help-28

[glass crystal]

so now you should be able to find c right?

[sharp perch]

180-90+88

[glass crystal]

what?

where is c in this?

dont jump steps

[sharp perch]

The right angle is 90 right?

The OBA

[glass crystal]

no?

[sharp perch]

How do we get OBA then?

[glass crystal]

this

OBA =OAB

so

[sharp perch]

But Idk the value of the c

[glass crystal]

180 = ABO +OAB + AOB

180 = c + c + 88

[sharp perch]

92=2c

c=46

I feel dumb omg

How did I miss that

[glass crystal]

idk i'm not in your head

but if i had to guess

you are not trained enough in this kind of exercise

[sharp perch]

Nope

[glass crystal]

either geometrically or algebraically

[sharp perch]

No I'm pretty good at algebra

geometry meh

What about the d?

[glass crystal]

combine the two theorems i highlighted

to link d with AOB

[sharp perch]

Bet

[glass crystal]

these two

[sharp perch]

d=44?

[glass crystal]

you already knew that

what i wanted is an explanation

[sharp perch]

So

[full forum]

@sharp perch Has your question been resolved?

[sharp perch]

I'm not really sure but my initial guess was taking the 88 and dividing it by 2

[glass crystal]

yeah but thats a bit light as an explanation no?

[sharp perch]

It is

[glass crystal]

you need an actual proof

hint: talk about the point on the circle thats on the axis of symmetry of the AOB triangle

this point

D

[sharp perch]

Oh I thought you were talking about the the cross

[glass crystal]

ADB =?

[sharp perch]

D?

[glass crystal]

wdym,

you dont see D on the drawing?

i sent

[sharp perch]

Oh

I see it now

It's just in th bottom

No the triangle cross

It looks like an X

[glass crystal]

put your glasses on

[sharp perch]

To the left of the O

[glass crystal]

wtf

[sharp perch]

I'm just trying to get better at geometry man 😭

I've never solved anything like that before

[glass crystal]

no but

im not asking for you to be good right

away

[glass crystal]

but how do you see an x?

[sharp perch]

I'll draw it

[glass crystal]

like its not maths its seeing

so whatever

now you know where D is

use

[sharp perch]

It split AOB?

So instead of an 88 I have 44

[glass crystal]

yeah but this wording is very confusing

its not instead of

[sharp perch]

2 of them I meant

[glass crystal]

wdym

[sharp perch]

2 splits

44 44

2 new angles

[glass crystal]

you dont split it

it just happens to be half the other one

splitting would mean cutting it

[sharp perch]

I guess you're right

[glass crystal]

w/e maybe its just a wording issue

and now

ADB = d

because of

[sharp perch]

Could you elaborate more? or draw it please

I still haven't understood the use of the D

[full forum]

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[sharp perch]

.reopen

[full forum]

✅

[sharp perch]

@glass crystal

[glass crystal]

i introduced D to use this theorem

[sharp perch]

I can see the ACD

AOD is an angle?

Am I correct?

[glass crystal]

yes its an angle

but i could say 34*2 = 68 its true also but its not useful

you need to explain yourself

because it seems like you assume i'm in your head

and im not

if you just make sentences out of the blue like that i cant help you

[sharp perch]

I'm just not used to learning through texting

[glass crystal]

even if we were talking and you only said that

[sharp perch]

I'll try to explain

[glass crystal]

it would be the same

[sharp perch]

So about the theorem

I don't see any angles on the same segment

Don't they have to tocuh each other to complete the theorem?

[glass crystal]

which angles which segment?

what are you talking about

[sharp perch]

ACD

AOD

They are on the same chord I meant

But don't they have to be touching eachother?

[glass crystal]

ok so which theorem do you want to use?

and define "touching"

[sharp perch]

.

[glass crystal]

ok

so for this theorem

you need to angles on the same chord

but also

the angle must be on the circle

itself

it cant be on the center

like AOD

[sharp perch]

I see

So what's the solution for it

[glass crystal]

ADB = ACB

[sharp perch]

ADB= 44

Because D Is basically 88 but 2 halfs

[glass crystal]

D is a point

[sharp perch]

What is the purpose of a point, I've never seen anything like it before

[glass crystal]

no but

im not saying it has a purpose

[glass crystal]

just this sentence doesnt make sense

[sharp perch]

I wanna know why've added the D??

[glass crystal]

oh ok

[glass crystal]

to use this

you could have used it right away but since you struggled

i wanted a point that looked like the exemple

so you could recognize

the theorem

by yourself

[sharp perch]

I usually like to see the steps of the solving instead of solving it myself

I understand it much quicker

[glass crystal]

its very common and thats why i decomposed the solving into two parts

[glass crystal]

but you could have used this theorem right away

[sharp perch]

Just highlight it

[glass crystal]

highlight what?

[sharp perch]

Highlight this theorem

Applied on this triangle

[sharp perch]

.

[glass crystal]

the angle at the circumference is ACB

and the angle at the center is AOB

[glass crystal]

just angles not necessarely triangles

in this its jkust angles

[sharp perch]

Now I understood it

Thanks man

Sorry for being slow

[glass crystal]

no worries

your main issue was not the maths

[sharp perch]

Just trying to learn math in English is still a new concept to me and there's a lot of terms that I'm unfamiliar with I just learned what a circumference means lol

[glass crystal]

but the fact i was kinda speaking to a wall

be as explicit as possible

when talking about something you dont understand

help the person help you

[sharp perch]

I'll try to be better than my today's me lol

[glass crystal]

good luck

[sharp perch]

Anyways thanks for your patience and take care <3

[glass crystal]

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[dense fractal]

i need help with b

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[torn jolt]

I don't know how to solve this, I'm not supposed to use derivatives of inverse trigonometric functions

I begin by labelling the increase in AB as dA/dt

and I say that the rate of CAB is: dC/dt. By using chain rule, I create the equation dc/dt = da/dt * dc/da

So essentially I have to find dc/da which from my understanding is cos(CAB) = AB / 10, but derived

I'm not sure where to work from here.

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@torn jolt Has your question been resolved?

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[near rapids]

"A mother wants to prove that reading improves thinking process" can someone explain why is this a two-tailed test (statistics)?

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[full forum]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[gaunt bobcat]

I apologise for asking a very simple question but my brain is mush

Which one is the correct answer?

Top or bottom?

[rough tundra]

ah I see

$\frac{10}{6\sqrt{14}}=\frac{10}{6\sqrt{14}}\cdot\frac{\sqrt{14}}{\sqrt{14}}=\frac{10\sqrt{14}}{6\sqrt{14}^2}$

[glossy valve]

XxMrFancyu2xX

[rough tundra]

So what does that tell you about the denominator?

[gaunt bobcat]

So it will be 6 times 14?

[rough tundra]

👍

[gaunt bobcat]

Thanks

[rough tundra]

yw, have a good day! (and dont forget the close ur channel)

[gaunt bobcat]

Sure

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[sick prism]

hello

[sick prism]

does anyone know how to do the middle part?

also why did i get the intersections wrong

wait rlly?

how do u know

ah yes but it doesnt just mean reads both

some may read all 3

but thats even more confusing

thats y im asking

anyone?

[glossy valve]

Azka Aska

[terse karma]

Why?

Why?

9 people read all innit

Sorry

You got something wrong

[sick prism]

apparently the middle part is 24

[terse karma]

,w 59+80+88+61+40+47+43-370

[glossy valve]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by yes sam#5028

[terse karma]

,w 48/2

[glossy valve]

Results provided by WolframAlpha

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Requested by yes sam#5028

[terse karma]

This one is correct

[sick prism]

yes

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[pure ice]

36x – 8y2 when x = 3 and y = –6. Can someone please help explain why you get -108 as an outcome from this equation?

[light sonnet]

Is that $36x - 8y^2$?

[glossy valve]

dldh06

[pure ice]

The equation would be 36(3)-8(-6)^2

[light sonnet]

Yes

That's right

[light sonnet]

What did you get when you did this?

[pure ice]

108-96. but I know that is not what its supposed to be. I'm getting stumped by "-8(-6)^2"

[light sonnet]

Because $-8(-6)^2 \neq -8 * (-6) * 2$

[glossy valve]

dldh06

[light sonnet]

Do you know what (-6)^2 means?

[pure ice]

To the power of is that same number multiplied that many times? so in this case it would be (-6) x (-6)?

[light sonnet]

Yes

[pure ice]

And a negative multiplied by a negative creates a positive, right?

[light sonnet]

Yes

[pure ice]

gotcha. so 36(3)-8(-6)^2 would turn into 108-288

[light sonnet]

Yes

[pure ice]

Why does (-6) x 2 result in -12?

[light sonnet]

Do you know what 6 * 2 is?

[pure ice]

ah. yes. 6*6 is what result in 36

So originally I wasnt putting (-6) to the power of 2. I was doing (-6) * 2, which is just -6*2, which is -12

[light sonnet]

Yes

[pure ice]

Great, thank you for correcting my mistakes

Have a wonderful day

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[torn jolt]

I cant understand how to make an equation for all three ineaulities

ineqalteis

i cant speel

spell

idk where to put the points

[potent shale]

Can you draw the line x = 1?

and x = 5?

@torn jolt

[torn jolt]

no i cant

i dont know where to draw line

@potent shale

Its confusing because there are two signs for the 1st one

[potent shale]

I didn't ask about the first 1, I asked about x=1

Do you know how to draw x=1?

it's simply a vertical line at x=1

@torn jolt right?

[torn jolt]

ok and for x being less than

yeah

its a vertical line

[potent shale]

Ok, so x >= 1 is everything to the right of x=1

And x<= 5 is everything to the left of x=5

That's the first inequality that you have there $ 1 \leq x \leq 5$

@torn jolt got it?

[torn jolt]

yeah

so like this

the black lines are for y

the second one

idk about the last one

i mean its an equation for a straight line

y=-1x+3

i can put in (1,1)

so 1=-1(1)+3

ohhhhhhh

wait no

idk man

helpp

[brittle steeple]

That is not the line y = -x+3

[torn jolt]

bro i got a paper just tell me whwerew to do it

I just need this one example

I'll get the rest

Please

[brittle steeple]

if you can't graph y = -x+3 then you have big enough gaps in your knowledge already without being fed more solutions

sorry

[torn jolt]

Bro you show me this then I'll get it

[charred crag]

When x=0, y=3 so (0,3) is on the line, when x=1, y=2 so (1,2) is on the line, join those points to get the line for the last part

[torn jolt]

Thanks

[charred crag]

You get the following lines

For the last part to figure out if it's above the green line or below the green line you put in a point and see if the inequality works

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[torn jolt]

How can I solve this without converting to slope intercept form aka y=mx+b ?

[vast fossil]

Generally the system of equations
a1x + b1y = c1
a2x + b2y = c2
Has infinitely many solutions whenever a1/a2 = b1/b2 = c1/c2

You can solve for m and n here using this fact

[torn jolt]

so they all have to be equal to 1/4?

[vast fossil]

Yup

[torn jolt]

thx bro

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[cobalt atlas]

i noticed something here

If we collect the numbers

first one will gave us 15

and the answer is 2

and the third one will also gave us 15 and the answer is 2

ıt may has no relation

[potent shale]

What are those

[cobalt atlas]

the is some kinda of operation happing between the numbers

[potent shale]

Is it a riddle?

[cobalt atlas]

to gave us a number

[potent shale]

Does it have any context?

Or can it be anything?

[cobalt atlas]

just what in front of u

[cobalt atlas]

the same operation it has to work on the all options

i live in turkey and they have exam they call it yos
thats why im solving this kinda of questions

[potent shale]

Do you have an example that you know how to solve?

Something similar

[cobalt atlas]

but this is kinda of hard

but it may be like this

[torn jolt]

ohhh so that was the answer lol

that's crazy

[cobalt atlas]

it is

[potent shale]

I have an option

But it's probably wrong

[torn jolt]

(1+2+3+4)/5 = 2
(2+1+3+5)/1 = 11

[cobalt atlas]

anything

[potent shale]

I would do (sum(x_i) - 1)%12

[torn jolt]

(3+0+1+2)/1 = 6

[cobalt atlas]

wait what

[torn jolt]

sum the first 4 divide by the last

[cobalt atlas]

haaaaaa

[potent shale]

That works too 🙂

[cobalt atlas]

thank u BTW

[cobalt atlas]

and thank uuu

[torn jolt]

good luck with the studying

[cobalt atlas]

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[uneven bear]

$$\frac{-2 +- \sqrt{16 * (-1)}}{2}$$

[glossy valve]

sla-ppy

[fast peak]

\pm for +-

[rough tundra]

$\pm$

[fast peak]

\cdot or \times for multiplication

[glossy valve]

XxMrFancyu2xX

[rough tundra]

$\cdot > \times$

[glossy valve]

XxMrFancyu2xX

[uneven bear]

how does (16 * -1) become 4i here?

[fast peak]

sqrt of that is 4i

[uneven bear]

if we sqrt -1 it becomes i?

[fast peak]

yes

[uneven bear]

thats all i needed to know, thank you!

[fast peak]

thats the definition of i

i^2=-1

[uneven bear]

tyty <3

will try to remember \pm too guys, thanks

[uneven bear]

also true lmao

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[wispy gorge]

Is it correct to say that the standard rational and exponential functions doesn't have a maximum and minimum?

[plush egret]

can you clarify what you mean by these functions?

exponential functions are bounded on one side

(usually 0 is a bound in some way)

[wispy gorge]

I mean for the functions 1/x and 2^x. The rational function has horizontal asymptote and vertical asymptote. And the exponential function has a horizontal asymptote only. So you can't find the maximum or the minimum of these functions right? Because they have infinite values.

[plush egret]

you can bound 2^x below

otherwise i think youre right

[wispy gorge]

Ok thanks for the clarification

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[torn jolt]

Help

[full forum]

Please don't occupy multiple help channels.

[torn jolt]

No one is looking at mine!

😫

what are you trying to solve?

This

[torn jolt]

Look

on F?

Hm?

the light rays concentrate on the F to the left in the image i think

Idk

/:

are you supposed to show it using math or something

cus if not the answer is F to the left in the image

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

Yes using math

are there any points or equations or is that all of the text given?

like can you show the full problem

[torn jolt]

Thats all

[torn jolt]

There is not more

like whats e, d c, b, a are they related

this is f

right

?

Nonnonl

F

Is

Do you know ellipse?

c^2 = a^2 + b^2

C is Foyer

Foye is F

[torn jolt]

Could you solve this @rough tundra?

c is the focal point of both yes

i meant excercise c, but nevermind

[torn jolt]

Yeah

Do you understand anything?

i dont see the answer, there are a lot of variables in the general equations

[rough tundra]

I dont understand enough information in order to make sense of it

[torn jolt]

Kms

which textbook is it from?

are there some equations in the preceding chapter?

that could be relevant to this?

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[coral root]

Hi I am having trouble setting the domaine in y for this problem. I found that the domaine in x is -2>x>7

[glass crystal]

,w plot 2x^2-x-10, x²+4x+4, x=-3 to 8

[glossy valve]

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Requested by Benjamin#3570

[glass crystal]

looks like this is the right x domain

so ok lets go

$\int_{-2}^7 \int_{f(x)}^{g(x)} x^2y dy dx$

[glossy valve]

Benjamin

[coral root]

Why did you choose dydx over dxdy in this case?

[glass crystal]

because the way in which expressed the domain makes the y-boundaries depend on x

so i must integrate y first

[coral root]

Ahh okay

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[glass crystal]

so have you find something?

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[coral root]

No

This is what i did

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[vale karma]

Hi, it this solution correct for this exercise?

[full forum]

@vale karma Has your question been resolved?

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@vale karma Has your question been resolved?

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@vale karma Has your question been resolved?

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[fathom saddle]

Nothing. There is no value of x that gives sin(x) = 2

That factor gives no zeros. Ignore.

The solution is really
π/2 + kπ

That includes 3π/2, 5π/2, 7π/2...

Weird they didn't write those on the solution sheet, they should have

Another way to say it,
π/2 + (1)kπ

That's where the 1 comes from

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[turbid falcon]

what happens when i multiply 0 in an equation?

[eager crag]

you get0

[turbid falcon]

oh

i thought it removes information

about the equation

[eager crag]

it does

[turbid falcon]

how

[eager crag]

but u get 0 anywat

[turbid falcon]

but how

any examples?

[eager crag]

x-1=0

[turbid falcon]

?

i thought something like

i dont see how multiplying 0 relates to the equation u gave

[eager crag]

try multiplying 0

[turbid falcon]

0=0

how about this

x/200=0

multiplying both sides with 200

will remove information about the initial equation

[eager crag]

no

[turbid falcon]

why not

[eager crag]

because 200*0 = 0

sp x =0 stays the same

[turbid falcon]

so how does multiplying 0 in your equation do anything to it

i dont see how it will affect the information

[eager crag]

because ypu.dont have x anymore

[turbid falcon]

ok

thank you

i appreciate the help

cya

have a nice day

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[torpid siren]

is the only way to calculate this to do it the long way on excel

ie... go look for the expected value of each of these

and then plug into the formula

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[torpid siren]

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[warm pine]

Can anyone help me with this Question

[warm pine]

<@&286206848099549185>

no sorry i just started

oh cool but how should i start with it?

[stoic portal]

(v-u)

[warm pine]

yah i heard that (v-u) is a stop

But can you help me that how should i start with it ?

or find/Given

[stoic portal]

You could start by trying this

Not yet I guess

[warm pine]

i mean please i just started learning this.

[stoic portal]

Okay good so what is the final velocity

[warm pine]

5.00s?

[stoic portal]

Okay then whats the initial velocity?

[warm pine]

9.00

so 9+0=9?

oh wait sorry 9-0=-9

?

[stoic portal]

Thats right

[stoic portal]

Try again

[warm pine]

0.00?

[stoic portal]

Yepp

And whats the time

[warm pine]

give me sec

to solve

[stoic portal]

Sure tag me or Shivam once ure done

[warm pine]

@stoic portal @torn jolt 1.8

?

hello?

[stoic portal]

Yepp

[warm pine]

@stoic portal ??

[stoic portal]

You got it, don’t forget the units

[warm pine]

sorry so

1.8m/s^2?

[stoic portal]

Yep

1.8*

[warm pine]

idk the find/Given

sorry

how do i find or Given?

Can you help me with it?

[stoic portal]

What info is there in the question

That’s given

What did you just calculate… basically the main thing asked in the question

Thats your “to find”

[warm pine]

so the find is m/s?

i mean t?

[stoic portal]

So I’ll show you an example:
Given-
U=initial velocity =9m/s

Similarly write other details

[stoic portal]

Nope what did you calculate

[warm pine]

that's the only given

[stoic portal]

What does the question ask

[stoic portal]

What about v and t

Thats not given?

[warm pine]

so velocity and time?

oh did i pronounce it wrong

[stoic portal]

Final velocity and time, yes

[warm pine]

do i have to put the solution with it?

[stoic portal]

This is what you were trying to find right

[warm pine]

on the Given?

[stoic portal]

What is this

[stoic portal]

Nope

Solution comes after to find

[warm pine]

uhmm time?

[stoic portal]

Read the question

And tell me what you were trying to find/calculate

[warm pine]

average accelaration yes?

[stoic portal]

Yep

That’s the to find

[warm pine]

oh thanks i think i have an idea how to solve it rn

[stoic portal]

Great

R you in 9th grade?

[warm pine]

Alright Thank you @stoic portal your the best Keep it up!!

[warm pine]

Yep

[stoic portal]

Npp

[warm pine]

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[torn jolt]

Could someone help me, give me a tip, where is the mistake?
It's a basic linear equation as you can see... It seems that I've made some error a long the way.
The correct solution is 3.
But I got quadratic equation, and solution is obviously not 3.

[hot herald]

5x^2 - 1
isn't 5(x-1)

[torn jolt]

Yeah

thanks!

@hot herald thanks

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[full forum]

Please don't occupy multiple help channels.

[tall spindle]

need help setting up the equation

[willow wagon]

Ok

!status

[full forum]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tall spindle]

1

[willow wagon]

You just have to directly replace the arc length formula

[tall spindle]

what formula would I do

[willow wagon]

The circumference is 2×pi×r

[tall spindle]

which would turn to be 8 pi

[willow wagon]

And arc length= 2πr×theta/360

Where theta is in DEGREES

[tall spindle]

would i replace r with 4 or 8/9 pi

[willow wagon]

You'd have to convert it

[tall spindle]

so 0.28

[willow wagon]

Idk about the calculation

[tall spindle]

wait

2.79

my bad

[willow wagon]

Ok wait

I'll try it myself

[tall spindle]

okay

[willow wagon]

Read the question again please

Your answer must be in terms of pi

Times the fraction

[tall spindle]

demos says 2.79

[willow wagon]

Don't use a calculator

Please

It's an easy question

Did you get it?

[tall spindle]

i’m kind of lost

[willow wagon]

Do you follow me till here?

[tall spindle]

yeah

[willow wagon]

Ok so

Theta must be in degrees

For this formula

Convert 8π/9 into degrees

Or you don't wanna do that?

[tall spindle]

160 degrees

is that correct

[willow wagon]

No

You can just convert 360 into 2π then just use the radians for theta

That's easier

[tall spindle]

wdym

[willow wagon]

360°=2πRadians

Then after replacing 360 by 2π

Directly replace the angle as given in question

[tall spindle]

which would be 4

right

[willow wagon]

What 4?

[tall spindle]

4 pi

[tall spindle]

is the answer 32/9 pi

[willow wagon]

Yes

The pi is on the numerator

Was it correct?

@tall spindle

[tall spindle]

it wasn’t

68/9

pi

was the answer

[willow wagon]

Oh

[tall spindle]

yeah

[willow wagon]

💀

The area is 8π/9

I thought it was the angle

[tall spindle]

your good

[willow wagon]

Thanks

[tall spindle]

can you help me with one

if possible

[willow wagon]

Ok wait

[tall spindle]

okay

[willow wagon]

Answer should be 16/9

It's the same process

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[pale jackal]

Can someone sub 4 into that and tell me what they get

idk if im tripping

or if this mark scheme is wrong

so just want to make sure xD

and -1 pls

This was the original question

My thought process was to find the area under the line from A to B and subtract the area under the curve from A to B

So I found the coordinates which were A(-1, 11) and B(4, 6)

I then integrated the line and got 85/2 for the area under the line

I then integrated the curve and got 65/3

So I did 85/2 - 65/3

ffs, i did get the answer right

read my calculator wrong xD

sorry

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[silver pasture]

|3x+1| = 4-2x

[onyx glen]

!status

[full forum]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[silver pasture]

solving this modular function gives a fake solution

ok wait

[terse karma]

That's nice

[silver pasture]

plotted separately this has one intersection

[terse karma]

Yes

[silver pasture]

and together

am i stupid or thats illegal

[terse karma]

How did you get something like this?

What did you input?

[silver pasture]

lhs = f(X) and rhs = g(x)

then rhs- lhs =f(x)

[glossy valve]

fäf

[silver pasture]

yes it does

[terse karma]

Nah it won't work that way

[silver pasture]

the mod messes up?

[terse karma]

this is their difference function

[terse karma]

No you

[silver pasture]

ok wait how come

they are equal at that one point so when x-y then only at that point the difference function should equate to 0

[terse karma]

The graph doesn't seem right

[silver pasture]

but it is

i checked it 10 times already

[terse karma]

,w graph |3x+1| - (4-2x)

[glossy valve]

Results provided by WolframAlpha

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Requested by yes sam#5028

[silver pasture]

ok bye but

when i do get a fake intersection

how do i know its fake

[terse karma]

Okay

[silver pasture]

.close

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[torn jolt]

Can anyone explain why V0=vmax

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[hot star]

how do i find if this is convergent

[gritty rose]

Comparison test

Or limit test

[rare dock]

is it a series though?

[hot star]

yea it is

[gritty rose]

You should say that next time

[hot star]

its a sequence

okay

[gritty rose]

This is not a series

[hot star]

an= that thing

if n goes to inf

n e ways

is it just bc 9n grows faster than n?

but i dont think it does

[gritty rose]

Divide all terms by n then use limit laws

,tex .limit rules

[hot star]

divide n

[glossy valve]

riemann

[hot star]

1/9

so limit is 1/3?

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[severe basin]

A retailer sets the cost price 69% above the cost price. He offers 20% discount. He also gives a TV free on selling 12 TVs. Find the net profit percent.

[severe basin]

Let the initial cost price be x rupee.

Then, the selling price would for one TV would be (80/100) * (169/100) * x

Then I applied the profit percent formula

[onyx glen]

what's that -13x doing there?

ah, nevermind.

@severe basin is this a status 3 or a status 4

[severe basin]

!status

[full forum]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[severe basin]

3

and 4

,calc ((12 * 0.8 * 1.69) - 13) * 100

[glossy valve]

Result:

322.4

[severe basin]

Huh

@onyx glen What is the mistake in my work?

[onyx glen]

wait hold on

,calc 12 * 1.69 * 0.8

[glossy valve]

Result:

16.224

[onyx glen]

oh you forgot to divide by the price of the 13 TVs

denom should be 13x not just x

[full forum]

@severe basin Has your question been resolved?

[severe basin]

Oh yes

,calc ((12 * 0.8 * 1.69) - 13)/13) * 100

,calc (((12 * 0.8 * 1.69) - 13)/13) * 100

[glossy valve]

Result:

24.8

[severe basin]

The answer is given as 26.9%

They assumed C.P. to be 100 and did (20/100) * (169/100) * 100

I want to slap the person who wrote the answer key for this book

.close

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[sharp flame]

It's just a constant

In the first integral

You can evaluate it with trig sub

After completing the square

$x^2 - 2x + y$

[glossy valve]

NEONPerseus

[sharp flame]

Can you complete the square here

Inside the integral, y is a constant

I'm not sure what exactly you mean by "doesn't matter"

Are you familiar with common integration techniques?

[pine osprey]

Temmie667 could you please state your level of experience with calculus ?

[sharp flame]

u-sub, trig-sub, integration by parts

yes

You don't need trig sub here though nvm

Oh wait you do

Have you not been taught trig sub or are you just not comfortable with it

It's just a constant

Like 1, 2, e, π

Hmm

$\int \frac {\dd x}{x^2 + a^2}$

[glossy valve]

NEONPerseus

[sharp flame]

Have you learned a formula like this

Can you tell me what this evaluates to

Yes alright

Now can you please complete the square in the denominator

Do you not know completing the square?

$(x^2 - 2x) + y$

[glossy valve]

NEONPerseus

[sharp flame]

We need to modify the constant term in order to get a perfect square

That's very vague

Because then we can use your formula

Oh

I just did that to group the terms we care about

Can you tell me what would you add inside the bracket to make that term a perfect square

Good

Now just adding one is illegal

So we subtract as well

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

[glossy valve]

NEONPerseus

[sharp flame]

We have this now

Agreed?

$f(y) = \int_0^y \frac{\dd x}{(x - 1)^2 + y - 1}$

[glossy valve]

NEONPerseus

[sharp flame]

Because now we substitute x - 1 = u

All good now?

Can you substitute x - 1 = u and tell me what the new Integration limits will be?

Oh you'll see soon

Nice

$f(y) = \int_{-1}^{y - 1} \frac{\dd u}{u^2 + y - 1}$

[glossy valve]

NEONPerseus

[sharp flame]

So this is what we have now

We're gonna do a thing now

$\int_{-1}^{y - 1} \frac{\dd u}{u^2 + (\sqrt{y - 1})^2}$

[glossy valve]

NEONPerseus

[sharp flame]

Can you apply this formula now

yes

You can write it down and send a photo

Yes just the square root

So now we have f(y)

The limits you mean?

Yes

Yes

Sub in the upper limit and then from it, subtract the function evaluated at the lower limit

I'd think so

Can you simplify that

Yes you can do that

You should do that

All of them?

Wdym

Simplify as much as you can

It's alright

You certainly did complicate it

It's alright I'll walk you through the simplication

Before we begin

sqrt(y - 1) = t

I'm making this substitution so that it's easier for me to type it out with the bot

$\frac{1}{t} \left ( \arctan t - \arctan \frac{-1}{t} \right )$

[glossy valve]

NEONPerseus

[sharp flame]

Do you understand what I've done?

$\arctan (-x) = -\arctan x$

Yes

Do you know this formula

Well

You need to know this

[glossy valve]

NEONPerseus

[sharp flame]

Yes

$\frac{1}{t} \left ( \arctan t + \arctan \frac{1}{t} \right )$

[glossy valve]

NEONPerseus

[sharp flame]

$\arctan x = \arccot \frac 1x$

Do you know about this

[glossy valve]

NEONPerseus

[sharp flame]

Do you know what cot is

cot x = 1/tan x

No?

That's very odd

[sharp flame]

(for x > 0)

Alright

\frac 1t \left ( \arctan t + \arccot t \right \right )

$\frac 1t \left ( \arctan t + \arccot t \right )$

That's fair

[glossy valve]

NEONPerseus

[sharp flame]

$\arctan x + \arccot x = \frac{\pi}{2}$

[glossy valve]

NEONPerseus

[sharp flame]

Do you know about this

Well

This is a thing as well

And we're gonna have to use it

So now we have $f(y) = \frac{\pi}{2\sqrt{y - 1}}$

[glossy valve]

NEONPerseus

[sharp flame]

Ain't that lovely

Alright

What limits?

We already did that

It's alright

So now we need $\int_2^{10} f(y) \dd y$

[glossy valve]

NEONPerseus

[sharp flame]

$\frac{\pi}{2} \int_2^{10} \frac{\dd y}{\sqrt{y - 1}}$

[glossy valve]

NEONPerseus

[sharp flame]

That's just the domain of the function

It means we're not allowed to plug in values below 1

Pretty useless here

It's a formality thing

The term under the square root becomes negative

And that's a big no no

[sharp flame]

Do you know how to integrate this?

You don't need a formula here

Substitute y - 1 = u

Then you can apply the power rule

I think it would be just pi uh

,w integrate from 2 to 10 1/sqrt(x - 1)

[glossy valve]

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Requested by NEONPerseus#2128

[sharp flame]

No you're right

It's 2pi

Well done

This is it

Yes

For integrals it comes down the practice

You will recognize patterns on your own

And understand what to apply when

Also it's highly necessary that you strengthen your trigonometry and inverse trigonometry

You wouldn't have been able to do this without those

Many formulas

You should also learn trig sub

You'll remember them

Everyone does

You can close the channel if you're done

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[sick canyon]

How would i do this

I have all of the suvat values i can get and i assume i need to create two simultaneous equations but im not 100% sure

[dim compass]

,rotate