help-13

[cedar kiln]

@crimson sedge Has your question been resolved?

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[dark olive]

for 4=8cost

cos^-1(1/2) = π/3

But when I do 2√3 = 4sin2t

then (√3)/2 = sin2t

and 2t = sin^-1((√3)/2)

2t= π/3

t= π/6

where am I going wrong because the only solution is π/3

[crimson sedge]

Both pi/3 and pi/6 are solutions

[dark olive]

So is the answer sheet wrong?

[crimson sedge]

No, because 4 = 8 cos t has -pi/3 and pi/3 solutions

Their common solution is only pi/3

[dark olive]

But why is π/3 the only solution

Oh

okay

thansk

.close

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[crimson sedge]

Not sure where to start on this, need a memory jog:

[crimson sedge]

A & B

[bold vine]

^

[dusty hazel]

Find slope.

[crimson sedge]

For a

Find gradient

And use

y-b = m(x-a) formula

Sorry just B

[tropic oxide]

have you found the midpoint of AB?

[crimson sedge]

Midpoints between A and B is (x1+y1)/2, (x2+y2)/2

[tropic oxide]

......

[crimson sedge]

And again, find the gradient of OM

[tropic oxide]

guess someone had to give it away

[crimson sedge]

And show that OM = -1/AB

[young star]

you have to create a second line running through the points M (midpoint) and O (origin) which is (0, 0)

and show that the two gradients, when multiplied together, make -1

[crimson sedge]

Great, I remember now - thank you guys

.close

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[crimson sedge]

reclaim

[crimson sedge]

jeez i was gone for 45 minutes

[tropic oxide]

why'd you mark your question as resolved tho

[crimson sedge]

i never did

timed out i think

why did you choose to compare those angles tho?

why not CAB and CBA?

[tropic oxide]

those... are the same angles i talked about

just under different names

my choice of naming did not carry with it any special meaning, not in this case at least

[crimson sedge]

wait what

i was thinking that

but i wasnt sure how to prove it

my question is how does the shared base of AB prove their congruence

[tropic oxide]

it alone does not

[crimson sedge]

sorry gtg

gonna be back in 15 minutes or so

hopefully it doesnt time out again

[tropic oxide]

...

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

im back sorry

[crimson sedge]

and how about the fact that AM and AN are congreunt?

[tropic oxide]

they aren't

[crimson sedge]

they arent?

oh we are trying to prove that, right

[tropic oxide]

no we aren't

[crimson sedge]

[tropic oxide]

AM and AN are not congruent, cannot be proven congruent, and it is not our goal to prove them congruent

our goal is to prove AM = BN

here i was trying to appeal to your knowledge of the ASA congruence theorem.

[crimson sedge]

sorry my bad

a typo

[crimson sedge]

this is from the class matierial\

so if we know two of the angles, we know they are congruent?

so ABN and BAM are congruent because of their shared side AB and the fact that AM and BN are congruent

[tropic oxide]

no...

there is a side in angle-side-angle for a reason...

reading comprehension

[crimson sedge]

ah we need to know a common side also

which in this case can be AB

[tropic oxide]

now i am the one who has to go

[crimson sedge]

oh man

im still very very very lost

so ig we proved that BAM and ABN are congruent, but im not too certain

because if they are congruent, then AXN and BXM are congruent

which means that the angles will CAM and CBN will be equal, along with MAB and NBA

right?

<@&286206848099549185>

anyone pls

[dusty hazel]

Can you repost the question?

@crimson sedge

[crimson sedge]

Let triangle ABC be an isosceles triangle with BC=AC. Points M and N are on BC and AC, respectively, so that AM and BN are angle bisectors (that is, angle BAM= angle CAM and angle ABN= angle CBN). Show that AM=BN.

[dusty hazel]

Alright.

So

Do you know how to prove these congruent?

Do you have a certain issue?

Or need help to start this

[crimson sedge]

i think so

i think i can take it from here

maybe

[dusty hazel]

Do you have a figure? I'm lazy to make one XD.

[crimson sedge]

but im really unsure

[dusty hazel]

Good.

So do you have any ideas for how you'd prove those two triangles congruent?

You have AB = AB
This will always be in the criteria.

And now find a few angles that are equal.

[crimson sedge]

my shitty solution

Using the ASA (angle-side-angle) theorem, we can prove that BAM and ABN are congruent; this is because they both share a side AB, sidelengths AM and BN are equal, and angles CBA and CAB, which are congruent. We can then name the intersection point of AM and BN X. Because we proved BAM and ABN are congruent, we know that AXN and BXM are congruent also, because AXB intersects both BAM and ABN. Now, this means that angles CAM and CBN are congruent, along with MAB and NBA, showing that AM = BN.  

this is because they both share a side AB, sidelengths AM and BN are equal, and angles CBA and CAB, which are congruent.

[dusty hazel]

Wait I don't get it.
You have to show AM=BN

After showing that the triangles are congruent.

It is already proved.

Isn't it?

[crimson sedge]

you have to show that when AM=BN

tbh, i actually dont really know

but i gtg

sorry

[dusty hazel]

Lol

[crimson sedge]

i will come back with this tommorow

[dusty hazel]

Once the triangles are proved congruent.

By cpct

[crimson sedge]

cpct?

[dusty hazel]

You can say those two are equal.

Corresponding sides.

[crimson sedge]

yh

[dusty hazel]

Of congruent triangles.

[crimson sedge]

you mean BAM and ABN, right?

[dusty hazel]

Yes.

AM and BN are corresponding sides.

[crimson sedge]

yes

[dusty hazel]

So if these two triangles are congruent.
BA = AB
AM = BN
MB = NA

These are the results you get.

[crimson sedge]

and for the angle bisector stuff to hold, BAM and ABN have to be congruent?

[dusty hazel]

I think not necessarily.

[crimson sedge]

so i still dont see how to solve this

[crimson sedge]

right

[dusty hazel]

I mean if you have angle bisectors then these two triangles are definitely congruent.

So once congruent you have the results already.

Basically the only thing you have to do in the problem is prove them congruent.

Do you have any issue with that?

If not, you can just write because the triangles are congruent we have above results, the ones I mentioned above.

[crimson sedge]

but why?

can you elaborate

[dusty hazel]

You have to show two line segments are equal.

Both are part of two triangles.

So proving the triangles congruent absolutely helps.

Because congruent triangles have exactly same corresponding sides. They can overlap.

So that certainly shows the sides asked are equal.

Your why seems like why are we solving this question?
That I would not know, ask yourself.

[crimson sedge]

which two line segments?

[crimson sedge]

im just really confused

can you use the picture?

[dusty hazel]

I can see the picture.

[dusty hazel]

Triangles BAM and ABN are congruent.
You prove that by using ASA criteria. Once you do that you simply wrap the question by saying since the triangles are congruent line segment AM = BN

[crimson sedge]

sure

but then what does the triangles being congruent have to do with angle bisectors

ig it makes sense actually

how could i use ASA criteria to prove thsi

[dusty hazel]

Angle bisectors are given to prove the triangles congruent.

[crimson sedge]

ah

[dusty hazel]

see

CAB = CBA

Right?

isosceles triangle

[crimson sedge]

so the halfs are equal

[dusty hazel]

yeah

So
MAB = NBA
AB = AB
CAB = CBA

ASA respectively.

Two angles and one included side.

[crimson sedge]

yup

ok

We can use the ASA theorem to prove that BAM and ABN are congruent; CBA = CAB, MAB = NBA, and AB = AB, which is two angles and one included side, proving their congruence. Since these triangles are congruent, and AM = BN.

@dusty hazel

dont see where angle bisectors came in tho

[dusty hazel]

MAB = NBA

Why?

Because they are halves of equal angles.

[crimson sedge]

yes

[dusty hazel]

That's where angle bisectors come into play.

Angle bisectors gave us that result.

[crimson sedge]

but we dont need angle bisectors to know thats true

[dusty hazel]

Yes we just need to know those angles are equal.

With angle bisectors we know for sure they are equal.

[crimson sedge]

didnt say that in the problem statement

[dusty hazel]

That's because of the angle bisectors thingy.

Otherwise you would not know that's true.

[crimson sedge]

i dont see a BAM = ABN here

@dusty hazel

[dusty hazel]

Just because it's not written there doesn't mean it's not true lol.

[crimson sedge]

god help me

so how did you come up with MAB=NBA

im soosoosososoososososos confusededasedesdf

[dusty hazel]

Right.

You should have asked that in the first place.

MAB is half of CAB

NBA is half of CBA.

CAB = CBA.

[dusty hazel]

Tell me whY?

[crimson sedge]

because isosclels

triangle

[dusty hazel]

Right.

So their halves are also equal.

Like if both of those angles are 60.
Their halves are 30 each.

Which are equal also.

[crimson sedge]

ok, thanks

.close

[cedar kiln]

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[dusty hazel]

I can only hope you got it.
You probably didn't. But tomorrow like you told you'll be seeking help again. I hope you realise that then atleast! Have a nice day.

[crimson sedge]

no i get it

i dont need help anymore

[cedar kiln]

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[silver python]

lets say you have these things to pick from:

5 each from a,b
4 each from c,d,e
3 each from f,g,h,i
2 each from j
1 from k,l

what would be the probability that you choose exactly two from f

[silver python]

i cant wrap my head around how to solve this practice problem

[fair geyser]

i don't understand

so you pick 15 things total?

@silver python i can't understand the task

[silver python]

no, what is theporability that f will end sending exactly two contestants

[fair geyser]

ah

so like, f+g+h+i = 3

like you pick 3 times, and each time you have 1/4 chance it's from f?

there's too much left for guessing what it means

[cedar kiln]

@silver python Has your question been resolved?

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[tight geyser]

So here’s a problem that actually may be too easy but it’s frying my brain. Ana(name) and Vera(name) start reading at the same time a book with 180 pages. While Vera reads 2 pages per day more than Ana, she finishes it 1 day faster. How many pages per day did both read?

[fair geyser]

so the sum of their speeds

x is Ana's speed

180/x = 180/(x+2) + 1

ana's time is 1 more than vera's

find x, then x+x+2 is the answer

[tight geyser]

That was actually so ez wth, thanks

.close

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[radiant ibex]

A 250g sample of protactinium has a half-life of 17 days. Determine the amount of
protactinium left after 56 days.

[lyric jungle]

How many half-lives have occurred after 56 days?

[radiant ibex]

3.29

@lyric jungle

<@&286206848099549185>

[lyric jungle]

And do you know the equation for the amount of protactinium left after a certain time period?

[radiant ibex]

wdym

[lyric jungle]

Like the size of the sample that's left?

Do you know how the sample will decay?

[radiant ibex]

no

[lyric jungle]

Okay, $N = N_0/2^{#\text{half-lives passed}}$ where $N_0$ is the initial size/count rate/number of nuclei and N is the remaining number

[wraith dagger]

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

[lyric jungle]

Just plug in the numbers to get N

You know the number of half-lives that have passed

[radiant ibex]

N=N17/2

?

N=56 17/2

i9ts 75.987 grams

[cedar kiln]

@radiant ibex Has your question been resolved?

[solar bison]

@lyric jungle has given you everything you need, so go according to his/her equation

$new amount = (old amount) (0.5)^{(\frac{56}{17})}$

[wraith dagger]

Chris24

[cedar kiln]

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[ornate saffron]

Hello, I would like to know if $\vec{DE}$ or $\vec{DE'}$ goes thought the triangle ABC I wrote a system saying that if $k * \vec{DE} = j * \vec{AB} + i * \vec{AC}$.
On that way, if j + i under 1 and (k,i,j) under (1,1,1) and over (0,0,0) that means that the vector DE goes thought the triangle
So I tried to solve the system on x y z, but I don't find coherent values do you think that the problem comes from me or my hypothesis.
thanks a lot for the one who could help me

[wraith dagger]

desasteur

[cedar kiln]

@ornate saffron Has your question been resolved?

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[ornate saffron]

Hello, I would like to know if $\vec{DE}$ or $\vec{DE'}$ goes thought the triangle ABC I wrote a system saying that if $k * \vec{DE} = j * \vec{AB} + i * \vec{AC}$.
On that way, if j + i under 1 and (k,i,j) under (1,1,1) and over (0,0,0) that means that the vector DE goes thought the triangle
So I tried to solve the system on x y z, but I don't find coherent values do you think that the problem comes from me or my hypothesis.
thanks a lot for the one who could help me

[wraith dagger]

desasteur

[cedar kiln]

@ornate saffron Has your question been resolved?

[cedar kiln]

@ornate saffron Has your question been resolved?

[cedar kiln]

@ornate saffron Has your question been resolved?

[cedar kiln]

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[astral fulcrum]

Im having trouble setting up my calculus problem

[bold hinge]

Lmao

[astral fulcrum]

For both B and C I’m not sure how to set them up

[bold hinge]

Find the second derivative

[astral fulcrum]

can I ask how you would do that, I know the derivative rulers for fractions but i dont know if I can still use it due to the y^2 in the denominator

[bold hinge]

y = y(x)

y is a function of x

[cedar kiln]

@astral fulcrum Has your question been resolved?

[cedar kiln]

@astral fulcrum Has your question been resolved?

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[chilly dock]

I'm not getting correct answer for 1st question, can anyone help?

[tropic oxide]

what answer are you getting?

[chilly dock]

None of them

[tropic oxide]

show your work

[chilly dock]

Ok, wait, I did but cut that because of wrong answer, I'll do again and send

[tropic oxide]

so you tested it against every answer option and concluded that none of them are correct...

hm

give me a moment

[chilly dock]

yes

[leaden snow]

sure you checked (B) correctly?

[tropic oxide]

A, B and C all appear to be checked incorrectly

the value of g for option A is -3/4, not -3/2

is there a reason why you aren't just calculating the equation directly as opposed to this elimination of options by the way

[chilly dock]

How? It's -3/2

[tropic oxide]

the coefficient on x after normalization is -3/2, but in the equation form you wrote out the coefficient is 2g, not g.

[chilly dock]

Oh yes, ty

[chilly dock]

Only two points are given, so how can I find the equation?

though I can find family of circles

[tropic oxide]

you are given more than just two points

you're given that the circle touches (i.e. is tangent to) the y-axis at the origin.

[chilly dock]

Oh got it

Thanks

.close

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[torn burrow]

Hi, im working on probability math and ive got some questions i cant find out. First question is, if it only exists 20 emojies, what are the chances that a random sequence of 4 different emojies contains 😎 😍 🤝 👀 ? But not in a specific order. 🙂

[leaden snow]

@torn burrow So you're looking at sequences of the form (e1, e2, e3, e4) where the e_i are some emojis. You want it to contain the above 4 emojis in any order. Effectively, this reduces your problem down to finding the probability of picking 4 specific emojis from the 20 available emojis.

[torn burrow]

so 1/20 * 1/19 * 1/18 * 1/17?

[leaden snow]

To make it simpler, consider grouping the 20 emojis into 4 elements each, such that one group exactly contains the 4 emojis you want above. So you have 5 groups of 4 elements and they are all equally likely to be picked. What is the probability you pick the group containing the wanted emojis?

[torn burrow]

hmm then it would be 1/5?

[leaden snow]

ah wait, i might have misunderstood

[torn burrow]

np 🙂

[leaden snow]

so 1/20 * 1/19 * 1/18 * 1/17?
@torn burrow Okay so this is the probability that you pick the 4 emojis in a specific order, say the one you have written above. If you multiply this with the number of permutations you can make with 4 elements, you should get the answer

number of permutations = in how many ways can you arrange the 4 emojis

[torn burrow]

0.05 * 0.053 * 0.055 * 0.059 * 16 = 0.000137588

wait its * 24

[leaden snow]

try to write it as a fraction

[torn burrow]

alright

[leaden snow]

and yes 24 is correct

[torn burrow]

so 1/116280 * 24

24 out of 116280?

1/4845

[torn burrow]

24/116280 or 1/4845. does that sound correct? haha

[leaden snow]

1/4845 sounds good

[torn burrow]

How would it be if i only were to want 3 specific emojis though? and not 4?

[leaden snow]

you could also solve it very quickly using binomial coefficients (if you know those)

[torn burrow]

never heard of that before haha

[leaden snow]

For 3 you want to first get the probability of picking the 3 emojis in a specific order (as before) and then multiply it by the number of ways to arrange 3 items

[torn burrow]

so find permutations with 3 items?

1/20 * 1/19 * 1/18 * 6/1 then? 😄

[leaden snow]

Yes

[torn burrow]

cool

[leaden snow]

But can you pick each emoji of the 20 only once?

Say you pick "😁" does your set of 20 emojis then shrink down to 19 emojis or is it still 20?

[torn burrow]

Its still 20 in there

hmm will it be different then if we want to have 3? because one of them can come twice?

[torn burrow]

Oh nvm i think its only 19 left

If it only exists 20 emojies, what are the chances that a random sequence of 4 different emojies contains 😎 😍 🤝 ? But not in a specific order. 🙂 Anyone knows? 🙂

<@&286206848099549185>

[leaden snow]

@torn burrow So look at the sequence (e1, e2, e3, e4) again. Let's say the first 3 elements are the 3 emojis you want and the 4th is random.

To get this specific sequence you just have 1/20 x 1/19 x 1/18. But now we have more combinations! We have 17 choices for e4. And then we can proceed to permutate the sequence.

[torn burrow]

Oh welcome back!

😄

So i will have to find the permutartions of 17?

[leaden snow]

(😎 😍 🤝, X) where X is some other emoji. This is one specific sequence. The X can be chosen from 17 other emojis. That gives you 17 possibilities. Each of those 17 possible cases can be reordered in 4! ways

That only works given that you can choose an emoji only once, though

[torn burrow]

1/20 * 1/19 * 1/18 * 4! (4 * 3 * 2 =24) = 24/6840

Yea i read the question wrong i believe, i think its unique

Can i ask why the 17 possible cases can be reordered in 4! ways?

[leaden snow]

Imagine 4 empty boxes _ _ _ _ where you can place the emojis

• Placing the first item, you have 4 boxes you can choose to place it into
• 2nd item => 3 boxes
• 3rd item => 2 boxes
• 4th item => 1 box

which gives 4 x 3 x 2 x 1 = 4! options

[torn burrow]

ohh

makes sense

[leaden snow]

If they would not be unique, however, you could have duplicates which you can't count as different possibilities. So that would make the problem a little trickier

[torn burrow]

Yea alright 🙂

Thanks for the help!

[leaden snow]

Np!

[torn burrow]

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[crimson sedge]

-2x + 3y = -13
3x - 5y = 21

How do you solve this?

[obsidian coral]

Using elimination or substitution

[blazing furnace]

x=2

x^2=4

[obsidian coral]

If you're giving out the answer, don't

[blazing furnace]

what?

[obsidian coral]

Are you asking a question?

Because then read #❓how-to-get-help

[lusty violet]

Do you know the elimination method?

[crimson sedge]

Not really

[lusty violet]

Alright, I'm a bit rusty on this but basically you can multiply one of the two equations by a number and it will still be the same

For example

[obsidian coral]

Maybe looking at videos would be a good start

[lusty violet]

2x-y=2
x-2y=1

You can also put

4x-2y=4
x-2y=1

[crimson sedge]

I will look it up for sure

[lusty violet]

And it's the same

Do you understand? Sorry if I'm not making myself clear

[obsidian coral]

https://youtube.com/watch?v=cz6UmZLWgEw

Like that video

[crimson sedge]

Not really but I watch some videos to understand the concept then I will look at your explanation again, maybe then it will make sense. Than you

[crimson sedge]

I will, thank you

[cedar kiln]

@crimson sedge Has your question been resolved?

[summer swift]

Hm Is Simple

Basically you move around the numbers like a card game

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[wraith dagger]

kempiedempie

$\displaystyle f( x) =\ -$$\displaystyle \frac{2}{3} \ $$\displaystyle (cos\left(\frac{x}{2}\right)$)$\displaystyle ^{4}$



    $\displaystyle f´( x) =\ -\frac{2}{3} \ \cdot 4\cdot (cos\left(\frac{x}{2}\right) )^{3} \cdot \left( -sin\left(\frac{x}{2}\right)\right)$$\displaystyle \cdot \frac{1}{2}$
```Compilation error:```! Please use \mathaccent for accents in math mode.
\MT@orig@add@accent ...gnorespaces \relax \accent 
                                                  #1 #2\egroup \spacefactor ...
l.61     $\displaystyle f´
                           ( x) =\ -\frac{2}{3} \ \cdot 4\cdot (cos\left(\fr...
I'm changing \accent to \mathaccent here; wish me luck.
(Accents are not the same in formulas as they are in text.)```

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[drifting garnet]

I need help

[drifting garnet]

so I have a maths assignment for a ferris wheel which is the london eye

the dimensions are this

Now I’m up to question 4

i) and ii)

I tried to use desmos to find an eqation for terms of t and theater

and I came up with that

and the graph adds up put when I plug in the time it doesnt add up

which I need help with please

[drifting garnet]

would any one be able to give me a hand with this question?

[drifting garnet]

any <@&286206848099549185> able to help

[cedar kiln]

@drifting garnet Has your question been resolved?

[drifting garnet]

<@&286206848099549185> plz

[cedar kiln]

@drifting garnet Has your question been resolved?

[loud anchor]

part (i) LGTM

without knowledge about the (angular) speed it's impossible to do part (ii)

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[dense bramble]

So I am doing a work for my physics class, I have to analyse a basketball shot I did myself. I used the software Tracker and I have now a graph on Excel. I I found the initial speed and the amplitude of my angle. I have also the mass of my object, it is 0, 362 kg. But now I have to find the friction force, I know actually how to find it but on a inclined plane and not on a parabolic motion. Could someone help me with this problem ? I apologise if I don't use the exact words in English, I study in French.

[upper abyss]

Like air resistance?

[dense bramble]

yes

[upper abyss]

Well, you can approximate the second derivative of motion to find the sum of all forces on the ball

Then subtract out gravity to get the only force left, air resistance

Huh, that's only the trajectory though. Do you have any info in terms of time?

[dense bramble]

Actually I am going to calculate the time now, it's just going to take some minutes. I am coming in several minutes. Thank you a lot for your time

This is the formula of the time, but actually you can see that my motion doesn't do a full parabola. So should I first consider that's my ball is doing a full parabola and calculate the time and then subtract it with the time found from the parabolic motion of my last position and the "theoritical last position" (when there is a full parabola) ?

[cedar kiln]

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[fierce rune]

how should i start with this? I need a push

[cedar kiln]

@fierce rune Has your question been resolved?

[fierce rune]

<@&286206848099549185>

[cedar kiln]

@fierce rune Has your question been resolved?

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[tawny cradle]

Doing Algebra need some help with a few portions. possible to tell me if im wrong here? if so how should i have gotten the right answer?

[cedar kiln]

@tawny cradle Has your question been resolved?

[tawny cradle]

<@&286206848099549185>

[sleek condor]

you are right

[tawny cradle]

thank you

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[crimson dawn]

Is there a formula for calcuating how many angles can have a value of 90 deg in like a heptagon?

[crimson dawn]

It is an irregular heptagon

<@&286206848099549185>

[tight herald]

(n - 2) * 180deg is the total number of degrees,
5 * 180 = 900
So theoretically 9 angles since
900/90 = 10

I have a feeling this cannot be true though

Due to some geometry stuff

Yeah there has to be some 270s

[crimson dawn]

I made this

But the question is if there can be more?

[tight herald]

Let me try lol

I got 5

[crimson dawn]

how tf

[tight herald]

An odd shape

Let me see if I can draw in ms paint

[crimson dawn]

This should be good. Ms paint ;)

[tight herald]

Lol

[crimson dawn]

yeah

5

then

I dont think that there can be more in this

right?

[tight herald]

?

That is a 5 sided shape

[crimson dawn]

i know

I have 5, 6 and 7

[tight herald]

I think there might be something that shows in an odd numbered figure, there must be a 270 degree angle

Or maybe in an even too

Hmm

There has to be a 270 somewhere when it gets above 4

If the rest are 90

[crimson dawn]

anyways

Thanks for the help!

.close

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[trail kayak]

a sequence is a continual plugging in of n, with the respective results separated by commas, while
a series is the summation of said plugging in of n, correct?

[dire geode]

if that's how you understand it, sure. i'd stick to regular words though
https://en.wikipedia.org/wiki/Sequence

https://en.wikipedia.org/wiki/Series_(mathematics)

[trail kayak]

aight thanks

.close

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[trail kayak]

for this question, why does she subtract r x Sn?

[trail kayak]

or is that kinda j what u do

[upper abyss]

Do you see why doing this has worked?

[trail kayak]

nah i havent worked thru everything yet

[upper abyss]

You wouldn't know to do this

[trail kayak]

aight

[upper abyss]

Just, it works out really well

[trail kayak]

one other thing im a tad confused on tho, that being the first term w just a

lets say r = 3

-3 x Sn, for the first term, would equal -3a right

[upper abyss]

Yes

You can see there's -ar being crossed out there

[trail kayak]

dis stuff hurts my head gimme a sec

prolly j cuz im new to it

ah ok

so since n starts off at 1, according to this

then for the first one, u'd get -1 x a x r^(1-1)

which would equal - 1 x a x 1

which would give u -a

hmmm

why doesnt she subtract a then

[wheat otter]

Evaluate the following expression. (x ≠ (π + 2πn)/10, where n is a whole number)
​

sec 5x – cos 5x

​

a.    5 sin 5x cot x
b.    sin 5x tan 5x
c.    sin 5x csc 5x
d.    – 5 sin 5x cot 5x
e.    – sin 5x tan 5x

[trail kayak]

oh wait i get it

ah ok nvm

[ember python]

#❓how-to-get-help

[trail kayak]

.close

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[west dome]

What parts do you need help with and what have you done already

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[crisp tulip]

The graph of 4x + y =20 is shown below.

Which Of the following ordered pairs is in the solution set of 4x + y > 20

(0,20)
(5,0)
(0,5)
(20,0)

[crisp tulip]

im not sure which one

it is

[main sage]

ok

MY GUY

LIterally

Plug in x,y

[crisp tulip]

huh

[eternal comet]

You even have the graph

[crisp tulip]

where tf

bro

im so lost

[main sage]

Bro see how the answers are all

In the form

(x,y)

Take each of the answers

[crisp tulip]

yes

[main sage]

And just substitute it into the equation

Like multiply them

[eternal comet]

or even more easily

[main sage]

Hop in voice if u want further explanation

[eternal comet]

Look at the graph you are given

[crisp tulip]

ok

[crisp tulip]

i am looking

[main sage]

nerd

Hop in VC

Dw

[crisp tulip]

hello?

oh shit

i mean

<

ion know why

[main sage]

What's the sign

[crisp tulip]

its the opposite

<

[main sage]

Which Of the following ordered pairs is in the solution set of 4x + y > 20

(0,20)
(5,0)
(0,5)
(20,0)

[crisp tulip]

4x + y < 20

[main sage]

Which Of the following ordered pairs is in the solution set of 4x + y < 20

(0,20)
(5,0)
(0,5)
(20,0)

[crisp tulip]

my fault

[main sage]

SO BASICALLY

it's C

Because

5 is less than 20

U just gotta p lug in bro

[crisp tulip]

you know that was my first answer

but i didnt know if it was right

thank you sir

i may need more help

but thats ok

[main sage]

.close

[crisp tulip]

.close

[cedar kiln]

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[plucky umbra]

is the error in the 2nd line where it’s subtracting -6 from +6 and +5

[main sage]

bro

the first step

4(2x+5) = 8x+5?

Nope

It's wrong

Distribute it correctly

CROSS MULTIPLICATION @plucky umbra

[plucky umbra]

no no

[thin roost]

Ye

Correct

,w (x+3)/(4) =( 2x+5)/(2)

[plucky umbra]

did u read what i said im not talking ab the part after the fractions

[wraith dagger]

Results provided by WolframAlpha

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

Requested by ! बाशुदेव#5548

[thin roost]

💀

Let me do it

[main sage]

What

[plucky umbra]

LOOL

okay

[glass oasis]

but the part after the fractions is wrong

[plucky umbra]

oh lmfao wait

[thin roost]

Oh shit

[glass oasis]

like 4(2x+5) is not 8x+5

[thin roost]

Ye

It's

8x + 20

[plucky umbra]

yes

[glass oasis]

yhhh

[plucky umbra]

20

[thin roost]

I forgot that as well

[plucky umbra]

LOL i was just blind ig

[glass oasis]

it happens

[main sage]

That's literalyl what I freaking said

What is wrong with you

Bro what

You dismissed me

omfg

[glass oasis]

I didn't.

[thin roost]

Yk it happens sometime

[main sage]

not you

Ayesha

You know

[glass oasis]

ahhh

[main sage]

It happens sometimes

She said I couldn't read

Like just read what I said

Jesus christ

[plucky umbra]

ok 😃

[main sage]

Yeah leave

[thin roost]

Ayesha is a girl, and it's obvious that girls reject bois

Yk

[main sage]

Learn basic algebra kid

[glass oasis]

the single life :((

[thin roost]

Yep

Only frnd is math

[main sage]

I hate Math

[glass oasis]

tru

I like maths

[thin roost]

I love math

[glass oasis]

maths is like a multi tool

never know when you need it.

but very handy when you do

[thin roost]

U Chinese BTW??

[glass oasis]

yh

[thin roost]

I see

[glass oasis]

got that asian blood

within me

[thin roost]

Me too

[glass oasis]

the natural ability

[thin roost]

I'm indian

[glass oasis]

natural

[thin roost]

I'm asain as well

[glass oasis]

yahhh

ik

I can tell from ur name

[thin roost]

Ye

Ok

Now

Gtg

[glass oasis]

same

stuck on a question

kinda can't prove something

brain is blanking

[main sage]

send to me

Maybe i can help

[glass oasis]

its the same question

trying to get a proof rather than a counter-example

[cedar kiln]

@plucky umbra Has your question been resolved?

[cedar kiln]

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[short orbit]

I have a question. Is integration considered an NP-problem? For differentiation, we have a set of rules that allow us to solve any problem easily. But for integration, it's not so straight-forward. Also, if derivatives are P-type shouldn't that also make integration, the inverse of that, also a P-type so that theres just an easy way to find the integral of something as there is to find the derivative? (P-polynomial time, NP- Non-polynomial/exponential time)

[upper abyss]

To time a solution would be to imply there's some numerical input

[short orbit]

i mean generally.

to find the derivative, you use the chain rule a couple of times and done. So it's polynomial time. But for integrals, its more like trial and error for most problems, which is how most np's are

[upper abyss]

Polynomial time based on what input?

[short orbit]

uhm whatever limits for convenience ig

[upper abyss]

Powerful engines use a lot of different methods. However the Risch algorithm is kind of a "baseline"

[short orbit]

hm ill check that out

but is it as straight forward as a derivative?

[upper abyss]

I can't say I'm an expert so maybe you'll want to wait for one

But yeah it looks like getting integration algorithms right is difficult.

From what I'm reading anyway

[cedar kiln]

@short orbit Has your question been resolved?

[short orbit]

<@&286206848099549185> ?

[short orbit]

here's my q

[cedar kiln]

@short orbit Has your question been resolved?

[short orbit]

dude cmon

guaranteed brain exercise

[glass oasis]

my brain don't need exercise, it's already 5am here

[short orbit]

<@&286206848099549185>

have I made a mistake in my question or something that makes it confusing?

[cedar kiln]

@short orbit Has your question been resolved?

[cedar kiln]

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[shy garnet]

$\frac {x+5}{4x+6} = \frac {5}{13}\
\implies 7x = 35$
?????????

[wraith dagger]

Plumbum

[shy garnet]

how the hell does that expression imply that 7x = 35

[bold hinge]

Yes

Just solve for x

Lmao

[shy garnet]

...

See that's the t h i n g

Idk how to

[bold hinge]

Clear the denominators

[shy garnet]

....

So just multiply the LHS and RHS by 13?

[unique estuary]

Also multiply both sides by (4x+6)

[shy garnet]

To clear both denominators i see i see

$(x+5)(13) = 5(4x+6)$

So like that?

(4x²+6x+20x+30)(13) = (20x+30)(13)

Jesus is this seriously it

[unique estuary]

Remember you’re cancelling out the denominators right

[shy garnet]

Yeah

[unique estuary]

So

[shy garnet]

S o

[unique estuary]

You know how 5/13x13 would be 5

[shy garnet]

.

Fuck me

[cobalt kernel]

How exactly would I solve this

[wraith dagger]

Plumbum

[unique estuary]

Y’a that’s it

[shy garnet]

13x+65=20x+30
65-30=20x-13x
35=7x
X=5

Thanks

.close

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[cerulean star]

what is cuh

cuz?

cuz. watch the video, I have a feeling it will show you exactly how to do this stupidly easy problem.

it will tell you what it means to "cube" a number.

but if it doesn't, you can always Google it

I said you can google what it means to "cube" a number

but now I see that a more serious problem you have is reading comprehension

and I don't even mean that as an insult

you need more practice with that

ok, you've looked it up. That's good. But can you be more precise? what is "3"?

what is happening 3 times

great.

what is 3 referring to

what does that mean though

you are off there

good.

three factors of some number

$a\cross a\cross a = a^3$

yes

but now I'm screwing up

because it is 1:30am

[wraith dagger]

Disorganized

[cerulean star]

^ sorry

why what

that's it

why WHAT tho

are you asking where the "carrot symbol" is on your keyboard?

for exponents?

it's SHIFT + 6

are you drunk?

you sound like a drunk dude drowning in a bathtub XD

falling asleep in the tub or something

like you can't finish the thought

because you slipped under the water

ok do this

just READ...

hold shift...

and press the 6 key

there ya go.

yes, we are both excited

that this is going so well

fast why, if you gotta take a shit or something go do it

you're the idiot who can't watch video instructions

:P

for real?

#help-13 message

@crimson sedge your math life will never be easier than a question like this

they are asking you to turn a number sentence into an algebraic expression

the number sentence is

"5 is added to the cube of a number"

how do you write 5 in algebra?

5.

how do you write "added" in algebra?

5+

how do you write "the cube of some number, a" in algebra? We just did this part.

.

..

...

....

.....

......

.......

........

.........

..........

...........

............

maybe scroll the page up a little bit if you can't remember?

bye, cuh

[cedar kiln]

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[livid hound]

dont troll

and the level of that question isn't fitting for this server

and?

[calm sierra]

@lost monolith cut it out

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[balmy jewel]

where does the leap in logic that -4 < t < 4 implies -16 <= t^2 - 16 <= 0

where does the -16 and 0 come from I mean

oh nvm, they used zero.

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[tepid mauve]

i need help with this

[upper abyss]

Have you used normal distribution charts to convert between z-score and probabilities before?

[tepid mauve]

not really but i do know about the z scores and probabilities

somebody plz help me i will get it fast just dont know the procedure/formula

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[mint coyote]

Hello I want to solve for the x-intercept. Here is what I did so far. I have no idea how to solve the x-int in this question. Any help would be appreciated!

[south juniper]

better to write it as 4x^3 - 18x^2 - 3 = 0, and now you will have to check some values

Try plugging in factors of 12(cause of 4 in the first term and 3 in the last term) in that expression

Factors will be 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

hopefully you will be able to find one root

then the others you can find by long division(if possible)

[mint coyote]

Okay thanks you

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[trail kayak]

how did my teacher raise the 1 in the second expression to the n-1 power

[lament sonnet]

$a^n = a \times a^{n-1}$

[wraith dagger]

1345631

[trail kayak]

yeah but the 1 wasnt originally raised to the n power to begin with

[eternal comet]

it was

$1 = 1^n , \forall n \in \mathbb{R}$

[wraith dagger]

Remavas

[trail kayak]

?

[eternal comet]

1 raised to any power equals 1

[trail kayak]

ah ok

so outside of this context

i could write 1 = 1^x and it would be correct

[eternal comet]

I mean sure, wouldn't be that useful most of the time though

[trail kayak]

ight i gotchu thanks for the help

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.close

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[maiden phoenix]

How would I solve this?

[reef venture]

do you know the formula for the area of a sector?

[maiden phoenix]

Is it

x/360 * 2pir

x is theta

[reef venture]

that's the formula for the arc length

[maiden phoenix]

Oh

I cannot remember

[reef venture]

isntead of 2pir what should it be

2pir gives you the circumference, what's it for the area

[maiden phoenix]

Is it pir^2

[reef venture]

yes

so the formula for the area of the sector would be?

[maiden phoenix]

x/360 * pir^2

[reef venture]

correct

now to find the shaded area

you can subtract the area of the smaller sector from the bigger

[maiden phoenix]

Oh I see

I got 3/4 pi

[reef venture]

yep that's correct

[maiden phoenix]

For part b i got 7/2 pi

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[bright sorrel]

"6 students are put in a row ordered in a random manner. Two of them are twins. Find, using permutation (factoriel), for how many different ways they can be arranged so that the twins aren't next to each other."

[balmy apex]

what is your question

[bright sorrel]

Do I just use P6=6!=1x2x3x4x5x6 ?

[I][I]IIII

so I just exclude one time (which is when they are next to each other?)

I don't think I'm right

there are plenty of other orders in which they are next to each other

is it just exclude one time 6 times?

P6-6 ?

6!-6=714?

oh

isn't it

P6-P5?

6!-5!=600

right?

when 6! includes every time they are next to each other

and all those times they are next to each other are 5!

am I right?

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[midnight owl]

Having a bit of trouble understanding. For dz/dx, do I first take the derivative in respect to x then plug in values or plug in the values first before I differentiate?

i.e. dz/dx= 7-5y -> 7-5(-3) -> 22
or
dz/dx = 7(-2)-5(-3) -> -14+15 -> 1 (differentiate) = 0

[west dome]

That is not the correct partial

But that’s the idea, yeah

[midnight owl]

Can you help me get my mind around it?

[west dome]

The first thing you wrote that is

Yeah

[midnight owl]

i.e. dz/dx= 7-5y -> 7-5(-3) -> 22 this part you mean?

is not correct

[west dome]

The first equality is not

Lemme get a keyboard

[midnight owl]

sure np lol

Trying to read through the examples but am confusing myself

ah wait no dz/dx = 7

since -5y = 0 right

[west dome]

What is $\frac{\partial(7x-5y)}{\partial x}$

[wraith dagger]

Migillope

[west dome]

Do you understand how to do this?

[midnight owl]

Not sure tbh lol

I get confused with notation when it comes to differentiation tbh

[west dome]

You just differentiate each term wrt to x

How about $\frac{\partial 7x}{\partial x}$

[wraith dagger]

Migillope

[midnight owl]

Are you just asking what the derivative of 7x is?

Like I said sometimes notation confuses me

[west dome]

It’s important you understand the notation, it gives you key information

[midnight owl]

assuming it means derive 7x in terms of x?

[west dome]

Exactly

[midnight owl]

so 7 lol

[west dome]

Okay, what about $\frac{\partial 5y}{\partial x}$

[wraith dagger]

Migillope

[midnight owl]

so dz/dx is deriving z in regards to x

[west dome]

It’s not d

But yes, that’s the idea

[midnight owl]

I like to think of it as d for derive xD

plus idk how to type it

[west dome]

It’s not the same

[midnight owl]

this would be 0

[west dome]

d is derivative, this is partial derivative. You need partials for multivariate functions

[west dome]

Yes

[midnight owl]

well just pretend I'm writing the symbol then lol

[west dome]

So put it together, what is the answer to this

[midnight owl]

dz/dx = 7

for z = 7x-5y

[west dome]

Yeah

What about wrt y

[midnight owl]

dz/dy = -5

Now obviously I can't plug in values for this but let's say the equation is something like 7x^3

do I derive first then plug in the value?

Let's just say the full equation is 7x^3 + 5y^2

[west dome]

You can, but its constant so plugging in different values wont alter the output

[west dome]

But yes, that is correct

[midnight owl]

So I would do
dz/dx = 21x^2

[west dome]

It’s read as “the partial derivative of (equation) wrt (variable) evaluated at (point)”

[midnight owl]

then plug in -2 for x

[west dome]

If you’re evaluating at (-2, y) yes

[midnight owl]

yea!

Also, why is there a 3rd partial derivative

it lists dz/dx twice

[midnight owl]

in this ^

[west dome]

It asks for $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial x} \mid_{(-2,-3)}$

[wraith dagger]

Migillope

[midnight owl]

Ohhh

I thought it was asking to plug in the values for all of them

not just the last one

[west dome]

These are not the same, one is a function, the other is a real number (generally. In this case, the function for the first was constant)

[midnight owl]

Also, is this the same concept just different notation?

Assuming it is