boreal spruce]

Can anyone help me to have a check of my answers? Thanks!

[final saddle]

@boreal spruce Has your question been resolved?

[final saddle]

@boreal spruce Has your question been resolved?

[final saddle]

@boreal spruce Has your question been resolved?

[final saddle]

Channel closed

Closed by @boreal spruce

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[storm void]

Is their some series or sumth?

I dk how to do this

[silver maple]

Find I_0, I_1 etc

[storm void]

x and ln(sinx)

But

how do i use u then

theres no cotx in that

x ln(sinx) , -x - cotx ,

oh iseeee

they cancel

nah man

tf

I10

i do 10 integrations

tf

[silver maple]

There should be some general pattern you can find

[storm void]

i think i ned

General form of I(n)

[silver maple]

Maybe I_n = 1_(n-1) some recursive formula

[storm void]

oo

yeee

I(n+2) = abc - I(n)

abc is uhhh

cot^(n+1)x/n+1

@silver maple what now

[silver maple]

I don't know

[storm void]

ah ok

i think i found it

Yee got it

Just had to put n in that 0 123 add allofthen

.close

[final saddle]

Channel closed

Closed by @storm void

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[hollow flume]

Can someone verify this ?

[static fractal]

looks fine

[hollow flume]

Ok but how ?

I mean the steps that led to it.

[hollow flume]

.

[static fractal]

\begin{align*}
x^3+x-1&=0\
x^3+x&=1\
x(x^2+1)&=1\
x&=\frac{1}{x^2+1}
\end{align*}

[soft zealot]

Desync

[hollow flume]

ah

well that was ez

thank you.

.close

[final saddle]

Channel closed

Closed by @hollow flume

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[split oak]

Solve the compound inequality and give your answer in interval notation.

4x-4>0 AND -1x-5>=-7

[final saddle]

@split oak Has your question been resolved?

[craggy plank]

!status

[final saddle]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[modern wraith]

Does the number $\binom{k}{k_1,k_2,\dots,k_n} / n!$ have a special name?

[soft zealot]

bigpufik

[modern wraith]

if no, were does it appear?

[final saddle]

@modern wraith Has your question been resolved?

[modern wraith]

<@&286206848099549185>

<@&286206848099549185>

[scarlet plank]

,rccw

[scarlet plank]

So I’m doing a physics problem right

Accl=(m1*g)/M1+M2

M1 is the weight in 10 gram increments

What it’s pulling is 500g

[modern wraith]

.close

[final saddle]

Channel closed

Closed by @modern wraith

Use .reopen if this was a mistake.

[scarlet plank]

So like the formula I have is the weight*gravity/ the sum of the two

Ignoring friction

But like

The data vs theoretical is so off it’s crazy

Any suggestion on what I missed???

.close

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[warm python]

$\sin^4\left(\frac{\pi}{8}\right)+\sin^4\left(\frac{3\pi}{8}\right)+\sin^4\left(\frac{5\pi}{8}\right)+\sin^4\left(\frac{7\pi}{\left(8\right)}\right)$

[soft zealot]

Why am. I here

[warm python]

I first re-wrote the last two terms to obtain

$2\sin^4\left(\frac{\pi}{8}\right)+2\sin^4\left(\frac{3\pi}{8}\right)$

[soft zealot]

Why am. I here

[warm python]

now to solve this do I need to find sin(pi/8) or is there a way around that

oh

I just use the half angle formlae, right?

[cold gorge]

Do you realise

3pi/8 = pi/2 - pi/8

[warm python]

$\left(\frac{\left(1-\cos\left(\frac{\pi}{4}\right)\right)^2}{4}\right)$

[soft zealot]

Why am. I here

[warm python]

oh

so that's just cos^4(pi/8)

I complete the square then, I pressume?

[cold gorge]

yeah pretty much.

Then you can use sin(pi/4)

[warm python]

hmm, $1=sin^4(pi/8)+cos^4(pi/8)+2sin^2(pi/8)cos^2(pi/8)$

[soft zealot]

Why am. I here

[warm python]

I then use sin(2a)

got it

that's much faster, thanks!

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[warm python]

$m^2\cos\left(\frac{2\pi}{15}\right)\cos\left(\frac{4\pi}{15}\right)\cos\left(\frac{8\pi}{15}\right)\cos\left(\frac{14\pi}{15}\right)=n^2$

[soft zealot]

Why am. I here

[warm python]

I started by re-wirting this as

$-m^2\cos\left(\frac{2\pi}{15}\right)\cos\left(\frac{4\pi}{15}\right)\cos\left(\frac{7\pi}{15}\right)\cos\left(\frac{14\pi}{15}\right)=n^2$

now I use the double angle identities, I guess?

though won't that be rather nasty

[tranquil pine]

i dont see what did you re write

[warm python]

cos(8pi/15)=-cos(7pi/5)

[soft zealot]

Why am. I here

[tranquil pine]

oh okay

what are we supposed to do in this ?

[warm python]

oh , forgot to mentiom

find(m^2-n^2)/n^2

[tranquil pine]

okay

[warm python]

yeah, that doesn't seem to help too much

[warm python]

this

[compact breach]

What are m and n?

I feel like my method is rather too long for this one

[warm python]

just two constnats, I think

[warm python]

what was your method? product to sum?

[compact breach]

I think

I have found a way to solve this

But the only problem lies in finding the value of cos14pi/15

,w cos(14pi/15)

[soft zealot]

Results provided by WolframAlpha

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

Requested by coldtee

[compact breach]

Wait a min

Isnt that cos2npi/15

Ughhh

[warm python]

no, that would be -cos(13π/15)

[compact breach]

What do you mean

[warm python]

nvm

sorry

[cold gorge]

Yeah I'm done I think.

@warm python still need help?

[compact breach]

I feel like it would be a lot easier with 16pi/15

[cold gorge]

You can generate that!

[warm python]

yeah please

[cold gorge]

That's exactly how it's done.

So like

[compact breach]

What I did was multiply 2sin2pi/15

[cold gorge]

Yes, yes.

[compact breach]

Divided by 2

Then its a pattern from there

[cold gorge]

You multiply by 2^4 and sin(pi/15)

And then divide by this.

[compact breach]

You get m^2/n^2 ratio use dividendo

[warm python]

oh, ok

[compact breach]

But 14pi/15 is so odd here

Or maybe Im being dumb

[cold gorge]

that's -cos(pi/15)

Multiplied with 2sin(pi/15) , it's sin(2pi/15)

And so on.

[compact breach]

Ohhh

Lmao

I paired wrong

[warm python]

ykw, this seems really interesting, I want to think about this a bit more, can I close this for now? Sorry

[cold gorge]

Sure.

[warm python]

thanks

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[cold gorge]

(Dividendo)*

[compact breach]

My bad

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[maiden cairn]

can someone pls help me with this

[trail crest]

Did you expand it

[maiden cairn]

i tried, im not able to solve it. when i put it in the calculator, it either says timed out or gives me different values each time

[compact breach]

Show your work

[compact breach]

You made a mistake

2^{10-r} as well

Not just 2

[maiden cairn]

Oh yea

Thanks

[final saddle]

@maiden cairn Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[opaque shore]

One way to find the sum of all natural numbers up to n, S_n, is to say something like:

S_n = 1+2+3+...+n
So:
S_n = An^2+Bn+C -- why??
Conditions:
* S_(n+1) = S_n + (n+1)
* S_1 = 1

Now, find A, B & C such that the conditions are true.
An^2+Bn+C+(n+1) = A(n+1)^2+B(n+1)+C
<-> An^2+Bn+C+n+1=An^2+2An+A+Bn+B+C
<-> An^2 + (B+1)n + (C+1) = An^2 + (2A+B)n + A+B+C
So we get the following equations:
* A=A
* B+1=2A+B
* A+B+C=C+1
We now solve these.

B+1=2A+B <-> 2A=1 <-> A=1/2
A+B+C=C+1 <-> A+B=1 <-> B=1/2
Since A=1/2 and B=1/2, C=0.

So:
S_n=1/2n^2+1/2n
=1/2(n^2+n)

I understand the idea of assuming that something can be written as something else and then calculating the constants, but I don't understand why you assume that e.g. this sum can be written as An^2+Bn+C or why the sum 1+2^2+3^2+4^2+...+n^2 can be written as An^3+Bn^2+Cn+D? Please help ♥️

[opaque shore]

(oops I didn't give any argument to make sure that S_1=1 but I suppose you'd just test the equation? Or is there a better way? I would like someone to tell me what the absolute best way to approach these things is)

[stuck tide]

You don't assume them to be anything, they just turned out to be regular polynomials

Take fibonacci series to account

[opaque shore]

You do assume that S_n is a quadratic

[trail mango]

yes you do

[stuck tide]

You don't have to

[stuck tide]

Wdym?

[opaque shore]

With this method you do have to

[trail mango]

you do for this method to work

[opaque shore]

I'm asking about this method specifically to be clear

[stuck tide]

You can prove the sum of n numbers without assuming S_n to be anything

[opaque shore]

But then you're not using this method are you?

[trail mango]

dawg i think you're misunderstanding the question

[opaque shore]

My goal isn't to prove what the sum of those n numbers is. That's easy. My goal is to learn the reasoning behind doing it with this particular method (which is "overkill" here)

[stuck tide]

Is he asking why 1 + 2 ... is quadratic and 1^2 + 2^2 ... is cubic?

[opaque shore]

Yeah I'm asking why you can assume that 1+2+... is quadratic and why e.g. 1^2+2^2+... is cubic

[trail mango]

pretty much

[trail crest]

I can only give you like a motivation why you would assume it.

Say f(n) is the sum of first n numbers to the m'th power.
Then f(n + 1) - f(n) = (n + 1)^m
And that looks like a function of degree m + 1

[stuck tide]

Yeah, that's actually enough evidence if you assume it has to be a polynomial

[opaque shore]

That's basically the condition I wrote as well, but generalized to mth power

[stuck tide]

And not only does it look like one, if it's a polynomial it has to have degree m+1

Because the biggest degree term will cancel

[trail crest]

Yes. I mean it isnt a proof that f is polynomial of degree m + 1. But it is enough motivation that you can assume it is and find out if it is yourself

[stuck tide]

Or actually

Hmm

No actually it can be anything bigger than m

[trail crest]

Like you can have assume it is then prove your result via induction

[trail mango]

there's a simpler answer

[opaque shore]

For assuming that 1^2+2^2+3^2+... is quadratic my book says "Since there are n terms and the biggest one is of size n^2, it is reasonable to think that S_n can be written An^3+Bn^2+Cn+D ..."

I don't understand the full reasoning there though

[stuck tide]

Yeah that's not enough information

[trail mango]

the growth of the S if S satisfies S_(n+1) = S_n + (n+1) is linear, so S is quadratic by basic calculus

similar with higher orders

[trail crest]

I mean for a polynomial to change for a square it really has to be 3rd degree polynomial

Everything above is too much and everything under is too little

If it is a polynomial then it has to be 3rd degree i think

[stuck tide]

Isn't that what casework said too

[opaque shore]

yeah that's fair. This is before calculus (I haven't started with it) but I understand

[stuck tide]

Actually it must be m+1, and can't be anything higher or lower, If you take (m+1)th derivative:
f^(m+1)(n+1) = f^(m+1)(n)
so f^(m+1)(n) = C
so degree of f must be m+1

And by just observing, it can't be lower than m+1

Not sure if there's another way to show this

[opaque shore]

Btw what is it called when you have some equation which you just assume to be of some form, perhaps with an educated guess, and then calculate the values for the constants to satisfy the conditions? There's a word for it in my language but I don't know if there is in english

(google translate wasn't helping)

[stuck tide]

What language do you speak, and what's the word

[opaque shore]

swedish. Word is "ansats"

or "ansättning"

[trail crest]

So basically like bashing

But that isnt a translation

It just means to brute force

[opaque shore]

So there's no commonly used word in math for this?

[stuck tide]

Not that I'm aware of

[opaque shore]

So you're supposed to just write "Let ... = ..." or "Assume that ... = ..." in all these cases?

[stuck tide]

You mean as like a math symbol?

[opaque shore]

No it's just a nice word

[stuck tide]

I think I don't get the purpose of the word

What

[opaque shore]

looks like german

Is ansatz actually english hold up

[stuck tide]

I think it is

I bet it is commonly used

[opaque shore]

Yeah "Ansatz is german but is also used in english"

damn

Well now I know 😄 not sure if I'm supposed to use it in mathematical text though

ur chatgpt response seems to suggest it's ok but i don't trust chatgpt

[stuck tide]

Google backs it up too

[opaque shore]

TIL 😄

[stuck tide]

Or just use the word "motivation"

"by using the motivation we got from <insert step>"

[opaque shore]

It's not really the same thing

An ansats in swedish is basically when you make some assumption, work it out and then confirm it latern on when it actually gives you solutions

[stuck tide]

So basically ramanujan = ansats

[formal trail]

https://math.stackexchange.com/questions/3253938/what-ansatz-means

[opaque shore]

in this page they use the word ansatz similarly to how it's used in swedish

You can change the word a little to make it a bit more ergonomic in swedish but yeah it's basically the same

[stuck tide]

👀

[opaque shore]

😂

[stuck tide]

Ironically, obscure is an obscure word.

[opaque shore]

true

[stuck tide]

Anyways I think we got way off topic

[opaque shore]

yeah

Well

[stuck tide]

https://tenor.com/view/the-more-you-know-gif-10358303

[opaque shore]

I'm still a bit sad I didn't understand the full reasoning behind what the book says because I feel like there has to be something you can add to it for it to make perfect sense

I guess I'll just let it go

[stuck tide]

The base case is I think easy to understand

1 + 2 + ...

Well now that I said it, it is not easy

It is only obvious that it can't be linear

[stuck tide]

Yeah

[opaque shore]

Well I think the base case is easy now

You basically have a bunch of numbers in a pattern and the difference between those numbers is just growing by some constant

You can view this as having acceleraiton=1. Then velocity (difference) is linear, and then position is quadratic

[stuck tide]

Like a geometrical meaning?

[opaque shore]

The book says: Since there are n terms and the biggest one is of size n^2, it is reasonable to believe that S_n can be written as An^3+Bn^2+Cn+D

I just don't understand why "it's reasonably to believe that S_n can be written as ..." from that

[stuck tide]

(Probably)Because it has to be higher than 2

[opaque shore]

So just An^4+... feels to high and An^2+... is too low?

[stuck tide]

Yeah

And quadratic is obviously impossible

👀

[opaque shore]

i havent had sleep ok

[stuck tide]

We are going down hill in channel list

[opaque shore]

we sure are

[stuck tide]

I think we just have to let it go, we proved it too

[opaque shore]

ok

well thanks for helping!

[stuck tide]

You're welcome!

[opaque shore]

.close

[final saddle]

Channel closed

Closed by @opaque shore

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[idle blaze]

(tan-3)(tan+2)

[idle blaze]

what are the 4 solutions?

[opaque shore]

huh

[idle blaze]

I get -63

which somehow isn’t a solution

[opaque shore]

(tan-3)(tan+2) isn't an equation

[idle blaze]

=0

[opaque shore]

you're not gonna get help if nobody understands what you're asking

[idle blaze]

(tan-3)(tan+2)=0

[opaque shore]

You can't just write tan-3 and tan+2, do u mean tan(-3) and tan(2)?

nvm, I guess u mean tan(x)-3 and tan(x)+2?

[idle blaze]

yes the second

[opaque shore]

ok

Well

[idle blaze]

so x = 3 and -2

[opaque shore]

no

tan(x)=3 and -2

there are two values for tan(x)

which satisfy the equation

Then you need the arctan(x)

[idle blaze]

yes

so i do archtan-2

to get -63

but that’s wrong

[opaque shore]

Are we working with degrees or radians?

[idle blaze]

degrees

[opaque shore]

ok

So two of the solutions are arctan(-2) and arctan(3). arctan(x) doesn't give you all the possible values of x though

[idle blaze]

Yeah I learned the graphs for the rest

[opaque shore]

You were taught to use graphs to find the rest of the solutions?

[idle blaze]

yes

so i memorised the sin cos tan graphs

[opaque shore]

😮

Just so u know: y=tanx->x=arctan(y). The other values of x are x+n*pi for some integer n.

You can understand this with graphs. It takes pi radians for the tan function to complete one segment

And so at x+n*pi radians it will repeat itself

This means that there are infinitely many solutions to an equation like y=tanx

In your problem, you have tanx=3 and tanx=-2, and ur working with degrees. So instead of pi, we'll use 180.

tanx=3->x=arctan(3)+180n for some integer n
tanx=-2->x=arctan(-2)+180n for some integer n

* arctan(3)=71.5650512 degrees.
* arctan(-2)=-63.4349488 degrees.
* arctan(3)+180=251.5650512
* arctan(3)-180=-108.4349488
* arctan(3)-2*180=-288.4349488
* arctan(-2)+180=116.5650512
* arctan(-2)+2*180=296.5650512
* arctan(-2)-180=-243.4349488

and so on

There are infinitely many solutions.

The ones in the message above are all the solutions assuming x is in the interval -360<=x<=360 (degrees)

If there really are only four solutions, then the question is either wrong or there's something left out

Do you understand? y=arctan(x) gives one value for what y can be since arctan is a function. Thing is tan(y) is the same if we rotate y by 180 degrees, or 2*180 degrees, and so on

[idle blaze]

I understand

does this work the same way for cos and sin questions

[opaque shore]

not entirely the same

e.g. y=sin(x+n*pi) for some integer n will oscillate between being negative and positive, but the absolute value remains the same

Same for cos

Here is a picture of y=sinx and then I drew lines at x=pi, x=2pi and x=3pi

The sine wave is symmetrical in the sense that the bottom parts and the top parts have the same shape

This means that if you add pi to your value of x, the value of y will be negative that which it was before

For example, look at this:

At x=2+pi, y is negative.
At x=2+2pi, y is the same as it was before but instead positive. We just flipped the sine wave upside down basically

at x=2+3pi, y again became negative, and so on. But the absolute value of y remains the same

So, this is all because the sine wave repeats itself every pi units (and since the negative parts of the sine wave at x=a have the same absolute value as the positive parts of the sine wave at x=a+pi for some number a)

[idle blaze]

I get it

and hopefully cos follows the same rules sin does?

Oh actually cos just connected in my head

thank you a lot

.close

[final saddle]

Channel closed

Closed by @idle blaze

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[wind solstice]

some one just solve this

[median lagoon]

do you know what the symbols mean?

[wind solstice]

ye

[median lagoon]

lets start with x cap y then

what does x cap y look like or mean

[wind solstice]

its the intersection of x and y so c and f

[median lagoon]

good

now visualize that region

you now need to do that cup Z

what does that do

[wind solstice]

its a union so the answer would be a

[median lagoon]

bingo!

[wind solstice]

thank youuuu!!!!

.close

[final saddle]

Channel closed

Closed by @wind solstice

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[north sky]

Question:

"The population in a city follows this mathematical model (Mathematical model linked as an image with this post)

where t is the amount of years after the year 2010. After how many years will the population of the city have increased by 20%?"

I simply do not understand what process I'm meant to take in order to solve this question, I'm lost and unsure how to start.

Any help is appreciated. Thank you for taking your time to help! 🫰

[zenith pollen]

try to rewrite N as 20% larger than N0, then solve for t with logarithms

[north sky]

So I did 1.2N = 10^0.006t

=
lg (1,2N) / 0,006 = 0,006t / 0,006

=
t = lg (1.2N) / 0,006

= approx 13.2N

Though, I got the years correct (13.2), I'm still left with an N variable, am I allowed to just toss that and give an answer of 13.2 or what?

nvm i'm stupid

:D

1.2 = 10^0.006t is enuff no?

[zenith pollen]

right that fixes it haha

[north sky]

Thank you for the help! :D @zenith pollen I'll be clearing this channel for now, so other can use it!

.clear

.close

[final saddle]

Channel closed

Closed by @north sky

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[proven bay]

can someone give me a rough idea of how to solve these, I feel like I got the general idea but I just need a good explanation

[final saddle]

@proven bay Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[lunar pivot]

hello?

[final saddle]

Please don't occupy multiple help channels.

[lunar pivot]

hello?

need help with this it is on identifying features on quadratics

🤦

.close

[final saddle]

Channel closed

Closed by @lunar pivot

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[fleet grove]

hello everyone, having an issue with this integral. i can get to the point where it requires trig substitution but things gets a little messy for me after that. currently at:

[royal gust]

What's the original?

[fleet grove]

^

[final saddle]

@fleet grove Has your question been resolved?

[fleet grove]

?

[vital surge]

oof this is slightly unfortunate

[vital surge]

if i got here i'd probably just finish it with trig sub

it's fairly doable although not very fun

[final saddle]

@fleet grove Has your question been resolved?

[fleet grove]

yeah its not

i think i got it right but the professor answer is different

sooo

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[errant mist]

This is a goes of elevation and depression

[errant mist]

Can someone please help me with these

This is the format my teacher uses

That's for angles of elevation tho i don't have a angle of depression format

Can someone help me

<@&286206848099549185>

[final saddle]

@errant mist Has your question been resolved?

[errant mist]

someone please help me

[mint orbit]

theres so many problems

which one do you wanna do

[errant mist]

theres only 4

[errant mist]

question 1 and 4

[mint orbit]

lets do 1

[errant mist]

ok

[mint orbit]

lemme see

[errant mist]

first i would need to draw the angle but i dont know it it should look

[errant mist]

right here

[mint orbit]

From a point A, 100m above sea level, a sailor sights a boat at an angle of depression as 27 degrees. Calculate the horizontal distance fo the boat from the sailor.

[errant mist]

yea

[mint orbit]

damnit i keep forgetting i dont have a god damn drawing pad

do you know what an angle of depression is

[errant mist]

kinda

[mint orbit]

does this help to draw a picture

[errant mist]

That's what my teacher showed us

Ignore the top

[mint orbit]

i mean using this image can you make a picture of the sailor

in the problem

can you draw a triangle with the given angle

[errant mist]

not really

[mint orbit]

well okay the sailor is up on a pole right

[errant mist]

the triangle shouldnt be the specific angle

[errant mist]

yes

[mint orbit]

and he sees a boat

its presumably on the surface of the water

Can you see how this makes a triangle?

You should be able to label at least...one side and one angle if so

[errant mist]

wait let me draw how i think it should look and show you

[mint orbit]

okay, sure

[mint orbit]

youre almost there, except the sailor is up at the top

otherwise, i think everything in this picture is right

its more like this

[errant mist]

Ohh

Ohhhh

Wait

So he's looking down?

[mint orbit]

yea

hes in a tower or whatever, 100 meters above sea level

and hes looking down at the surface of the water, where he sees a boat

[errant mist]

A light house?

[mint orbit]

yea, sure

i was imagining a crows nest tbh

[errant mist]

Ok I understand that part

[mint orbit]

these things

[errant mist]

Let me right it

[errant mist]

Oh

[errant mist]

Oh I see

So I finish drawing the triangle

Now for the question

@mint orbit

[mint orbit]

yea so youre on the way here

i just added an extra angle marker here from your images

can you see how the red angle is complement to the 27 degrees?

i mean, together they must be 90 degrees

we wanna use this to solve for the red angle (red in my image)

[errant mist]

sorry im back something ergent happened

[errant mist]

Should the 27 degree be in the curve thing

[mint orbit]

curve thing?

[errant mist]

That's what my teacher says

[errant mist]

To close the black and green line

[errant mist]

Oh I see

[errant mist]

Wait

[errant mist]

I'm suppose to be trying to find the missing part

[mint orbit]

the problem is we have one side and one angle

[errant mist]

Which in this case I think it's the bottom line that's adjacent

[mint orbit]

its not enough to solve for what we need

[errant mist]

Oh...

But my teacher only use the degree and the side that has the measurement

[errant mist]

So in this case we have the opposite and hypotonuse

And I'm trying to get the adjacent which is the bottom line

[mint orbit]

im running out of colors

yea want the bottom line, yea

i drew a red arrow

but we have one side length

100m

and one angle

90 degrees

do you see how 27 degrees is outside the triangle?

[errant mist]

Um not really cuz my teacher didn't tell us about that

[mint orbit]

this is just definitions

you see the side with the red arrow, thats what we want to know, yea?

[errant mist]

Yes

[mint orbit]

and the information were given is the height, 100 m

thats part of the triangle

and were given the 27 degrees angle of depression

[errant mist]

Yes

[mint orbit]

that is not part of the triangle

[errant mist]

Oh...

[mint orbit]

its outside the triangle, you see?

it connects a side of the triangle and just that green line

[errant mist]

Wsit

[mint orbit]

that green line isnt part of the triangle

[errant mist]

Right here the angle of depression shows that it goes inside

[errant mist]

Is that what I should do?

[mint orbit]

you need another angle inside the triangle

[errant mist]

So I just put the 27 degrees at the bottom inside

[mint orbit]

if you understand why thats true, sure=

[errant mist]

Cus that's what I think I should do cus that's what my teacher did

Ok wait

[mint orbit]

you should know why its true

but it happens to be true, so, sure

[errant mist]

What next

Now can we start to find the length of the bottom line?

[mint orbit]

you can find it now

[errant mist]

Because we are calculating the distance of the sailor from the boat horizontally

[mint orbit]

yea, you definitely want the bottom

[errant mist]

Ok how do I do that now

So we have the oppsire

Opposite

[mint orbit]

and you want the adjacent

[errant mist]

And hypotoneus

So that's Sin?

Wait first

[mint orbit]

SOH CAH TOA

[errant mist]

I write

Given: opp/angle
Need: adj?

[errant mist]

That's what my teacher do

[errant mist]

Yes

[mint orbit]

so not sine

[errant mist]

Oh

But we have the opposite

And the degree is on the hypotonues

[mint orbit]

dont over think it

[errant mist]

I don't understand

What do we use then

The opposite and adjacent?

[mint orbit]

you have the opposite, like you said

[errant mist]

The opposite we have measurements and the adjacent we need measurements

[mint orbit]

yes

$\tan \theta = \frac{opposite}{adjacent}$

[soft zealot]

jan Niku

[mint orbit]

so rearrange for what you dont know

$adjacent = \frac{opposite}{\tan \theta}$

[soft zealot]

jan Niku

[mint orbit]

heres an explicit formula for the side you want

[errant mist]

why we dont use the hypotonuese?

[mint orbit]

we dont have or want it

[errant mist]

oh

[mint orbit]

we dont know what it is, and we havent been asked to find it

so that means we shouldnt use any formula that involves it

[errant mist]

ohhh

oh i understand

so we are given: opp/angle

we need: adj

and then Tan =opp/adj

since thats what we using

[mint orbit]

this requires that you can identify that you know the side opposite the angle

and you don't care about the hypotenuse

[errant mist]

yes so we ignore that'

[errant mist]

so is this correct so far

[mint orbit]

yes

you should be able to identity that you want to use tangent here

[errant mist]

ok

so what after that

[mint orbit]

you may wanna get in the habit of writing stuff out and circling or coloring or otherwise marking stuff

like, you could write out this

[errant mist]

ok wait

[mint orbit]

like we just know this equation

[errant mist]

yea

[mint orbit]

from SOH CAH TOA

[errant mist]

im writing it

[mint orbit]

and i looked at the diagram and i saw

we know theta (its the angle)

and we know opp

so i drew a green line next to each

and we dont know adj, but we want to

so i drew a red line

if you write an equation with all green lines except one red line

you can solve it for the answer

[errant mist]

im not following

[mint orbit]

its not important its just to help you but if you dont follow it it doesnt matter

[mint orbit]

theres nothing left to do but identify you are done

you need a calculator now

you can solve for the answer

[errant mist]

ohhh

wait

dont we have to cross multiply

miss told me about something like that

[mint orbit]

you can use whatever tool is helpful to you

[errant mist]

no i mean dont we need to cross multiply before we get to our answer

ok so

after writing TanQ= opp/adj

wait

@mint orbit put a random letter at the bottom line

right?

[mint orbit]

what? why?

[errant mist]

so we can acknowledge it

or should i just say adj

[errant mist]

my teacher did it

[mint orbit]

all you need to do is isolate adjacent

[errant mist]

ok

[errant mist]

so after this

[mint orbit]

right, just isolate the thing you want

[errant mist]

do i write Tan27*=I/100 x 100?

the 100 is the 100m

cuz thats what my teacher told us

to do for angle of elevation

and they are kinda simiplar

[mint orbit]

no

[mint orbit]

you can write this

then use a calculator

[errant mist]

oh

um

what exactly should i put in the calculator

100(Tan27)?

@mint orbit

[mint orbit]

i cannot really say anything else @errant mist

i gave you the answer

you just type it into the calculator

[errant mist]

ok thxs

[final saddle]

@errant mist Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[ionic hound]

I have a question about restrictions

[fading dock]

fire away

[ionic hound]

Ok so let's say I had a denominator of:

Where x + 4 is under the square root

When finding the restrictions, would I say whatever is under the square root can not be greater than or equal to 0, and then for the entire expression, would I say it can not equal 0?

[pseudo knot]

Yep

[ionic hound]

Thank you

[fading dock]

actually you would say that whatever is under the square root cannot be less than 0

but yeah

[ionic hound]

Would it just be less than, or less than and equal to?

[fading dock]

less than. it's fine for it to be equal to 0 because the square root of 0 is just 0

you would write that $x + 4 \geq 0$

[soft zealot]

Awesam

[ionic hound]

Ah

Thank you

.close

[final saddle]

Channel closed

Closed by @ionic hound

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• 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.

[pine axle]

The smallest possible integer having the remainders 2,3 and 6 when divided by 3,5 and 11 respectively lies between what?

41 and 50, 61 and 70, 71 and 80 81 and 90 or 91 and 100

[pine axle]

I know it’s 81 and 90, I just don’t know how to solve it without blind guessing

[signal vector]

Are you aware of the Chinese remainder theorem?