help-28

[slate thunder]

I see

[chilly mulch]

i can do the rest on my own

[slate thunder]

Umm u don't need to know the function to solve this

[chilly mulch]

the function shown isnt a 2nd degree or a straight line so idk what function it is

[slate thunder]

Like u said

[chilly mulch]

wait do they want me to count the squares?

i hate those

[slate thunder]

Ummm all it's asking is the area under the curve between 3 and 5

U can approximate it

Using trapezoids

U don't need the functions formula

[chilly mulch]

Idk what the hell a trapezoid is

Never heard of it

They probably dont want me to do that or i would have known what it is

[slate thunder]

Ok maybe u haven't learnt it uet

So try to approximate it using rectangle strips

That's the only hint I can give u

[chilly mulch]

Id say the area between 0 and 5 is around 20

And thats divided by 2

So 10

[slate thunder]

Umm

How did u even say that

And the final answer is asking between 3 and 5

Not between 0 and 5

Are you clear with what a integral is?

The fundamental

[chilly mulch]

Yes i am

But i need to know both the areas..

Between 0 and 5 and 0 and 3

[slate thunder]

But u will substract them

[chilly mulch]

And how will i subtract if i dont know what the other area is?

[slate thunder]

Dude

Won't u get the area between

3 and 5

Which u can approximate using strips

Of width 1

[chilly mulch]

Wait oh right

I got 8 squares

As the answer then

[slate thunder]

Between 3 and 5

?

[chilly mulch]

Yea

[slate thunder]

Uh

I think u made a mistake

Counting it

[chilly mulch]

There are 7 whole squares between 3 and 5

And 2 half squares

[slate thunder]

*including 5

Itself

Ig

[chilly mulch]

What?

[slate thunder]

Ur removing the squares in the fifth column

[chilly mulch]

Im not supposed to go past x=5

[slate thunder]

Yes but at x=5

[chilly mulch]

What

[slate thunder]

At the column where x=5

How many squares are there

U totally removed them

[chilly mulch]

I didnt remove anything

What are you even counting

[slate thunder]

The number of squares between 3 and 5 including 3 and 5

[chilly mulch]

Could you mark on the paper what squares you are counting?

[slate thunder]

Oh mb I didn't notice it

[chilly mulch]

….

[slate thunder]

Mb

But ya what u did also known as trapezoidal integral considering u included the 0.5 squares

[chilly mulch]

Okay

So is 8 correct as an answer?

[slate thunder]

Ig

An approximate

Value

[chilly mulch]

Okay

I have another question

When they ask to decide ALL primitive functions do i include the c?

[slate thunder]

As primitive is same as indefinite integral

I think so

[full forum]

@chilly mulch Has your question been resolved?

[chilly mulch]

okay i need more help decide a primitive function so that F(0)=1

F(x)=3x+1 would that work?

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@chilly mulch Has your question been resolved?

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@chilly mulch Has your question been resolved?

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[torn jolt]

I'm trying to figure out how to get a point to follow a circle continuously.

[velvet spoke]

what exactly do you mean by that?

[torn jolt]

So i was messing around in desmos and i made a circle right. x^2+y^2=1. I'm trying to understand how to make a point follow the circumference of the circle

[velvet spoke]

so you want to parametrize the circle?

[torn jolt]

yeah

[velvet spoke]

you can find x and y of any point on the circle using sin and cos

and given the radius

[torn jolt]

ah

ok ill try that

ty

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[torpid pecan]

6✓5 + 6✓3

[torpid pecan]

is it possible to further simplify it

[hollow geode]

No

[amber radish]

You could factor

but simplify no

[torpid pecan]

okay

thank you

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[olive sparrow]

hey

[olive sparrow]

Can u check my answers?

It's integral using reciprocal substitution

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[hoary needle]

What's 3x14

[torn jolt]

show your work

[hoary needle]

I need to know

[torn jolt]

the Rules are to show the work

at least what you attempted to do

[hoary needle]

O

I did 3x14 = 43

[torn jolt]

yeah but what about the work

[hoary needle]

What about the work

[torn jolt]

you just wrote a result

without the working out

how did you get it?

[hoary needle]

I did it In my head

[torn jolt]

how?

[hoary needle]

I thinked

[torn jolt]

hm.

Maybe someone else will help you better

[hoary needle]

Is it right?

[torn jolt]

I don't believe so

[hoary needle]

What's the right answer

[torn jolt]

we don't give answers her

it's a help channel

[hoary needle]

Can you help me find the answer

[torn jolt]

ofc

Do you know what digits in decimal numbers means?

so what is 25

25 = 2 * 10 + 5 * 1

[hoary needle]

It's 42

Because

x shared into 3 groups = 14

We have to fund out x

So we times 14 and 3 together

And that's 42

[torn jolt]

I am not sure I see your working out, but sure

that is the correct result

arrivederci

[hoary needle]

I did this

And then 14 × 3 is 42 which is x

And x is the answer

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@hoary needle Has your question been resolved?

[hoary needle]

No

I need this person to see my working out

[red verge]

Yes that’s right

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[red verge]

https://media.discordapp.net/attachments/903486480985489478/956821414932013056/unknown.png

[red verge]

Yeah

But there’s like a relationship between height and volume

And length and weight so it didn’t work out properly

[onyx glen]

that was a 7 hour delay...

anyway, volume is proportional to the 3rd power of height

[dire tiger]

Can anyone help me with (f*g)(x) and (f/g)(x)

[red verge]

How do I relate cost with this?

[onyx glen]

@dire tiger this channel is occupied. please read #❓how-to-get-help and post in an available channel

[onyx glen]

i was about to say before we got interrupted

so for #46 the ratio of prices, and hence the ratio of volumes, can be calculated as 35.99/3.98, which will then need to be cube-rooted to get the ratio of the heights.

[red verge]

Hmm okay

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[oak urchin]

shouldnt option 2 be correct too?

[oak urchin]

and here, why is option 2 wrong?

[wise wyvern]

Since that 2k + 2k is not something you can assume.

Those two k may or not be same.

If it's the same, then that would be correct.

But it's not always the case.

For example take an even number 2 which can be written as (2)(1) and another even number 4 which can be written as (2)(2) so their sum is 6 which can not be written that way.

[oak urchin]

oh thank you!

so for some cases, the substitution won't work basically?

[wise wyvern]

Right.

Because, if you write 2k+2k it means the numbers are the same.

[hoary summit]

They actually use this kind of notation a lot in gcse maths proofs

It always bugged me then

Using the same variable when the integers aren’t necessarily the same

[wise wyvern]

Exactly.

[oak urchin]

haha got me confused at first, now I understand

[oak urchin]

what about this one tho?

[hoary summit]

It assumes what you were trying to prove

It’s like saying that 1 + 1 = 2

Because 1 add 1 is 2

Hence 1 + 1 = 2

You need a slightly different angle

To attack to problem from

(For example taking a/b and c/d as arbitrary rational numbers)

[oak urchin]

hmmm kinda confused with that one.. is it basically getting ahead of itself?

[hoary summit]

Pretty much

You can’t prove something by assuming it’s true

In fact you asked why option 2 was not wrong

Sorry

Yeah it’s a perfectly fine step given option 1

But option 1 is the problem

So the thing is false, but option 2 is fine

[oak urchin]

wait wot

even more confused now haha

imma get into that more later

how come the answer here is false?

<@&286206848099549185>

[wise wyvern]

$g(r^2) \neq (g(r))^2$

[glossy valve]

What the hell am I doing here?

[wise wyvern]

I suppose this should be the explanation.

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[oak urchin]

thank you @wise wyvern ❤️

[wise wyvern]

You're welcome!

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[wary nest]

What is the probability of an even number of heads when flipping n coins?

[wary nest]

for this one i would need to take the binomial coefficient and divide it by 2^n right?

2 being the 2 sides of the coin

n being the number of flips

n = n

r = 2H which represents even number of heads

[gritty rose]

what's your final formula?

you're on the right track

[wary nest]

how do i write binomial coefficent

[gritty rose]

i think the answer is a sum of binomial coefficients for each even number 2, 4, ..., 2n

[wary nest]

in latex

[gritty rose]

$\binom{n}{k}$

[glossy valve]

riemann

[gritty rose]

nCk is also common if you want

[wary nest]

oh ok

$\binom{n}{2H} / {2^n}$

[glossy valve]

trameski8

[wary nest]

or H can be x tbh

no matter what number we insert to H or x itll always be even

so yeahs thats the solutions

for a series of combinations binomial coefficient is the way to go

right?

@gritty rose

[gritty rose]

You need a summation of these

[wary nest]

why?

[gritty rose]

Your formula only captures a single even number

Is that what you're calculating?

[wary nest]

oh so from 1 to infinity right?

no we want all even numbers

0 heads wouldnt be an even number

since no flips are taken place

so no events

like u said

[gritty rose]

You only need to sum to n

[wary nest]

oh wait

not infinity

since we want to know when flipping N coins

what if n isnt that large

so 1 to n

right?

[gritty rose]

https://math.stackexchange.com/a/2524798

[wary nest]

$\sum_{i=1}^{n} \binom{n}{2i} / {2^n}$

[glossy valve]

trameski8

[wary nest]

this is my final solution

we want to keep track of all even numbers with n amount of flips

so the max is going to be n

the starting point will be 1 since thats where even starts

we cant have 0 H be even since no flips are taken place, and because of that there is no event

its pretty similar to the link you sent me

@gritty rose

[gritty rose]

your H isn't defined

the answer you get should be equivalent to the one in the link

Either change H to i or vice versa

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@wary nest Has your question been resolved?

[wary nest]

$\sum_{i=1}^{n} \binom{n}{2i} / {2^n}$

[glossy valve]

trameski8

[wary nest]

like this?

[dire linden]

Now you should be able to evaluate the sum.

[wary nest]

so if we have 1000 flips

and we are trying to get the even number of heads from that

n = 1000

i = 1

plug it in

[dire linden]

Yes, but remember to account this for all consecutive i's

All to 1000 at least

[wary nest]

yeah

what if i dont wanna write all those numbers out?

[gritty rose]

the upper limit should be n/2 if n is even or (n-1)/2 if n is odd

[wary nest]

why n/2?

[gritty rose]

do you know what the upper limit in a sum means?

[wary nest]

no

if we plug in 1

into n/2

wouldnt that be odd?

[gritty rose]

it means the last term in the sum is i = n

so your formula for the last term would read "n choose 2n divided by 2^n" which is just zero and nonsense combinatorially

[wary nest]

oh

[gritty rose]

.

[wary nest]

n/2 means even

$\sum_{i=1}^{n} \binom{n/2}{2i} / {2^n}$

[glossy valve]

trameski8

[dire linden]

now the result wouldn't be considered undefined

uhmmm no

now for all consecutive i's to n would be worse now that it would be n/2 choose 2n which is undefined as well

[wary nest]

oh snap

[dire linden]

thus making the equation "worse"

[wary nest]

the upper limit in the summaton

[dire linden]

yep

[wary nest]

$\sum_{i=1}^{1n/2} \binom{n}{2i} / {2^n}$

[glossy valve]

trameski8

[wary nest]

so for the 1000 example

all the numbers from 1 to 500 will be replaced with i

the n inside the binomial coeffienct will carry the n= 1000

am i right?

@gritty rose

[gritty rose]

What does 1n/2 mean?

[gritty rose]

It's just this I don't know why you're trying to come up with something brand new

[wary nest]

isnt 1n/2 the same as n/2?

$\sum_{i=1}^{n/2} \binom{n}{2i} / {2^n}$

[glossy valve]

trameski8

[wary nest]

@gritty rose is this better?

[gritty rose]

That only works for even n

You need one that works for odd n

Indices in summation notation are always integers or positive or negative infinity

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[slender lynx]

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[subtle tangle]

can anyone help me with this question?

[subtle tangle]

why is there a negative

how would i draw this out?

[nova basin]

A + (B U C) is blue + green. However it counts the part in the middle twice (the red part), so we subtract it once

[subtle tangle]

oooh

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[wary nest]

which is what i want

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[potent ice]

I don’t know how to approach these type of questions

can I just treat it as simultaneous equations

<@&286206848099549185>

[queen pond]

using matrices?

[potent ice]

What is that?

I’ve never heard of that lol

[carmine minnow]

probably can't use matrices, it's nonlinear

but these are diophantine equations

so you need to use quite a bit of number theory stuff

[potent ice]

oh

[carmine minnow]

cubes work pretty well with mod 9

[potent ice]

<@&286206848099549185>

.close

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[surreal spade]

.open

<@&286206848099549185>

[surreal spade]

how do i use this

[hollow geode]

.

Read

[surreal spade]

oh ok

[hollow zephyr]

Goodnight

[surreal spade]

i just need help finding area

[plush egret]

identify the shape

[hollow geode]

Ok, post your work / what have you tried?

[surreal spade]

i did 5*8

and it was wrong

b*h

for parallelogram

what

[hollow geode]

5*8 is correct.

[hollow zephyr]

When the teacher is sus

[plush egret]

did you type the unit

[hollow zephyr]

[surreal spade]

bro i literally told him

[surreal spade]

meters squared right

[plush egret]

yes

[surreal spade]

wtff

[hollow zephyr]

But did you type it?

[surreal spade]

yeah i did

[hollow zephyr]

Ss?

[plush egret]

sometimes teachers are wrong

u have to move on with your life

mb your teacher is learning how to find area too

[surreal spade]

LMFOA

[plush egret]

[surreal spade]

dont kill me bruh alright thanks this is so bs

[hollow zephyr]

Can you screenshot your answer

[surreal spade]

I PUT

40m^2

[hollow zephyr]

Ok

That should be right

[plush egret]

yea

[surreal spade]

alright

bye

thanks

.close

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[hollow moth]

im lost on this question

[hollow moth]

i didnt mean to select e

that was an accident

is there a typo in the question? cuz since both chain functions are equal to x, doesn't that mean that those functions are equivalent to each other?

if i were to guess tho i would think its d

[hearty ferry]

f(x) = g(x) = x satisfies the 1st 2 equations but not the f(3) = 8 and the f'(3) = 9

[hollow moth]

but im stuck between d and c

[hearty ferry]

i mean the basic idea is to use the chain rule

[hollow moth]

okay so give me a sec

okay i found the derivatives of both functions but now im stuck

wait

yeah i need help

[hearty ferry]

another thing is to plug in known values to try and get new values

[hollow moth]

would you be able to walk me through the problem pls

i got the derivatives:

g'(f(x)) (f'(x))

and f'(g(x)) (g'(x))

[hearty ferry]

g'(f(x)) f'(x) = ?

did you differentiate the other side aswell or not

[hollow moth]

my bad just corrected it

oh

so that equals 1

[hearty ferry]

i mean the question only gives one value of x that you can plug in to f(x) and f'(x)

so it makes sense to plug in that value

[hollow moth]

wait so its e, right?

[hearty ferry]

that only gives you g'

now you need to find g(8) by plugging in some value of x into one of the starting equations

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[fierce marsh]

(28)4+8(985

[fierce marsh]

<@&286206848099549185>

<@&286206848099549185>

[torn jolt]

whats your question

doesn't make much sense

@fierce marsh

[fierce marsh]

So on (28)4 do I multiple

[torn jolt]

tell me the whole question first

im guessing you are expanding, right?

[fierce marsh]

I think

I'm dumb

[torn jolt]

write it all out

[fierce marsh]

Ok hold on

[torn jolt]

so your question is (28)4 + 8(985)

@fierce marsh

ping me when you ready

[fierce marsh]

Yea that's my question I was looking for a 🖊️

[torn jolt]

so you'll be expanding

do you know what to do

[fierce marsh]

Kinda

Can you show me

[torn jolt]

yes

so basically everything inside the bracket

will be timed by the number outside the bracket

[fierce marsh]

Ok

[torn jolt]

that would mean

[fierce marsh]

Then I'll add those and get my answers right

[torn jolt]

yes

can you do that

[fierce marsh]

Yes

Are you a teacher

[torn jolt]

no

[fierce marsh]

Ok

[torn jolt]

year 10 student

[fierce marsh]

Oh

[torn jolt]

lol

so is it all good

[fierce marsh]

I'll close it

.close

[full forum]

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[fierce marsh]

No

[torn jolt]

i can still help you solve it

i know what im doing

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[stoic bough]

In the question: x/8 + 3 = 2 Why do you minus 3 on both sides first, and why not multiply. Following the pemdas

[hollow geode]

cause PEMDAS is for simplifying expressions

this is solving for x

[stoic bough]

So which rules do you follow when solving for x

[hollow geode]

There's no set rules perse

you do the opposite as you try to get x=

[stoic bough]

im not following what you mean, with opposite

[hollow geode]

if you have x+4=2 for example

if I subtract 4 from both sides, I get rid of the 4 on the left

[stoic bough]

yes

[hollow geode]

that's what I mean by opposite

similar for multiplication and division

[stoic bough]

so you mean i need to get rid of single numbers first. like 4, 2 etc. And not multiplication and division

?

[hollow geode]

yes

cause if you subtract 3 from both sides of your equation

you get x/8=-1

which is closer to having x=

[stoic bough]

i see, thank you. Definetly helps a lot.

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[upbeat cape]

the right answer should be2/3

idk where i wrong

.

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[eager pike]

hey can anyone help me with this

[native portal]

get rid of the /8 first then the -14

[upbeat cape]

.open

none aswered my question

nwm

[native portal]

wdym

[stable wadi]

idk how

[native portal]

is that a different question

[stable wadi]

no i tried moving thing around

[native portal]

oh

[stable wadi]

no idea how to solve

[native portal]

also

idk either

i have found a solution

but that was by turning it into an easier equation

[stable wadi]

ok how

[native portal]

do you know how to use fractional powers

i took the fractions away

[stable wadi]

ok

[native portal]

so x^3/2 would be sqrt(x)^3

[stable wadi]

yes

[native portal]

$x^{\frac{3}{2}}$

[glossy valve]

ShadoeStorm

[native portal]

would be $sqrt(x)$

omg

wtf is this

$sqrt(x)$

$\sqrt{x}}$

[glossy valve]

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

[stable wadi]

what can you do with that?? nothing

whats the solution man

[native portal]

i did sqrt(16x)

not 16sqrt(x)

ffs

[stable wadi]

all solving websites only give estimation

[native portal]

yeah

idk

its much harder than i thought

[zenith kernel]

Let x^2=y then y^3-16y+16=0 is a cubic function

There is formula for cubic functions

[stable wadi]

how to do that? i know square

[zenith kernel]

Ignore the words, just the last few lines. You see expression of z_1 and z_2 there? Start from there. The three roots of x^3+px+q is the y_1,y_2,y_3 at the bottom where ω=-(1/2)+(1/2)sqrt(-3)

[stable wadi]

hm? what is q

[zenith kernel]

x^3+px+q

What?

[stable wadi]

what is that

[zenith kernel]

I just told you

The cubic function is x^3+px+q

The three roots of this is the y_1,y_2,y_3 at the bottom. The expression of z_1 and z_2 are a few lines above it

[stable wadi]

yes so x^3+px+q = 0... yes?

[zenith kernel]

Yeah

[stable wadi]

never seen this function ever

[zenith kernel]

Any cubic function x^3+ax^2+bx+c you can let y=x-(a/3) to eliminate the term of x^2,to make the function be of that form

So generally all we need to do is to solve cubic functions of the form x^3+px+q
And your question happens to be of that form

[stable wadi]

what is p

[zenith kernel]

You don’t read my message completely?

I just told you three times

The cubic function is x^3+px+q

complex number okay?

Or any element in a field of characteristic 0

[stable wadi]

yes, i dont have all letter

[zenith kernel]

Like when x^3+7x-13 then p=7,q=-13 alright?

[stable wadi]

yes

so in my case i place both 16 for p and q

[zenith kernel]

Your case p=-16,q=16

[stable wadi]

this the formula i got from: x*(x^(1/2))*(x^(1/4))... = 16

so left side is:

[native portal]

have you learnt cubic functions

cause if you havent then i think this question is just nonsense

and idk why your teacher gave it to you

[stable wadi]

i was solving this and got that from this

maybe i made mistake

[stable wadi]

i got this

from

[zenith kernel]

Yeah

So if you want only the real root then y_1 below is it

Otherwise all three of them

[stable wadi]

how do i get omega? do i need to solve

i think i made mistake

i need to solve this

so i did this

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[stable wadi]

.close

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[burnt helm]

Hello

[burnt helm]

I need help with this math question here.

The Topic is Classifying Polynomials

[zenith kernel]

The degree depends on whether c=0

[burnt helm]

ok so?

[zenith kernel]

So 0 if c is not zero

When c=0 different author have different definition. Some people don’t define degree of 0, however most of people define the degree of 0 to be -infinity

[burnt helm]

so does -c represent

a polynomial

or not

[zenith kernel]

Yes

[burnt helm]

a binomial?

actually no

[zenith kernel]

It can be a polynomial of any number of variables

[zenith kernel]

Monomial

[burnt helm]

and degree of 0

also why monomial

[zenith kernel]

No

[burnt helm]

oh

monomial

[zenith kernel]

Like I said when c doesn’t equal 0, the degree is 0

[burnt helm]

is 1 term

what was is the degree

[zenith kernel]

0 or -infinity

Or

[burnt helm]

i cant really

[zenith kernel]

0 or undefined

[burnt helm]

say infinity

[zenith kernel]

Then your question is incomplete

[burnt helm]

the degree

was 1

not 0

[zenith kernel]

What?

c is a variable?

[burnt helm]

yea

[zenith kernel]

Not a constant?

Okay then

[zenith kernel]

It really should be complete

[burnt helm]

is this correct?

[zenith kernel]

Binomial

Others are correct

[burnt helm]

kk

bionmal

cuz i realized

there were 2 ms

lmfao

correct?

[zenith kernel]

Monomial

Others are correct

[burnt helm]

what would this be

a monomial as well?

[zenith kernel]

bi

[burnt helm]

last 1

i think

[hot herald]

count the number of terms and know your prefixes

[burnt helm]

finished thanks

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[young storm]

How can I find the missing arc angles?

[young storm]

Nvm got it

.close

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[soft beacon]

Hello !
Im a computer science student in first year and our proffesor gave us "challenges" to code and on is in my opinion impossible .

i need to find a way to multiply decimal number without multiplying or subtracting .

how ?
please help .
its been 5 hours

[hot herald]

i suppose you could do repeated addition

and string manipulation to shift the decimal point

[soft beacon]

good point

imma try that

but there's no math tricks that exist like log(x) roughtly equaling x ?

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[drifting willow]

How do you find W?

I know y is 32

and that 2 angles are congruent

but I dont know which ones

[tough vigil]

if its an isosceles triangle doesn't w and x need to be equal angle size?

[drifting willow]

yes

ohhh

i got it

thanks

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[ocean quarry]

yo

[ocean quarry]

im usign the values

-2, -1, 0, 1, 2. for y

and x

2 1 0 1 2

[gritty rose]

What even is the question

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@ocean quarry Has your question been resolved?

[tidal citrus]

same

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[dim plover]

Can anyone help me with the insertion sorting of these numbers

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[dim plover]

<@&286206848099549185>

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[mellow solstice]

I need help learning how to add, subtract, divide and multiply rational expressions

[mellow solstice]

questions like these Im completely lost and I need someone to teach me step by step

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@mellow solstice Has your question been resolved?

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@mellow solstice Has your question been resolved?

[sonic coral]

I can give you a hand with these

@mellow solstice you still there?

[mellow solstice]

yeah

it has to be answered like this tho this is how my teacher teaches it

[atomic blade]

Do you need to solve it in terms of x, like a function?

That's what I'm assuming

Try to simplify them into one fraction

@mellow solstice do you have an answer key

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[tulip comet]

I have used the comparison test to show that the series $\sum_{n=0}^{\infty}\frac{z^{n!}}{n!}$ has a convergence radius R≤1, now I have to prove that the series has a natural boundary past the unitary circle

[glossy valve]

IsaacGuillen

[tulip comet]

any advice?

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[torn jolt]

Name : Joshua N
Topic : Geometry , Perimeter Of Polygons
Grade : 9th Grade , Freshmen
Timezone : Eastern , EST New York

[livid ridge]

Sksksk

[torn jolt]

lol

[tough vigil]

have u tried anything?

[torn jolt]

I’ve tried re - reading it and trying to understand what it even is asking for and how to solve it but I can’t seem to understand anything and that’s why I asked here

[tough vigil]

so you need to find the perimeter. how can you find the 2 missing sides?

[torn jolt]

Idk

[tough vigil]

if one side is 15 ft.

and the opposing side is 5 ft plus x

what would x be?

in other words 15 = 5+x

that is how you can find the larger missing length

@torn jolt

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@torn jolt Has your question been resolved?

[torn jolt]

Back

So 15 = 5+x?

That’s the equation?

@tough vigil

[tough vigil]

yes

to find one of the missing sides

cause once you have all the sides, you just need to add them up and multiply by the amount per ft which is in the question

[torn jolt]

X = 10?

Idk

[tough vigil]

yes

so that is one of the two missing sides

[torn jolt]

15 = 5 + 10

What do I do now

[tough vigil]

using the same logic and method of setting up an eq, can u make an eq for the other missing side?

[torn jolt]

7+12=X

???

[tough vigil]

close

12 -7

since 7+ x should be 12

does that make sense?

[torn jolt]

Is it 110

the answer

[tough vigil]

did u find length of all the sides, add them together then multiply by 2.5? cause if so, assuming you did the math right, it should be good

[tough vigil]

sorry, its a little blurry

[torn jolt]

I need help with this now

[tough vigil]

okay

[torn jolt]

10+10+x=46?

X = 26?

[tough vigil]

how did u get this?

you cannot use Pythagoras theorem since it is not a right angle triangle. however u can turn it into one

[torn jolt]

Is the answer 6.78

[tough vigil]

how did u solve it?

[torn jolt]

Pythagorean theoro

Theorem

[tough vigil]

did u split the triangle in half first?

so you had two right angle triangles

[torn jolt]

Wait no

I just did

The square root of 46

[tough vigil]

once u split the one triangle

[torn jolt]

And round it to the nearest hundredth

[tough vigil]

you want to treat them individually using soh cah toa

[torn jolt]

Wait is my answer right

[tough vigil]

and using the angle given, but divided in half since u divided the triangle

[torn jolt]

Was my answer right

[tough vigil]

i did not get that

also 6. 78 doesn't make sense given one side is already 10

[torn jolt]

oh

What did you do

[tough vigil]

i first split the triangle

so there are two right angle triangles

i also split the angle

so 46/2

once you look at the triangle like that, do u think u can figure out how to use soh cah toa to find then half of the base?

[torn jolt]

I think so

So

A is unknown too

On both sides

So how do I find the soh - cah- toa

[tough vigil]

how would u find x?

[torn jolt]

Soh

[tough vigil]

yes

and what would x be?

[torn jolt]

23/10

[tough vigil]

23 is an angle

[torn jolt]

Oops

X/10

[tough vigil]

yes

[torn jolt]

So what do I do

[tough vigil]

so sin 23 = x/10

[torn jolt]

Oh

[tough vigil]

what is x?

[torn jolt]

3.91

Nearest hundredth

[tough vigil]

great

[torn jolt]

Is that the final answer

[tough vigil]

ik its messy, but looking at the picture, does what we just did make a little more sense in the context of the whole problem

now you have 1 x

or half of the base

x=3.91

but there are two xs in the eq

[torn jolt]

So I need to x2?

Multiply by 2?

[tough vigil]

and u need to find the whole perimeter as your final answer

yes

[torn jolt]

7.82?

[tough vigil]

yes

now add up the two other sides

and that is the perimeter

[torn jolt]

27.82

[tough vigil]

yes

nice

[torn jolt]

Is that all

[tough vigil]

yup

thats the answer

i hope that made some sense

by breaking up the triangle

[torn jolt]

Alright tysm

[tough vigil]

since you cannot use soh ca toa on a isosceles triangle

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[kind jay]

can't you swap places

put d/dx inside sum

[neat dirge]

yeah that makes sense

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[nocturne creek]

How do i do this without a calculator?

[torn jolt]

Try completing the square maybe?

[nocturne creek]

Like (r+1)^2>2+r?

[ember sage]

r² + r > 1

add 1/4 on both sides to complete the square

r² + r + (1/4) > 5/4

(r + ½)² > 5/4

√[(r + ½)²] > √(5/4)

r + ½ > ±(√5/2)

[ember sage]

you can probably see the answer from here

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[nocturne creek]

Yes i got it thank you

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[crimson perch]

I am just working this equation out, its a word question, and I've put in all the information, i am just having trouble moving forward with the quotient rule

[torn jolt]

What are you looking to do here

You can use the power rule for logarithms aswell

[crimson perch]

looking to solve for

S

[torn jolt]

Rule 6 would help

[crimson perch]

does 10 at the front cancel the other 10 out?

[torn jolt]

apply the rules I sent

[crimson perch]

is this how you place it into the power rule?

[nocturne creek]

On the 3rd step you can 10log10(10^8) and then you can apply the rule no.6

I recognise this formula from sound waves, nightmares :')

[crimson perch]

yes i am currently living in this nightmare ha

how does it become did you plus the 10^-4 with 10^-12?

to get (10^8)

[nocturne creek]

No i just in the step for S=10log10( inside just do the powers of 10 and you get 10^8)

10^(-4+12)

[nocturne creek]

You can also not do the powers of 10 inside and minus them using log rules like you did, i get the same ans for both

[crimson perch]

does it not equal 10log10(10^-16) because -4 -12 is -16?

if i subtract the powers of 10

[nocturne creek]

The 10^-12 in denominator, so sign changes

[crimson perch]

ohhhhhh thank you ha, i'll see how i go

i've just written out the rule 6 with some terms im familiar with

[nocturne creek]

You should recheck the 2nd step :x

[crimson perch]

sorry i'm super stuck i feel like im at a block

so im at 10log10(10^8)

next step from that is to write it in the form of rule 6

log10^8

wait is the answer 10^8

[nocturne creek]

According to me no, but I've only studied log at a surface level💀

[nocturne creek]

According to rule 6 what is ur b and k

[crimson perch]

b= 10 and k ^8

[nocturne creek]

what do you mean by k^8?

The b is correct

[crimson perch]

sorry k is 10^8

[nocturne creek]

How 🤔

Take the rule and write your equation side by side

Then see what k is

[crimson perch]

apologies im dying ha, k is just 8?

[nocturne creek]

Yes

Now do you know what to do

[crimson perch]

not really sorry, so now my formula looks like log10(10^8)=8

?

[nocturne creek]

Yes but in ur equation you see you already have a 10 in front

So basically its 10(log10(10^8))

[crimson perch]

can i use the change of base rule on this now?

10x log8/log10

sorry im feeling very lost with this whole question

[nocturne creek]

Im not sure? Why would we need to change bases?
Formula for change of base is like
Log(base a)c/log(base a)b = log (base b) c?

[nocturne creek]

You already know what log 10(10^8) is

All you have is a 10 multiplied outside

10*8= 80

[crimson perch]

okay, i'll write it out

[nocturne creek]

Did u understand?

[crimson perch]

yes it just clicked, log10(10^8) = 8 there for 10*log(10^8) is 80

i was getting confused with all the 10s i think

[nocturne creek]

Yes but this log(10) is 1 only is the base is 10, in some places i find log(x) where its implied base is e(maths) then its log(10) is not 1, other places mostly physics and chem bases are 10

[crimson perch]

okay, for our course we are only 10 and e as our base

[nocturne creek]

If its e, one way our teacher taught us was write the expression for base 10 just divide by 2.303?

But if you guys have log values given in exam i doubt itd be a problem

[crimson perch]

yes i think so

thank you for being patient with me

[nocturne creek]

Np i just have free time i like to waste :')

[crimson perch]

this if my final working

[nocturne creek]

Wait

3rd step writing is still incorrect

[crimson perch]

10log10(10^8)=80?

[nocturne creek]

Sry abt my handwriting 💀 this is my non dominant hand

[crimson perch]

thats okay, thank you! in the brackets, is it (8log10^10

[nocturne creek]

10 is in base, and 10 is in argument

[crimson perch]

yep thats what i meant! thank you again

how does the working out of within the brackets actually work?

[nocturne creek]

You mean 8 log10(10)?

[crimson perch]

yes

[nocturne creek]

Let 10^x=y
log(base10)y=x
Our expression 8log(base 10)10 says y=10 thus 10^x=10^1
x=1 therefore log(base 10)10= 1
8log(base10)10 is just 8 multiplied with log (base10)10 so 8

You can just memorize the rules, you wont need to show this in the exam working probably

[crimson perch]

awesome, thank you so much. I was just curious for my understanding

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