help-27

[forest geode]

Is this right?

[ripe haven]

Yes

[forest geode]

Question: howd you mark so fast

@ripe haven

[ripe haven]

?

[forest geode]

How did you mark it so fast

[devout snow]

@forest geode Has your question been resolved?

[devout snow]

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[restive river]

Is this correct, question 1b

[manic condor]

I don't think you have done the part of proving p(k+1) is true when p(k) is true correctly.

[restive river]

I got stuck on 2^k+1+ 3^k+1 < 4^k+1

Should i mulitiply both sides with 4?

[manic condor]

No. Firstly, you aren't supposed to use the statement P(k+1) at all.

You start with P(k)

Manipulate it into showing that p(k+1) is true.

Fixed

[manic condor]

Not supposed to*

[restive river]

Oki first P(k) = 2^k + 3^k < 4^k right

[manic condor]

Yes

[restive river]

Okay afterwards it would P(k+1)

[manic condor]

You manipulate this expression. Try thinking of some way to get terms of p(k+1) appear.

[restive river]

I would multliply both sides by 4 so that 4*4^k is 4 ^k+1 there we have k+1

[manic condor]

Yes. Go on. That should work.

[restive river]

4 (2^k + 3^k) < 4^k+1

[manic condor]

Yes. Now expand the left side.

Simplify.

[restive river]

2^k+2 + 4 (3^k) < 4^k+1

Im unsure about 4 (3^k)

[manic condor]

Now, You can easily make the left side into required expression.

[manic condor]

What do you mean?

[restive river]

Was 4 (3^k) correct?

[manic condor]

Yes

2^(k+2) + 4 (3^k) < 4^k+1

Don't forget the bracket

[restive river]

2^(k+2) + 4 (3^k) < 4^k+1 so what more must we do?

[manic condor]

Well, first off, we know that 2^(k+2) > 2^(k+1)

so, we can replace 2^(k+2) with 2^(k+1) and our inequality holds.

So what do we get now?

[restive river]

2^(k+1) + 4 (3^k) < 4^k+1?

[manic condor]

Yes. Now, You can similarly replace 4(3^k) by 3(3^k).

As we are replacing by a smaller value, inequality still holds.

Btw, before doing both of these steps, write that.

[manic condor]

Write this before switching.

Then write: 4(3^k) > 3(3^k)

before switching last one.

[restive river]

Yes

2^(k+1) + 3^(k+1) < 4^k+1 should be our answer when we switch?

[manic condor]

After the both switch, yes.

That's just p(k+1)

So we have shown that when p(k) holds, p(k+1) holds.

[restive river]

Yes

[manic condor]

Don't forget the parentheses.

[restive river]

One question with switch

This my first day with induction, when you said 2^(k+2) > 2^(k+1) where does k+2 go

Thanks for the help

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[maiden zephyr]

help

[maiden zephyr]

if they are cance;

then why does she right back 2 a in denominator

why

[little bronze]

i see what u mean

she canceled out 2 from the same term

[dense jay]

seems like an error

[little bronze]

yeah

[little bronze]

but it depends

Like what if hes trying to prove that LHS = RHS

[maiden zephyr]

oh nvm xD

[little bronze]

lmao

[maiden zephyr]

i just unpause and she said sorry guys is a mistake

and re writes A

okay

nvm oops

[little bronze]

nice lol

[dense jay]

[maiden zephyr]

🤣

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[faint mountain]

my guess is (-x)^3 -2 but how do i show 2 different transformations?

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[faint mountain]

its wraps

.close

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[urban aurora]

Why can you not use this formula to find the surface area of a sphere?
For the volume you can take the integral from 0 to 4 of pi*f(x)^2 dx so I don't get why you can't do that here?

[pseudo basin]

well, not squaring the function under the integral sign definitely was a bad move

[urban aurora]

I am wanting to find the surface area though, not the volume.

[pseudo basin]

ah

https://tutorial.math.lamar.edu/classes/calcii/surfacearea.aspx

[urban aurora]

I see why that works, but I am not sure why what I tried does not work?

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[restive river]

I was studying exact differential equations

[restive river]

In it there was a condition for a DE to be exact

In that if it's expressed in the form Mdx + Ndy = 0, where M and N are functions of x,y

(Here, say F is an implicit function, such
that F = arbitrary C is a solution)

So the condition was, that M, N should have continuous first order partial derivatives in a region in XY plane, whose boundary is a closed curve with no holes

[restive river]

And here M and N and partial derivatives of F with respect to x and y respectively

[restive river]

So , I didn't understand this particular condition

Can someone explain?

[restive river]

(PS. The other condition was that M and N need to be defined)

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<@&286206848099549185>

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[lapis cargo]

Hello! I am struggling with finding the point of intersection for two tangent lines on a vector curve. I know the method in which one would apply this toward finding the intersect of two vectors but this is proving difficult.

[lapis cargo]

The work I have is above, but as I get to the point in which to equate each componenet of the vectors, it becomes impossible to isolate variables.

Thank you in advance

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[clever hemlock]

How can I show a function is increasing from a certain interval without calculus

[strange nimbus]

You could probably show that f(x + a) - f(x) > 0 for positive a with both x and x + a in the interval.

Like f(x) = x² is increasing on [0, 10) because f(x + a) - f(x) = x² + 2ax + a² - x² = 2ax + a² > 0 since a is positive and x is nonnegative.

[clever hemlock]

Okay thanks. Ill see if this works.

.closed

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[strange nimbus]

No problem.

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[strange nimbus]

How far have you gotten?

[last crescent]

idk where to start tbh

[strange nimbus]

OK, so for part a, they say g(x) = f(x) - 2.

In the table, they ask for g'(x) values.

So, what's g'(x)?

[last crescent]

f'(x)?

bc -2 deriv is just 0

[strange nimbus]

Right. So, fill out that row.

[last crescent]

would d be the same one

like its just f'x

[strange nimbus]

How would you get s'(x)?

[last crescent]

derive f(x+2) which is f'(x)?

or f'(1)?

[strange nimbus]

Not exactly.

Use the chain rule.

[last crescent]

is it just x+2?

[strange nimbus]

No, it has f' in it.

Do you have a good handle on the chain rule?

[last crescent]

i think so

i solved it by 1(x+2) times 1

[strange nimbus]

OK, so show your steps.

[last crescent]

bc x+2 deriv is just 1

[strange nimbus]

Right, (x + 2)' is 1.

[last crescent]

so s'x = f'(x+2)

[strange nimbus]

Right.

So, fill in that row as much as you can.

[last crescent]

oh ok i get it thank you

[strange nimbus]

You're welcome.

[last crescent]

hey if youre still here could you help me with b?

[strange nimbus]

OK, so h(x) = 2f(x).

What's h'(x)?

[last crescent]

so i did h'(x)= 0f(x) + 2f'(x)

idk if thats how u do it

[strange nimbus]

Oh, no, you'd use the constant multiple rule.

[last crescent]

whats that rule again?

[strange nimbus]

Oh, I see you used the product rule. That's fine. The constant multiplier rule is just if you have (25 f(x))', you get 25 (f(x))'.

You just say it's the constant multiple you already had times the derivative of the rest of it.

[last crescent]

oh thats nice

[strange nimbus]

Like 20x³ -> 20(3x²) -> 60x².

[last crescent]

ok thank you

[strange nimbus]

No problem.

[last crescent]

for r'(x) i got f'(-3 + 0x) but im like 100% i did something wrong

for c.)

[strange nimbus]

Oh, you need the chain rule for that.

What comes right after r(x) = f(-3x)?

[last crescent]

i dont know

[strange nimbus]

OK, so with the chain rule, you have a function with a more complex argument.

So, here we have f(-3x).

What you do is just take the derivative of the function, like f'(-3x).

Then you multiply that by the derivative of the inside.

So, like f'(-3x) (-3x)'.

Does that make sense?

[last crescent]

im confused about the second multiple

like f'(-3x)

u derived f'

but where did the f go for -3x'

[strange nimbus]

Well, the idea is that you leave the inside alone when you do the function's derivative.

So, like f(-3x) -> f'(-3x).

That's just the derivative of f with the same thing inside.

Then, to handle the inside, you do the derivative of the inside and multiply it in.

f(3x) -> f'(3x) times (3x)'.

[last crescent]

so would you do the product rule for 3x'?

[strange nimbus]

I'd use the constant multiple rule.

You can use the product rule, but it's easier with the constant multiple rule.

I also made a slight error when I changed -3x to 3x.

[last crescent]

no worries

[strange nimbus]

So, you have f'(-3x) times (-3x)'.

[last crescent]

so using the constant multiple rule it would be f'(-3x) times -3

[strange nimbus]

Right.

So, -3 f'(-3x).

[last crescent]

so then if i were to plug in -2 for the table. it would be -18?

[strange nimbus]

You mean x = -2?

[last crescent]

yeah

[strange nimbus]

For that, you'd have -3 f'(-3(-2)), which is -3 f'(6).

[last crescent]

you don't plug in -3 to the 6?

or multiply the -3 to the 6?

[strange nimbus]

Nope, it stays outside.

[last crescent]

interesting

[strange nimbus]

It's kind of like 3g(5x) or something.

f' is a function just like g.

So, the outside is separated from the inside.

[last crescent]

ok thank you so much

[strange nimbus]

You're welcome.

[last crescent]

youre really smart lol

are you in college?

[strange nimbus]

I was a while back.

[last crescent]

how do i make the channel unoccupied?

i finished the problem

[strange nimbus]

Oh, you just say .close.

[last crescent]

.close

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[silk sparrow]

for question C, I got
y = (11/4)x - 2
which isn't the given answer, but both my dad and a family friend got the same answer as me

[strange nimbus]

,rccw

[winter patrol]

show the work that lead to thatresult

[silk sparrow]

let me re-do it in a neat way
hang on

[strange nimbus]

Yes, that's correct.

[woven radish]

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[silk sparrow]

@winter patrol

[strange nimbus]

,w Plot[{y == (2x^2+x-3)/x, y == (11x-36)/4}, {x, -5, 5}]

[woven radish]

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[strange nimbus]

,w tangent to (2x^2 + x - 3)/x at x = 2

[woven radish]

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[silk sparrow]

ok so it's just the wrong answer, then
cheers

.close

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[restive river]

<@&286206848099549185>

[dense jay]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[dense jay]

#❓how-to-get-help i recommend reading through this at least briefly

[storm crater]

What is the question anyway?

[kindred mantle]

u claimed a channel now

so now ask ur question

[kindred mantle]

so what is the question asking

[kindred mantle]

is it asking to find the angle R?

[kindred mantle]

ok bro

one at a time

[restive river]

for village w

aight

[kindred mantle]

well it needs the angle in degrees yes?

[restive river]

yes

[kindred mantle]

if its asking for this

what do you notice

about the shape

[restive river]

it has 3 angles

[kindred mantle]

would it be fair to say the angles form a circle?

r+84+125 = a circle?

[restive river]

yh so = 360

[kindred mantle]

yes

so if we know

that the angels have to add up to 360

and we have 2 of them

[restive river]

r=360-125-84

r=151 degress

[kindred mantle]

360-(125+84) is what you would be looking for

[restive river]

k

[kindred mantle]

i got 152

[kindred mantle]

oh i put 124 by mistake

my bad

yes

[restive river]

k

[kindred mantle]

so thats how u do that

[kindred mantle]

what are u trying to find in this?

[restive river]

wait

there another part to this question

[kindred mantle]

ok

[kindred mantle]

what class is this

i am not sure i understand what bearing means

[restive river]

its like yr 10 maths

[silk sparrow]

surely its more like year 7

[kindred mantle]

maybe less but

i dont know what it means by bearing

[kindred mantle]

thought this would be trig or some shit

[silk sparrow]

assume north is 0 degree

[restive river]

i got trigonometry too

[kindred mantle]

huh

i never heard of this

[silk sparrow]

and if you put a compass on the origin, find what degree the vilage is

compass bearings

[kindred mantle]

im taking college physics and never heard this lol

[restive river]

damm

[kindred mantle]

well even then

what is north in this case

its straight up

the line labeled northi

if it wants

r to t

[silk sparrow]

the bearing is 360 - 125

[kindred mantle]

ok so if u need the angle bearing

[silk sparrow]

its like two in the morning for me

[kindred mantle]

what would you do

[silk sparrow]

i don't trust myself to do that subtraction

[kindred mantle]

or you can just give answer lol

yeah

but u see why

his answer is right

?

[restive river]

yh

next question

[kindred mantle]

ok yeah what is that asking

[kindred mantle]

oh ok

so you know how a circle

has 360 degrees

[restive river]

asking for 360 cause its a complete cricle minus 125 one side of it

[kindred mantle]

there is a similar rule for a triangle

[silk sparrow]

are you sure this is yr 10 maths

[kindred mantle]

do you know what the angles add up for a triangle?

[restive river]

180 degrees

[kindred mantle]

he sounds european

maybe thats why

idk

[kindred mantle]

yes

so if we know 2 angles

[silk sparrow]

i am in europe

[kindred mantle]

of that triangle

[silk sparrow]

learnt this in yr 8

[kindred mantle]

how do we find the last angle

[kindred mantle]

huh

idk then

[restive river]

im in yr 8

[kindred mantle]

ok well its ok

[restive river]

doing advanced math

[kindred mantle]

lets just focus on the problem

dw about it

we have 2 angles of a triangle

and we know all the angles

must add to 180

if we know 2

how do we find the last

[restive river]

i did

180 -143 for angle b

[restive river]

SEE

[kindred mantle]

oh ok

i looked at this wrong

ok i can sitll help

[restive river]

then + 2 angles and took 180

and got 67

for D

[silk sparrow]

Because of a rule, probably @kindred mantle knows the name, <BAE == <CED
If your curriculum is anything like mine then in the next few months you'll need to completely grasp that rule

[kindred mantle]

i dont remember the names i just know it lol

[silk sparrow]

<x also == <CED

[kindred mantle]

for these types of problems

i try to find the angles i know that i can find easily first

like the angle where it shows 143

lemme draw it that might help

143 plus the red angle

adds up to 180

because it is a flat line

you see that?

and angle a and e would be same

because of some rule i forget the name of

[restive river]

yh so 37 degees

u mind showing working for it too

[silk sparrow]

@restive river so basically, if we have two parallel lines and one line intersecting them, the angles in the same relative place are the same

[restive river]

our math teacher goes ballistic if u don't

[kindred mantle]

well the work for that would just be 180-143 which u said was 37

[silk sparrow]

you know basic algebra, yeah?

143 + 37 = 180

[kindred mantle]

which is right

[restive river]

yh

[kindred mantle]

ok and angle a and e are same

padfoot do you know that rule

[silk sparrow]

make 37 the subject of the equation

[kindred mantle]

i shouldnt be teaching this idk the names of the rules its been so long

[silk sparrow]

i don't know the name either

[kindred mantle]

i just know it

[restive river]

corrosponding

[silk sparrow]

it's not even been long

one year

and i've already forgotten

[silk sparrow]

yes

[kindred mantle]

yes that sounds familiar

ok well

so we know 2 angles of a triangle so

you know what to do to find the last one yeah?

[restive river]

ehhhh

[silk sparrow]

try

if you get it wrong its not a big deal

[kindred mantle]

yea

[silk sparrow]

but the only way to get better is practice

[kindred mantle]

ok remember

what does a triangle add up to

always

[restive river]

180

[kindred mantle]

ok

so if we know 2 angles of a triangle

[restive river]

-180 by it

[kindred mantle]

and we know what it should add to

[kindred mantle]

what

remember what i showed u with the circle

circles add up to 360

we had 2 angles

what did we do there

[restive river]

the 2 angles it should be 180-(37+76)

[kindred mantle]

yes

[silk sparrow]

wait how much algebra would a year 8 know
because if @restive river is comfortable with algebra we can just say
x + 37 + 76 = 180

[kindred mantle]

good job

[restive river]

i got the same answer

its 67

and thats what i found

[kindred mantle]

im not doing the calculations with u so im trusting u can do basic math atleast lol

but 67 sounds right

[restive river]

i can

[kindred mantle]

ok

so there is a rule

[restive river]

ik

[kindred mantle]

that i also forget the name of

[restive river]

vetically opposite angles

x=67

[kindred mantle]

yes

nice

[restive river]

i got that

i solved for b and d

cause straight line angle=180

[kindred mantle]

yes

[restive river]

37

[kindred mantle]

if u ever go to engineering school like i am this stuff becomes very important to know even if u dont remember names

in vector physics

this is required

[restive river]

180-(76+37)

[kindred mantle]

so make sure you know

[restive river]

67

[kindred mantle]

yup

[restive river]

d =67

corrosponding x=67

lmao i should've never doubted myself

[kindred mantle]

yeah no u got it

[restive river]

now this one

[silk sparrow]

yeah, never doubt yourself
try it and if you get it wrong
its eight grade maths, no harm
but if you get it right that feeling will be so good

[restive river]

aight thks

[restive river]

this one makes me wanna shit myself tbf

[silk sparrow]

tbf it doesn't click immediately for me either

lets make a equation first

[restive river]

make 2 shapes first right

[silk sparrow]

91.8 = 14x + (14-8) * (13-x) * 1/2

[silk sparrow]

yeah

[kindred mantle]

oh boy lol

[kindred mantle]

yes

[silk sparrow]

now write out what the area for both shapes are in terms of x

and add them together to equal 91.8

91.8 = (14x) + ((14-8) * (13-x) * 1/2 )

first bracket is the rectangle

second bracket is the triangle

and then solve the equation

[restive river]

k

[kindred mantle]

for future reference with these types of problems writing an algebraic equation (using the knowledge of area formulas for shapes like triangles) like padfoot did is the correct approach

[silk sparrow]

14

but yes

wait no

no

because the bottom triangle's base isn't 13

[restive river]

it isn't

we don't know

[silk sparrow]

but we don't need to know, because this is an algebratic equation

if we somehow did know what x was, how would you find the base?

[restive river]

trigonometry

[silk sparrow]

no

[restive river]

algebra

[silk sparrow]

sorta

hang on

that bit is x

the entire yellow bit(if you can see) is 13

therefore the bit that is only yellow is?

[restive river]

13-x

[silk sparrow]

yes

[restive river]

k

[silk sparrow]

so rewrite the equation

[restive river]

k

into what

[restive river]

cause im confused

@silk sparrow u there

[silk sparrow]

just write a new equation

bearing in mind that the triangle's base is 13 - x

[restive river]

so what would it be

theortetically

cause im confused still

[silk sparrow]

91.8 = 14x + (14-8) * (13-x) * 1/2

14x is the rectangle

the rest is the triangle

[restive river]

ok i did that

'

got this

@silk sparrow is this correct

[silk sparrow]

idk

too tired for that

but then what's the next step

assuming thtas correct

[kindred mantle]

assuming u did it right

this is just basic algebra after that

but i was takin a fat shit

[restive river]

k

[kindred mantle]

so i havnet read

the convo lol

so idk what steps u did alr

[restive river]

91.8 = 14x + (14-8) * (13-x) * 1/2= 11x+39

[kindred mantle]

do you know how to solve this

[restive river]

used mathway

im correct

[kindred mantle]

ok but do u know how to do this on ur own

u wont hav emathway on exam

[restive river]

i did it

i solved for it

[restive river]

re arrange to make x the subject

[kindred mantle]

u get x by itself yes

[restive river]

yes

[kindred mantle]

do you know the compounding interest formula

[restive river]

now formula for compound intrest

[restive river]

no

[kindred mantle]

principal is what u start with

so in this case it would be 40k yuan

[restive river]

so put A=40K WUAN(1+3.5/3)^3

[kindred mantle]

no ok

so u want to be careful

with r/n

[restive river]

K

[kindred mantle]

so wiht r

it is asking for interest rate as a decimal

not as a percent

3.5% is a percent

what is 3.5% as a decimal

[restive river]

so 10.5/3

[kindred mantle]

no no

ok so

[restive river]

0.035

[kindred mantle]

yes

that is 3.5 percent as a decimal

and for n

[restive river]

3

[kindred mantle]

it is not asking for amoutn of years

it is asking for how many times it compounds a year

u need to read this formula carefully

[restive river]

3.5x3

[kindred mantle]

t and n are different variables fora reason

[kindred mantle]

it increases

by 3.5%

how many times a year

?

[restive river]

3

[kindred mantle]

no the problem says

3.5% each year

that means for one year

it compounds 3.5% once

[restive river]

k

[kindred mantle]

it is asking how many times does the 3.5 compound

in a year

which is one

because sometimes u can have it compound 2 times a year

so it would be

0.035/1

and t is obviously 3

[restive river]

this

[kindred mantle]

yur

[restive river]

yes

[kindred mantle]

so what u get

assuming u do the math correctly

it should be correct

because formula is set up correctly now

[restive river]

44348.715 wuan

which is close too 443489 wuan

Wang invested P yuan. The value of his investment decreased by 6.5% each year. At the end of the first year, the value of Wang's investment was 30 481 yuan. (b) Work out the value of P.

what about this one

[restive river]

bro

[kindred mantle]

same shit

just instead of posititve

its a negative number

so -0.065/1

[restive river]

k

so

[kindred mantle]

oh wait

[kindred mantle]

ok this is still same

just different

set up formula same way

[kindred mantle]

and use this

but instead u solve for p

and not A

u know how to do that ?

[restive river]

k

ehhh

[kindred mantle]

bro

[restive river]

im asking is that formula

[kindred mantle]

^

so there

[restive river]

so now what

[kindred mantle]

r is interest rate as a decimal

n is amoutn of times it compounds a year

in this case its once a year

[restive river]

ok

[kindred mantle]

t is how many years

p is what u start with

[kindred mantle]

t is not 1

look carefully at the formula i gave

the exponent

is n*t

n may be one

but t is not 1

[restive river]

t is time

[kindred mantle]

oh ok this problem only does 1 year

ok then yes

then solve for p

[restive river]

so dis da equation

[kindred mantle]

yes

[restive river]

so i divide by 1-0.065

[kindred mantle]

ye

[kindred mantle]

yea

[kindred mantle]

ye

[restive river]

done

thks bro

[kindred mantle]

np

[restive river]

aight submitted

half an hour early

[kindred mantle]

nice

thats good cuz i had to go after this anyway

need to study for diff eq

[restive river]

k

[devout snow]

@restive river Has your question been resolved?

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[fringe reef]

https://gyazo.com/182f1bd13b8c96b496668b993fd153d8 just need help drawing the diagram for the question, can probably figure it out on my own once i get the diagram. Generally been really bad with these, so any tips on how to draw them would be excellent

[devout snow]

@fringe reef Has your question been resolved?

[restive river]

Hello

[restive river]

Do you know what vectors are?

[fringe reef]

yes

im just bad at piecing the diagrams together

[rugged jay]

@fringe reef are you familiar with either the unit circle, or do you have access to a calculator

[fringe reef]

i got a calculator

[rugged jay]

Okay

Do you know about trigonometry?

[fringe reef]

yes im in second level calculus, im just generally bad with making physics diagrams

i can 100% do the question, ive just been historically bad with making the triangles from a question

[rugged jay]

Oh

Sry i cant help with drawing triangles

[fringe reef]

okay lol

thank u tho

[restive river]

You can't help with drawing triangles?

[restive river]

on his first trip

what is the magnitude of the first vector

[rugged jay]

I mean i can draw them

[fringe reef]

vector A, 0.6km due north

[restive river]

which direction is north

[fringe reef]

up? is that a trick question?

[restive river]

Should it be?

[fringe reef]

sorry

i dont think so

[restive river]

What is the magnitude of the first second vector?

wait

back up a step

[fringe reef]

okay

[restive river]

Draw the first vector

[fringe reef]

drawn

[restive river]

so something like this

[fringe reef]

yup

[restive river]

so the person would be

at the end of the vector

then he would

move again

[fringe reef]

going 60* NW?

or w of n

[restive river]

so the second vector should start at the end of the first right?

[fringe reef]

yes i believe so

[restive river]

NW and w of n are the same thing

[fringe reef]

gotcha

[restive river]

Think about how you would draw 60* of east

its the same thing with north

just kinda rotated 90*

[fringe reef]

okay

[fringe reef]

so the next vector would be tail to tip of the previous one, heading 60* nw

[restive river]

mhmmm

[fringe reef]

so hold on -

this?

[restive river]

yes

[fringe reef]

then vector C of that diagram would be the conjoining line between them

[restive river]

Yeah, the hypotenuse of a triangle

[fringe reef]

and the second diagram would kind of be the opposite, 50* n of w for 0.8km, then due north for the next 1.2km

im assuming its north

[restive river]

idk

is that what it says

[fringe reef]

it says "straight" but since we went north the first time im assuming its north

[restive river]

You're going to the same location

[fringe reef]

unless it just means the closest 90* angle

yeah

oh

[devout snow]

@fringe reef Has your question been resolved?

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[devout snow]

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[spring sundial]

What is the notation $(\mathbb{Z}^+)^2$

[woven radish]

Kalgar

[spring sundial]

square positive integers?

[uncut crow]

cartesian product

[spring sundial]

or is it supposed to represent dimensionality

[pseudo basin]

no it's the set of all pairs of positive integers

[uncut crow]

Z^+ cross Z^+

[spring sundial]

ok so dimensionality

[pseudo basin]

$(m, n) \in (\bZ^+)^2$ is slightly fancy wording for $m, n \in \bZ$

[woven radish]

Ann

[pseudo basin]

$10 word

[spring sundial]

wot

What is $10 word

🤗

[pseudo basin]

it's when you use a word that's more complicated than necessary/appropriate for context.

[devout snow]

@spring sundial Has your question been resolved?

[devout snow]

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[devout snow]

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[eager lodge]

$(a+b)^2=a^2+2ab+b^2$

[woven radish]

WhereWolf(ping if needed)

[eager lodge]

$(a-b)^2=a^2-2ab+b^2$

[woven radish]

WhereWolf(ping if needed)

[modern tide]

x^2 - 4x + 4?

[devout snow]

@modern tide Has your question been resolved?

[modern tide]

@eager lodge

[eager lodge]

yes

[modern tide]

do I distribute 12 bfr

expanding

[devout snow]

@modern tide Has your question been resolved?

[modern tide]

mr. <@&286206848099549185>

[unborn dawn]

You expand first and then distribute. 12(y-1)^2 is the same as 12(y-1)(y-1) you can’t really expand the 12 into that.

[modern tide]

wait so what will that come out to

is 144y^2 - 144y + 144 correct

[unborn dawn]

Not exactly

Try FOILing the (y-1)^2 part first

What do you get?

[modern tide]

*y^2 + 1?

[unborn dawn]

Let’s look through each part of (y-1)(y-1)

So we have y^2 at the front, you’re right. Outer is y * -1 and inner is y*-1 so we’re gonna have a -2y in there. Last is -1*-1. So 1

[modern tide]

oops

[modern tide]

y^2 -2y + 1?

[devout snow]

@modern tide Has your question been resolved?

[devout snow]

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[keen wind]

what does this result mean ?

<@&286206848099549185>

[eager lodge]

when does log(x)=0

[keen wind]

When x is 1 ?

[eager lodge]

yep

also logarithm is an increasing function

[keen wind]

What does that mean ?

[eager lodge]

it means if a>b then log(a)>log(b)

[keen wind]

Ok 👌

[eager lodge]

thus if x>1 then log(x)>log(1)=0

[keen wind]

Yeh

Um .. I still don't understand

@eager lodge um sorry for pinging

[devout snow]

@keen wind Has your question been resolved?

[keen wind]

<@&286206848099549185>

<@&286206848099549185>

https://tenor.com/view/gameboyluke-please-help-me-reaching-out-gif-23555158

[keen wind]

<@&286206848099549185>

<@&286206848099549185> please help TwT

.close

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[crisp crater]

Hey

[crisp crater]

sorry for this dumb question

Could anyone explain what steps were made here to reach to the right part?

I just fail to see that

[boreal island]

(1 - x^3) = (1 - x^3)*1 right?

[crisp crater]

right

[boreal island]

now you can take a common (1 - x^3) and get (1-x^5)

so (1 - x^3) *1 - (1 - x^3) *x^5 = (1 - x^3) (1 - x^5)

[crisp crater]

oh ye i think i understand now

sorry and thanks ♥

[robust acorn]

.close

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[twilit estuary]

it didnt go into -1

[twilit estuary]

so u dont state it

?

[light fractal]

yes, if it not the output of any input, you don't state it in the range

[twilit estuary]

okok

tyty

.close

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[restive river]

Why is this wrong?

Or like what's going on here

[eager lodge]

,rotate

[red turret]

,rotate

[red turret]

nah nah

you cant integrate x with respect to y

[restive river]

Like I was doing exact differential equations, in it I encountered like partial derivatives of some F, and we can like integrate it, and there's like a some f(y) to be added in order to

[restive river]

Um like

[eager lodge]

Partial derivative assume that x and y are independent

Which is not the case here

[restive river]

Oh is that so

Whenever we take partial derivatives, they are independent?

[eager lodge]

We treat them as independent

There might be times where they are dependent but the partial derivative is still useful

[restive river]

Wait

I'll put something on paper

And send here

Just a min

We do something like thar

Often here the integral Mdx term, M is often a function of both x and y

[eager lodge]

What's wrong

[restive river]

Like here if we can integrate y wrt x

Then why not in y'x = 1 cade

Case

[eager lodge]

As i said x and y are independent here

[restive river]

Like why are y and x not dependent on each other in exact differential equations case

[restive river]

Yea why is that so in exact differential equations?

[eager lodge]

?

[restive river]

In exact differential equations

We solve by assuming that

There is a function of x,y

Such that F = arbitrary C

Is the implicit solution

In that case we write the DE down as Mdx + Ndy = 0

Where M and N are partial derivatives of F with respect to x and y respectively

And then we integrate M wrt x

And N wrt y

Once we establish that they are exact

That the DE is exact I mean*

So in that case we are freely integrating y wrt x

And all that

[eager lodge]

Hmm I'm not good enough at differential equations

[restive river]

Oh

.close

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[normal hamlet]

how does it go from 9-(x+7) to 2-x?

[zenith jacinth]

2-x = -1(x-2)

9-(x+7) = 9-x-7

[normal hamlet]

ah

thankx

.closr

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[twilit estuary]

how do i find domain and range

of it

x^2= 2y+1

[deep vortex]

Solve for y

[twilit estuary]

sub 0

and solve

[twilit estuary]

okok

.close

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[static pollen]

how does left derive to right

[woven radish]

Dyssrupt

[red turret]

negative exponent ^

[static pollen]

ah

ty

.close

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[cursive pagoda]

got this down to ln(|x|)=t^3 +C but dont know where to go from there

[woven radish]

Dyssrupt

[cursive pagoda]

so it becomes x = e^t^3 +c?

[red turret]

yes

to simplify it further, you can use exponent laws

[cursive pagoda]

interesting, i dont comprehend logarithims at all

[woven radish]

Dyssrupt

[red turret]

product rule ^

[red turret]

for this

[cursive pagoda]

im confused how product rule is done on e^t^3 +C

[woven radish]

Dyssrupt

[cursive pagoda]

but is e^C =1 or =C

[red turret]

huh?

[cursive pagoda]

idk can you explain how id go about product rule here im lost

[woven radish]

Dyssrupt

[red turret]

now e^c is also a constant value, so lets name it k

[woven radish]

Dyssrupt

[cursive pagoda]

ahh okay thats where i was confused so what i was saying before e^C=/1 but e^C=C, idk if thats improper writing but my professor has us keep using C as our constants even through its transitions

thank you!

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[fallen wadi]

can someone solve these two questions pls

[fallen wadi]

please solve them on paper or screen and send phto it would be a great help 🥹

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fallen wadi]

its not homework

its an assignment

[safe knoll]

not about homework , its about copying

[copper quail]

I think the point is so that you understand it

[fallen wadi]

i am not copying sir / maam

jzt need help

[safe knoll]

both are easy questions btw , in second question use the value of x which is 1/2

and in first question , cuz 1/x is in denominator , it would go up and multiply and then apply the limit and u get ur answer

[fallen wadi]

aight got the first one now using l hospital

like in 2nd wat after putting x=1/2

yea

[safe knoll]

just put x = 1/2 in the expression and simplify

the answer for second should be 0 , why have u written -1/pi?

[fallen wadi]

i havent written

[safe knoll]

the brackets , i thought it was the answer

[fallen wadi]

thats exactly i dont know how pls teach 🙏

[safe knoll]

what do u not know

(x^2 - 1/4) tan pi x
just use 1/2 instead of x in this expression

[fallen wadi]

thats not how limits work

[fallen wadi]

why would i ask if it was that easy 😭

[devout snow]

@fallen wadi Has your question been resolved?

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[obsidian shuttle]

i don't understand what i did wrong

[obsidian shuttle]

my book says that it's equal to x<2, but I don't undestrand what I should do with the numerator

[patent marsh]

so there's an easier way to go about this rather than trying to use quadratics

consider this

your first two steps are great

[obsidian shuttle]

ok

[patent marsh]

oh wait I misread that as 3^(x-2), my b. Your method is correct.

but the answer should be x > 2

since you have 3^x > 9, then you get xlog_3(3) > log_3(9) --> x > 2

3^x < -2 is not possible

[obsidian shuttle]

not x<2?

[patent marsh]

nope!

just as a test, let's graph it and see

wait crap

dude it's not my morning

I was doing it as > rather than <

[obsidian shuttle]

lol

[patent marsh]

yeah it should be x < 2

[obsidian shuttle]

i'm on this exercise more than an hour

i'm out of my mind too

[patent marsh]

Ok so to the point where you're at t^2 - 7t - 18 < 0 is correct

now you need to find the roots which are (t - 9)(t + 2) < 0

so then you get -2 < t < 9

[obsidian shuttle]

Shouldn't the > always be used in fractions?

[patent marsh]

only if the value is negative or your taking the recipricol of both sides

[obsidian shuttle]

oh, so that's the thing

[patent marsh]

bingo, sorry it took a second to get there, lol

I need a nap

[obsidian shuttle]

do it then : )

[patent marsh]

lmao I think I will