help-27

[restive river]

b=-3

[heady willow]

what do u do with those

i got those values

[restive river]

y=x^2-3x-18

Complete the square

[heady willow]

Oh

what do you mean by complete the square

[restive river]

Change it into turning point form

[heady willow]

how would you do that

[restive river]

Completing the square

Make a perfect square

[heady willow]

sorry but i dont get what you mean by that

[restive river]

Search up completing the square and watch a YouTube video on it

[heady willow]

ok thank you for your help

i apologize for being dumb ig

[restive river]

No problem, you are not dumb, you just haven’t learnt completing the square

[heady willow]

thank you

i will close the ticket

.close

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[cobalt cloak]

i took an exam and got it wrong but what is the relationship betwween pi^2 and g

[white ravine]

g like the gravitational constant?

[cobalt cloak]

yeah

[tiny carbon]

This is a mathematical coincidence I believe

[cobalt cloak]

thats what i thought too

but this was a 5 mark question

which is why i got confused

[white ravine]

you can use simple pendulum

i think

since that uses g

do you know the formula of a single pendulum?

[cobalt cloak]

its like

2pi sqrt (l/G)

[white ravine]

= what

[cobalt cloak]

period

[white ravine]

yeah

[cobalt cloak]

or T

[white ravine]

and solve for g

[cobalt cloak]

which ever notation is best

[white ravine]

and you can find a relationship for pi^2 and g

[cobalt cloak]

hmm i see what you are getting at but i dont think the prof would give something that simple for the class

[white ravine]

you sure

[cobalt cloak]

yeah this is ODE

apparently so

[white ravine]

it is a relationship between pi^2 and g

[cobalt cloak]

yeah it is

it just seems too simple for the class

[white ravine]

an ODE?

wait

[cobalt cloak]

cause i think my prof wants me to use ODE

idk tho

[graceful cosmos]

That question, as stated, is stupid. I'd suggest going to the TAs and demanding the mark back on that one

[cobalt cloak]

yeah i agree

that or i just totally missed something in the lecture

[fleet mauve]

nothing, except for mathematical relation in values

[cobalt cloak]

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[timid siren]

hey I'm trying to understand what's going on in here. This is about solving the curvature of plot c(t)

[timid siren]

my understanding of what |c'|^3 should be is |sqrt(c_x'^2 ´+ c_y'^2)|^3 and this results in a more complex result than |t|^3

oh wait had a sign error, nvm

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[bronze junco]

Is that where the angle of depression is?

[supple knot]

yes
https://www.cuemath.com/trigonometry/angle-of-depression/

[bronze junco]

So can you say that tan(15)= x/50?

40*

[supple knot]

label your picture with lengths

[bronze junco]

Wait no it’s 40

60*

50*

Is this right?

Ok

13

TOS

[wanton star]

...

[bronze junco]

You gotta be over 13 to be on discord

[surreal mason]

Goodbye

[bronze junco]

I’m turning 14 this year

Farewell

[wanton star]

F

[bronze junco]

Anyways, did I set my equation correctly?

I’m getting that side is like 13.3 and that doesn’t seem right

<@&286206848099549185>

[supple knot]

,calc tan(15 * pi / 180) * 50

[woven radish]

Result:

13.397459621556

[supple knot]

your label's wrong

[bronze junco]

Hmmm

Lemme go check the answer key

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[wet fox]

can someone explain as to how u get the coordinates

[placid rover]

Look for a gif online

[wet fox]

ahh makes sense now

thanks

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[rotund copper]

i need help

[rotund copper]

i dont understand this

@jagged harbor

@restive river

[languid ocean]

there are 4 types of cubes in the 12x12 cubes

those inside the big cube (no exterior faces therefore orientation doesnt matter)

[rotund copper]

what do you mean by that

[languid ocean]

those with 1 exterior face (basically, not on a side or corner) (and not inside the cube)

[rotund copper]

so um

uhh

how do i get answer

[languid ocean]

find the 2 other types of cubes first-

[rotund copper]

huh

the ones on the side and corner

[languid ocean]

yep!

now, which face of the cubes on the surface should point outwards?

[rotund copper]

1

100

[languid ocean]

yeah!

how about the cubes on the side?

[rotund copper]

c

[languid ocean]

uhhh, no. those cubes all have 2 exterior faces.

[rotund copper]

what

c and 100

?

[languid ocean]

you want to find the sides of these cubes that point outwards

yeah, that's c and 100

and how about the cubes at the corners?

[rotund copper]

c 100 c

[languid ocean]

and that's 2c+100. now, you need a formula for the sum of all exterior faces, which should look like this:
(number of cubes on the surface)(100) + (number of cubes on the sides)(100+c) + (number of cubes at the corners)(100+2c)

[rotund copper]

so

it would be

(864)(100)+(144)(100+c)+(6)(100+2c)

@languid ocean

[languid ocean]

no, the number of cubes on the surface shouldnt be 864?

[rotund copper]

what

12x12=144

[languid ocean]

well

[rotund copper]

144x6 = 864

[languid ocean]

oops my fault. by "surface" i implicitly meant "only the cubes with 1 exterior face", which means "excluding the sides and corners"

[rotund copper]

o

so its

(833)(100)+(144)(100+c)+(6)(100+2c)

would that be right?

[languid ocean]

still no

there are less than 833 "surface" cubes

each side of the big cube has (12-2)(12-2)=100 small cubes on the "surface"

[rotund copper]

ocky

so

(100)(100)+(144)(100+c)+(6)(100+2c)

right?

[languid ocean]

it's (12-2)(12-2) since , well, the 2 outer columns and rows consists of cubes on the sides and corners

[languid ocean]

there are 6 sides of the big cube though....

[rotund copper]

(600)(100)+(144)(100+c)+(6)(100+2c)

im gonna punch something

[languid ocean]

now, there aren't 144 cubes on the "sides" either (probably also my fault, bc by using "side" i implicitly meant "small cubes with 2 exterior faces" which excludes the 2 corner cubes at the endpoints of each edge)

there are 12 edges of the cube

and each edge has 12-2 cubes on the "sides"

[rotund copper]

ok

(864)(100)+(100)(100+c)+(6)(100+2c)

is that right now?

[languid ocean]

huh? no
there are still only 600 cubes with 1 exterior face

[rotund copper]

DAYUM

[languid ocean]

and there are 12 edges with 10 cubes on the "sides" each

[rotund copper]

oosps

(600)(100)+(100)(100+c)+(6)(100+2c)

i just accidentally wrote the last one wrong

[languid ocean]

the number of cubes on the

"side"

isnt 100?

(also, sorry if my terms are confusing. here's a long overdue diagram on a not12x12 cube - white="surface", orange="side", purple=corner)

[rotund copper]

well there are 6 sides

and jkust the side cubes

is

10x10

100x6

600

100 each side

[languid ocean]

(600)(100)+(100)(100+c)+(6)(100+2c)
^ i mean this. there are 12 edges and 10 edge cubes for each edge.

[rotund copper]

o

[devout snow]

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[marsh edge]

are probabilities and areas the same when it comes to finding the area in a normal distribution curve?

[devout snow]

@marsh edge Has your question been resolved?

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[restive river]

Hi! pls help

[restive river]

.close

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[tired turtle]

my question

Answer I'm getting

<@&286206848099549185> help pwease

[restive river]

Ok so will i explan it or just say the answer

Im explaining it

[tired turtle]

i dont want anwer

i want to know what am i doing wrong

[restive river]

So one minute work for pipe a and b is 1/20 and 1/36 right

Sorry 1/30

[tired turtle]

ye

if we take lcm

its 60

then 3+2 / 60

[restive river]

Yeah

[tired turtle]

which is 5/60

and answer is 20

[restive river]

60/5 is 12

Not 20

Rest is ok

[tired turtle]

OH SHTI

ok i realised

[restive river]

Lol

[tired turtle]

thank u so much

[restive river]

Np

[tired turtle]

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[restive river]

Hello. How would you go about solving:
y = eˣ/ cos(x)
for -π/2 < x < π/2
the curve has 1 stationary point and I'm tasked with finding its x-coordinate.

[restive river]

What I did: differentiated to get an equation of this

Then equated it to zero and removed the denominator and eˣ and ended up with cosx = -sinx
This is sent me down more of an intuitive route rather than a route that was systematic. The model answer here shows a tan(x) being used. How would that be reached?

[patent tartan]

you can also rewrite the derivative as $e^x \sec(x) \qty(\tan(x) + 1)$

[woven radish]

Navix

[patent tartan]

or $e^x \cdot \frac{\tan(x) + 1}{\cos(x)}$

[woven radish]

Navix

[restive river]

Okay both make sense

[restive river]

I understand now, thank you

[restive river]

Though you left me curious as to how this one would be used to find the answer

[patent tartan]

we want $$e^x \cdot \frac{\tan(x) + 1}{\cos(x)} = 0$$ this expression can only be zero iff $$\tan(x) + 1 = 0$$

[woven radish]

Navix

[restive river]

Alrighty then thanks bro

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[devout snow]

@surreal pulsar Has your question been resolved?

[surreal pulsar]

<@&286206848099549185>

[devout snow]

@surreal pulsar Has your question been resolved?

[devout snow]

@surreal pulsar Has your question been resolved?

[polar bolt]

what? No RHS is taking inf of M while LHS is taking sup of |X(\omega)|

[surreal pulsar]

well my idea was, the left side is the smallest upper bound of $X(\omega)$ and the right set consists of all M that are larger than $X(\omega)$ and if I then take the smallest lower bound of this set, I would have thought that both would be the same.

[woven radish]

Michael

[polar bolt]

RHS will give an M

[surreal pulsar]

but doesn't the left side do that too? Apparently I do not understand something fundamentally

I also get a real number as the result on the left-hand side. Maybe I should have added that $X$ is a mapping from $\Omega$ into the real numbers.

[woven radish]

Michael

[polar bolt]

yes then (assuming LHS can't take inf as a value)

[surreal pulsar]

okay ty

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[acoustic stone]

https://cdn.discordapp.com/attachments/937097171889688657/947622345407864872/20220227_173246.jpg
confused about the substitution portion, not sure what numbers should go where

[formal haven]

@acoustic stone have you completed step 2 yet?

[rocky dragon]

use botton equations and isolate either x or y

[acoustic stone]

i have not

[rocky dragon]

then play in that equation into top equation for which ever variable you solved for

[formal haven]

so solve for either x or y in the second equation

x-y-2=0

[rocky dragon]

x is the easiest

[formal haven]

they're same difficulty

[rocky dragon]

well yeah just add/subtract

but i just saw its -y-2

so add y and 2 to other side

¯_(ツ)_/¯

[acoustic stone]

so x=y+2 correct?

[rocky dragon]

yes

now plug y+2 for x in the first equation

and solve for y

and then use the answer to get x

[acoustic stone]

okay so i have 2y+2+3y-9=0

[rocky dragon]

and solve for y

[acoustic stone]

now im not sure how to solve for y

this is like my biggest struggle in algebra

[rocky dragon]

get all variables on one side and constants on other

[tiny carbon]

Be careful, it should be 2(y+2)

[acoustic stone]

oh ty

alright tysm :) <3

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[fossil summit]

What is the integral of f''(3x)?
I understand that it will involve integration by parts, but would the integral of f''(3x) be f'(3x) or would it be (1/3)(f'(3x))?
I also understand that the integral of f''(x) = f'(x) too so I kind of applied this same principle.

[torn vessel]

which one do you think?

and why?

[narrow plank]

Try integrating it

It may help doing a u-sub first.

$\int f''(3x) , dx$

[woven radish]

Shen

[devout snow]

@fossil summit Has your question been resolved?

[fossil summit]

Than you shen, that makes more sense doing u sub with 3x = u and then (1/3) du = dx

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[umbral saffron]

How would I find the inverse of this function?

[umbral saffron]

I think it would have something to do with Log but none of what I've been doing has worked

[sour swan]

well yes, you're thinking it the right way

just to help you

you can use this property of logarithms

also you should use some other property, make sure you have them in mind

[umbral saffron]

Wait I think I got it

Let me try out what I got

Oh cool it worked

Alright thanks 👍

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[restive river]

How would I do this?

I tried to fabricate a second equation, but that failed. I believe the key to solving this lies in 'm and n are positive Integers', but I cannot seem to Identify how to use it.

Perhaps someone could assist me with this?

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[restive river]

<@&286206848099549185>

[restive river]

What do you have so far?

[supple knot]

Read

[restive river]

Oh, yup thanks.

So one fact is that gcd(m,n)|(m+n)

You also know that if x=y then both x and y have the same prime factors to the same powers.

And so in your equation, m,n must account for the constant factors 3 and 5.

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[lean matrix]

To get maximum bound numerator must be high and denominator should be low and vice versa for minimum

Now can you do it?

[obsidian magnet]

i wii try

will*

can you do it for me and explain

[lean matrix]

Well do you know what will be circumference C?

[obsidian magnet]

no

[lean matrix]

Do you understand how to round off to significant value

https://youtu.be/l2yuDvwYq5g

[obsidian magnet]

yes

just leave it i know how to do it

i figure it out

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[indigo bloom]

I'm trying to multiply coefficient to theta but, here is the problem. How can I unwrap the sin function on this equation? It is one of the forms in the cross product.

[devout snow]

@indigo bloom Has your question been resolved?

[indigo bloom]

<@&286206848099549185>

[indigo bloom]

Let me change the question a little. How can I multiply coefficient to the theta?

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[indigo bloom]

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[steel comet]

wait

-153 is the answer

@obtuse slate

[modern glade]

its like -9-11-13-15-17-19-21-23-25

[steel comet]

yep

[obtuse slate]

do we go up to -25?

[steel comet]

yes

[obtuse slate]

which formula did you used?

[steel comet]

its not a formula

[modern glade]

difference of 2

[steel comet]

by looking at the behavious, we can say we keep subtracting by a diffrence of 2

[steel comet]

@obtuse slate check this out

[obtuse slate]

common difference of -2
and a1 is -9

[steel comet]

-9+-11+-13+-15+-17+-19+-21+-23+-25

this is what it will turn into

understood?

[obtuse slate]

ye. i thought i had to use the arithmetic formula

thanks

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[restive river]

simplify...

-3(4a - 3) - 20a = 9 So first -3 gets multiplied by the numbers inside the brackets -3 * 4a = -12a -3 * -3 = 9 Therefore -12a + 9 - 20a = 9 Subtract 9 from both sides we are left with -12a - 20a = 0 -1(12a + 20a) = 0 12a + 20a = 0 32a = 0 -> combine the terms a = 0

isnt that simple enough from the solution i already gave above 🤣

whats -12a-20a

I dont have the energy to explain to u really lel

put -32a

anyways close the channel if ur done

yes

[devout snow]

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[obtuse nymph]

system of equations.
I have to solve the following:
3x + 3y +2z = 5
2x + 4y + 3z = 4
-5x + 2y + 4z = -9
I have already tried several different options, but nothing has brought me to the solution which my teacher gave me (which is x=1, y=2, z=-2).

[slender mirage]

Hi !

Tuff Tuff ?

[obtuse nymph]

hi!

[slender mirage]

Hey !

Do I have your attention 👀

[obtuse nymph]

Full Attention!

[slender mirage]

Add the three equations first !!

You'll get: $$9y + 9z = 0 \implies y = -z$$

[woven radish]

Ansh

[obtuse nymph]

Ah!

That makes sense

[slender mirage]

Now plug this in any two of your three equations

[woven radish]

Ansh

[slender mirage]

Clearly, x = 1 and y = -2, z = 2

[obtuse nymph]

Oh! I get it now! Thank you so much!

.close

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[oblique tundra]

how would I go about solving this?

[graceful cosmos]

Gotta know your transformations.
Might it help if I write it as:
y = 5f(2(x + 3))?

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[hot lagoon]

How do I solve this?
3 * 16^x + 2 * 81^x = 5 * 36^x

[slender mirage]

Write $t =\qty(\frac{4}{9})^x$ and convert the given equation into a quadratic in t

[woven radish]

Ansh

[hot lagoon]

damn, I would never have though of that. Thank you

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[full prawn]

Find the perimiter of the fidget spinner with the help of the equilateral triangle ABC. The radius of each and every circle in the following picture is equal to 2 cm.

Now, yes, it's completely possible to find the perimeter of the spinner without the help of triangle. However, the question is asking me to do it using triangle, specifically, and I am struggling to find any way of finding the perimeter using the triangle
I would appreciate assistance

[full prawn]

<@&286206848099549185>

[sand thorn]

Bruhhhhh

[full prawn]

?

[sand thorn]

Just a funny question, find the perimeter of the fidget spinner

Cool problem tho

Ok

Yeah idk dude that’s dumb

[frozen elm]

Just use arclength formula

[sand thorn]

He must use the triangle

[frozen elm]

Oh

[full prawn]

the question asks that you should be able to find the perimeter of the spinner by finding the perimeter of the triangle ABC

<@&286206848099549185>

<@&286206848099549185>

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[full prawn]

.reopen

[devout snow]

✅

[full prawn]

<@&286206848099549185>

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[stiff raven]

Is there a field of maths that looks at the prime factors after constant addition

[devout snow]

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.closw

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[restive river]

How do i write $$3^x-3^x^+^2$$

[woven radish]

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

[restive river]

in the form

$$a(3^x)$$

[woven radish]

Prem

[formal haven]

Use your exponent rules

Laws of indices

@restive river

[restive river]

So a = -8?

.close

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[devout snow]

@hollow moat Has your question been resolved?

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[restive river]

is it B?

[placid rover]

how many radians in a circle (or revolution)

Then
how many revolutions per minute

And finally conclude how many radians per minute.

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[pine storm]

What's wrong in this procedure?

Because the answer is wrong

[mild vine]

You steps can lead you to miss maybe one answer

If you want to do this, try multiply both side with (x-5)²

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[pine storm]

Could you please show me how to do it?

[mild vine]

Multiply both side with (x-5)² first

[pine storm]

After this line?

[mild vine]

Yup

[unborn crown]

Well there's another way to do it without multiplying by (x-5)^2

[mild vine]

Ahhhh ok

[unborn crown]

From your second line, simplify it to one fraction to get (x+5)/(2x-10)

[mild vine]

You can also teach me

[mild vine]

I don't like fraction 😂

[unborn crown]

The root of that function is x=-5 and the asymtote of that function is x=5

[mild vine]

I learned this technique from an Australian maths teacher

[unborn crown]

Use a sign test to find out that for the function to be greater than zero, it has to be less than -5 or more than 5

[pine storm]

Eddie woo?

[mild vine]

https://youtu.be/NDIjVhwWcWc

[mild vine]

Yup

[unborn crown]

Using graphs is way easier imo

You can't just multiply both sides by x-3 also because x-3 could either be negative or positive and you wouldn't know whether to flip the inequality sign or not

[pine storm]

Actually I am out for tuition, i am in train, i am not able to pull out my notebook and write the solution, so could you please wait for a few minutes?

[mild vine]

So instead, we can multiply both side with (x-3)²

[unborn crown]

Yea or you can just use graph which is way easier

[mild vine]

Ahh ok, just sometimes I want to learn different methods to solve problems

[pine storm]

I did it this way, right?

[mild vine]

You can or you can use his @unborn crown method

[pine storm]

But could you please tell me what's wrong with the one which I showed?

[mild vine]

Like what he said

[pine storm]

Okay

[devout snow]

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[restive river]

Help

[restive river]

the number of ways a student can wear his 6 shirts, 4 pants, and 2 shoes

<@&286206848099549185>

Don’t ping helpers immediately

Read #❓how-to-get-help

[stiff raven]

How do u become a helper

[restive river]

Just ask a mod

Anyway so about ur question

THE NO. Of ways the student can buy his shirt is 6, right

*i mean wear

Cuz he has 6 shirts

Right @restive river ?

U there?

Yeah

Iam here

Why it's just 6? @restive river

[sand thorn]

it's not

[restive river]

Because he has 6 shirts

[restive river]

It is

Im explaining step by step

Ok so the no. Of ways the student can wear pants r 4

Cuz he has 4 pants

U get me?

Okay

Yesh

Yeah

Ok

So the total no. Of ways he can wear shirts AND pants is 6x4=24 right?

Yes

And he has two shoes

So what is the total no. Of ways he can wear all his garments?

[restive river]

Using this logic

12

24x2

48?

Yup

That’s the answer

So the answer is 48 ways possible outcome

So when u get a question like this, u multiply the values

[restive river]

Yes

Ohh thanks can I ask one last

Sure

[pseudo basin]

do not use the letter x for multiplication @restive river

[restive river]

Yeah sorry

I mean 24*2

[restive river]

Rolling a yellow and a red cube

Give the number of possible outcomes

[restive river]

U mean yellow and red dice?

Cube

[pseudo basin]

🎲

[sand thorn]

lol

[pseudo basin]

this?

[restive river]

Cube…

That's what in the the questions

[restive river]

I think so

This number 2

Ok but i don’t really know what they mean. Maybe a cube with both yellow and red sides…

Yeah

[sand thorn]

lol that makes no sense

[restive river]

Ikr

Im a bit confused

[sand thorn]

let's just assume it's a yellow die and a red die and move forward

[restive river]

Yeah

[sand thorn]

any other interpretation doesn't really make sense lol

[restive river]

True

So if it is a yellow and red die

[pseudo basin]

mental math

[formal haven]

Just say there's 1 outcome that both cubes land face up each time

[sand thorn]

lol stupid mental math

[restive river]

Wdym

[restive river]

Yeah all of this is mental math

[restive river]

I don’t know what u mean

[restive river]

Oh ok

[sand thorn]

An outcome for this problem would be like "rolling yellow 2 and red 5"

[restive river]

And because my math teacher didn't discuss well no one passing yet at desired Time haha

[sand thorn]

so we need to count the number of possibilities

[restive river]

Ok so we are taking it as die

Ok

So the no. Of possibilities of each cube is 6

Because they have numbers from 1 to 6

Right @restive river ?

Huh

Im assuming they r die

[sand thorn]

there are 6 faces on a cube

each face is numbered 1 to 6

[restive river]

Yup

[sand thorn]

an outcome is whatever number you get when it lands face up

[restive river]

But it's yellow and red

Sure

[sand thorn]

right, there is a yellow cube and a red cube

you are rolling them simultaneously

[restive river]

So the yellow cube has 6 options, Y1 Y2 Y3 Y4 Y5 Y6

And the red cube has 6 options R1 R2 R3 R4 R5 R6

Y is yellow and R is red

And the answer is 12 possible outcome?

So the total no. Of outcomes should be 6*6, which gives us 36 outcomes

[restive river]

6*6 actually, i think u did 6+6 by mistake

Since we r rolling both the die simultaneously

Ohh okay thanks

Very last one🥺

Question 😃

This number 5

If repitition is allowed, each digit has 5 options right

Yeah

For repitition allowed

[sand thorn]

what nah

it's 5 * 5 * 5 = 125

[restive river]

Sorry i mean 5^3

125

Because it's 3 digit number that's why three 5?

[sand thorn]

yeah

5 options for each digit

[restive river]

5 options for 3 digits yeah

Ok so now for repition not allowed

Wait what imma put now

[sand thorn]

it's 125 for the first part

[restive river]

125

Ohh okay

So for the second part

The first digit will hv 5 options, the next will have 4, the next will have 3 and so on…

Since no number can be repeated

[sand thorn]

it's important to understand why

the first has 5 options because there are 5 digits to choose from

the next one only has 4 options, because you used one of the numbers for the first digit

Similarly, the next one has only 3, because you used the two numbers on the first two digits

[restive river]

Yes

Then?

What's should I put?🤔

In the repetition is not allowed

@restive river

@sand thorn

[sand thorn]

bruh

5 * 4 * 3 = 60, for repetition not allowed

[restive river]

Ohh okay thanks

Can I ask @sand thorn

[sand thorn]

sure

[restive river]

How to write the *

I didn't know 😅

U can write the normal multiplication sign on pen and paper

This is chat, that is why we r using that symbol

This

Ok

[sand thorn]

that's okay

but generally don't use "x" for multiplication

it can be confused with the variable letter x

[restive river]

In pen and paper he can

In sums like these

[sand thorn]

sure

[restive river]

Ok then

Olq

Is this right?

Yes

U got why these answers are correct right?

[main gull]

It honestly depends on what math level the person is at and whether or not the person can decipher their own handwriting and make sense of it

[restive river]

Exactly

Thanks guys iam 2 more to go

Hahha can u still help me

Sure

[sand thorn]

yeah

you're right

[restive river]

This number 6

[sand thorn]

3 * 5 = 15

[restive river]

Just it?

[sand thorn]

that's it

it's mental math

[restive river]

Ohhh wait one last

[sand thorn]

k

[sand thorn]

4 * 3 * 2 * 1 = 24

[restive river]

Yup

What book is this from btw

Can I get a correct there with no explanation?

[restive river]

Yeah its mental math

Yeah this will do

[restive river]

Our school book

Wait let me send

Which grade r u in

1

10

Oh ok

Grade dumb 10😅

Hahah

U hv boards on?

Like board exams

Yeah when finished college I think

We have boards in grade 10 too

[restive river]

When you finished college?

[restive river]

Yeah

[restive river]

Why so early what is that for?

Umm i live in india

So we hv boards for grade 10 n 12

Thank god that’s still 2 years away👼

[devout snow]

@restive river Has your question been resolved?

[restive river]

Is it hard M

??

[restive river]

No

Why would it be hard?

Anyway if ur done u can close the channel with .closr

*.close

[restive river]

Sorry I don’t take friend requests from people i dont know

Uhh okay

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[reef abyss]

yellow

[reef abyss]

Its been some time I dont even knwo the steps to go about this

[devout snow]

@reef abyss Has your question been resolved?

[reef abyss]

act prep class assigned work 😦

[devout snow]

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[devout snow]

@modest jacinth Has your question been resolved?

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@modest jacinth Has your question been resolved?

[main gull]

Don't open multiple channels

Even if you have multiple questions, you just use one channel

[modest jacinth]

Oh okay sorry didn't know that

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[golden gorge]

From sat practice test, how do I find x degrees?

It gives 35 degrees for both side of the polygon thing inside the circle

X is also the center of the circle

Nvm I figured it out

.close

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[timber pebble]

i know this is probability so maybe no luck but

[timber pebble]

im trying to sort out the last question listed here

well really, I'm trying to think through what this problem is even saying

the calculations specifically are less important

although i guess im interested in those too

are we saying that like

idk im not really understanding the interaction between these two distributions and what they represent

[devout snow]

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[timber pebble]

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[viscid crown]

x is the number of times a dice is rolled until an odd number occurs in the dice. I win 10 - x dollars if x rolls are needed for x = 1, 2 but I lose 10 dollars if x > 2. How do I determine the probability that I lose money?

[viscid crown]

x=1 happens when i roll odd number in first time, so my highest winning would be here
x=2 happens when i roll 1 even then 1 odd number, netting a total of 2 rolls and so, i win 10-2 dollars
x>2 happens when we have at least 2 even numbers and more until on the last roll we get odd number, but this doesnt matter since i always lose 10 dollars regardless

does this mean that probability of x=1 is 1/2 and probability of x=2 is 1/4?

[hazy totem]

Yes, that is right

[viscid crown]

so then is it true that probability of x>2 is (1-(1/2 + 1/4))?

[hazy totem]

Yes

The probability of x > 2 is also the probability of x not being 1 or 2

(if you had to be formal you might worry about x being infinite, but actually that doesn't matter here, you only care about x not being 1 or 2)

[viscid crown]

yeah, so this means 25% chance i lose money, thats kinda alot

[hazy totem]

Yes, but now you have to see what the expectancy is

You do have a 50% chance to win a fair bit of money

The weight of the probabilities make the game (and the exercise)

[viscid crown]

ya

wait but, when x=2, it still counts as winning right

so doesnt it mean my expected value of winning is 75%?

[hazy totem]

Oh wait, probability that you lose money

Then yes, you have a 75% chance of winning money

Hence a 25% chance of losing money

Although, I'll compute that expected value rq

After some computation, on average you win $4 each time you play the game

If you see that at a casino, assume they will soon go bankrupt

[viscid crown]

lol, so that means if we set 6 as the number, so 6-x being the winning amount for x=1,2, then it would be on average 0 then right?

usually casinos want to have <=0 dollar win right on avg

[hazy totem]

What would be the losing amount, 6 also?

[viscid crown]

no 10

6-x is winning amount but losing is 10

[hazy totem]

Let a be the winning amount

Then the expected value is (a-1)/2+(a-2)/4-10/4 = a/2+a/4-1/2-1/2-10/4 = 3a/4 - 14/4

So, the average score is ≤ 0 if and only if a ≤ 14/3 ≅ 4.6

[viscid crown]

so does this mean that if we set the losing amount to 14.6, then we can balance it out?

assuming you still win 10-x for x=1,2

[hazy totem]

Let's compute it

Let a be the losing amount, and set 10 to be the winning amount

Expected value is 9/2+8/4-a/4=(26-a)/4

So you only have an average score ≤ 0 if a ≥ 26

Your arguments didn't quite work because of the slight offsets and the way the probabilities are weighted skew everything

[viscid crown]

wait isnt it (26-a)/4

[hazy totem]

derp

[viscid crown]

interesting so that means it must at least be 26 for winning to be 0 on avg

[hazy totem]

Yup

[viscid crown]

kinda big jump from 10

[hazy totem]

yup

[viscid crown]

to calculate variance of our winning, would it be like ((a-1)/2 - 3a/4 - 14/4)^2 + ((a-2)/4 - 3a/4 - 14/4)^2 + ((10/4 - 3a/4-14/4))^2))/2

cuz expected value of winning is 3a/4 - 14/4 right

[devout snow]

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[timber pebble]

I need to ask for help on creating a matrix with a specific eigenvalues

[timber pebble]

I feel like its trivial but I cannot sort it out

I want to create a 2x2 matrix with a repeated, real eigenvalue

i need to make the discriminant 0, right?

or is there some additional requirement

i guess i also want it to be positive

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[plucky maple]

can sum1 help me pls

[formal haven]

@plucky maple Do you know how a and b modify an exponential equation?

[plucky maple]

i just finished up with that but been on break for 3 days and forgot lol

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[distant plume]

anyone got an idea?

[tiny carbon]

Have you tried writing it as an equation first? I would start there

[distant plume]

ye

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[marble osprey]

How do I solve using quadratic formula

[languid ocean]

so you don't even know the quadratic formula?

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[woven radish]

abelian revolutionist (meg)

[marble osprey]

I do

I just dont know what to do from x= 5+-squareroot of 25+96 / 12

@languid ocean

<@&286206848099549185>

[fleet mauve]

$x= \frac{5±\sqrt(25+96)}{12}$

[woven radish]

hoi

[fleet mauve]

Is it?

[marble osprey]

yes thats it

[fleet mauve]

You gotta solve it, first with + sign between 5 and √... And then with - sign

This gives 2 roots of quadratic eqn

[marble osprey]

I only get to x=5 +- square root of 121 over 12

[fleet mauve]

And 121 is square of ??

[marble osprey]

11

[fleet mauve]

Yeah

[marble osprey]

so 5+-11/12

?

[fleet mauve]

Yup

[marble osprey]

now what

[fleet mauve]

^

[marble osprey]

but is 5+-11/12 is just it simplified

[fleet mauve]

You got two roots ( 5+11)/2 and (5-11)/2

[marble osprey]

yes

over /12

[fleet mauve]

You can calculate these values right

It's not caclulated yet

[marble osprey]

16/12, 6/12

[fleet mauve]

-6/12*

[marble osprey]

oh yes

[fleet mauve]

Yeah simplify it to lowest factors

[marble osprey]

x = 4/3, -1/2

[fleet mauve]

Yup

[marble osprey]

Okay I have one more

[fleet mauve]

👍

[marble osprey]

Do you have time if not totally good

[fleet mauve]

You can ask

[marble osprey]

I’m going to walk through what I’m gonna do

I have x= -7+- squareroot 49-72 / 6

.close

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[lone gazelle]

One message removed from a suspended account.

[lone gazelle]

One message removed from a suspended account.

[languid ocean]

just repeated multiplication?

[lone gazelle]

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[main gull]

Did you look back at the lesson or notes?

[lone gazelle]

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[lone gazelle]

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[main gull]

No

https://www.youtube.com/watch?v=2TYO7Da6yrM&ab_channel=TaylorJ'sMathMaterials

Not sure how good that video is but it should help out

[lone gazelle]

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[restive river]

I need help with this question

<@&286206848099549185>

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@restive river Has your question been resolved?

[wicked rover]

.close

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[rare mantle]

I'm confused how I would even go about solving this

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[devout snow]

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[shy coyote]

3(4d+1) -9d =(2-d) i need it solved

[fervent maple]

Expand the brackets, what u get

[shy coyote]

ok

3 (4d + 1) - 9d =6 (2 - d) this is it expanded

[fervent maple]

No

[restive river]

distributive property, i have forgotten my 1st grade property names

a(b+c)=ab+ac

[shy coyote]

idk how this works its my first time here

[shy nova]

Same here, I'm new

[shy coyote]

idk how i do that bcs my teacher is making this confusing on ,me

[main gull]

Sounds like you need to look over that material

[main gull]

#❓how-to-get-help

[fervent maple]

Watch a video about it on YouTube

[shy nova]

I need help with real analysis

[fervent maple]

We help with the problems, not the concepts

[restive river]

khan academy

life saver

[shy coyote]

ok

[fervent maple]

Type ‘distributive property’

[restive river]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities

this and distributive property videos

[shy coyote]

k ty

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[twin crescent]

Explain why the polynomial p defined by $p(x) = x^6 + 100x^2 + 5$ has no real zeros.

[woven radish]

Jef Costello

[sonic smelt]

Because it's always positive?

[modern glade]

You can see this will never going to give you negative values ,so that means never going to cut x axis that means never going to give you roots( real)

[twin crescent]

I see

yeah I see it now, thanks :')

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[devout snow]

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[rain quiver]

Can anyone help me please?

[restive river]

By similar they mean angles are same?

But not lenghts

@rain quiver u there?

[rain quiver]

I'm here.

I think I have to find the length of x and y.

[restive river]

Umm so when angles are same side lenghts have changed think of it as the triangle scaled by some factor

Like

Let's say in the green triangle

One side length is $l_1$