help-0

[trail cairn]

A builder buys 9 boxes containing 1000
screws to build a deck.
a. What is the order of magnitude of the
total number of screws?
Once the deck is completed, the number
of screws left is 90.
b. What is the order of magnitude of the
number of screws that are left?

[limpid turret]

what have you tried

[trail cairn]

yes but idk what im doing

[limpid turret]

mind showing your work?

[trail cairn]

im confusing myself

i dont have it on paper i was just typing it

[sullen vector]

Isn't it 9×1000 screws?

[trail cairn]

i did that

but idk if thats right

[limpid turret]

why not?

[sullen vector]

I don't get what is meant by order of magnitude

[limpid turret]

What has you doubting?

[sullen vector]

Is this supposed to be physics?

[trail cairn]

i feel dumb

[trail cairn]

no

math

[limpid turret]

Order of magnitude is how many digits are in the number. 5 has magnitude 1, 2910 has magnitude 4

Decimals get negative magnitude. 0.1 has magnitude -1, 0.00090000 has magnitude -4

[limpid turret]

^

[trail cairn]

idk

what im doing

i need help

[sullen vector]

I guess you would abd to put it in scientific notation

Have*

[limpid turret]

you are correct so far. So far, you have it all right

[trail cairn]

the only thing i did is 9x1000

[limpid turret]

If you show what you did, I can help you. Otherwise, I have no idea where you made a mistake

[trail cairn]

thats all i did

and i gave up

[limpid turret]

Up to now, this is correct. You have 9 boxes, each with 1000 screws, so that 9x1000 screws total

[trail cairn]

9000

[sullen vector]

9×10^3

I think that's the answer

[trail cairn]

i dont get a and b

A builder buys 9 boxes containing 1000
screws to build a deck.
**a **What is the order of magnitude of the
total number of screws?
Once the deck is completed, the number
of screws left is 90.
b What is the order of magnitude of the
number of screws that are left?

[sullen vector]

Wouldn't that be 9×10^1?

In scientific notation

9.0×10^1

[limpid turret]

@trail cairn, you found the total number of screws to be 9000

[trail cairn]

yh

[limpid turret]

And you knew how to get order of magnitude here.

[trail cairn]

i forgot

how i did that

[limpid turret]

I made an error here. magnitudes should be 0 and 3, not 1 and 4. Sorry, mb

I gave you definition of order of magnitude

Order of magnitude = # of digits - 1

[trail cairn]

isnt it 3

for 9000

is that it for a

are we doing b now

[limpid turret]

sure

you ask the questions, so we'll do whatever you need help with

[sullen vector]

And then I need help 😅😅

[trail cairn]

b What is the order of magnitude of the
number of screws that are left?

[sullen vector]

It's 9×10^1

=90

[pseudo ice]

For your question, you can post it in one of the Math Help available channels if you actually want help with something

[limpid turret]

You need this bit for part B

[trail cairn]

yeah

i do

so what do i do

[limpid turret]

Problem says 90 screws are left

[limpid turret]

^

[trail cairn]

can i put it in a notation

so like 9x..=90

[sullen vector]

Thank you!

[limpid turret]

yes you can

Find the order of magnitude, then do 9x10^(order of magnitude)

[trail cairn]

so like 9x10^1=90 ?

i think

so

[limpid turret]

Welcome to the server, @trail cairn and @sullen vector

[limpid turret]

perfect

[trail cairn]

your leaving

??

[limpid turret]

oops typo

[sullen vector]

Hey

[limpid turret]

fixed

[trail cairn]

i can ask for more help

[limpid turret]

Remember that 10^1 is just 10. And 9x10 is indeed 90

[trail cairn]

ill try and do some

[trail cairn]

ok

oh yeah their was this one page i could not wrap my brain across

can you help me

[limpid turret]

I can try

General do here: Do not ask to ask, just ask

I obviously cannot answer everything, but someone will hopefully come along

[trail cairn]

I felt like it was rude if I didn’t ask frist

[limpid turret]

Fair

[limpid turret]

which question?

[trail cairn]

the whole page

so like 1

[limpid turret]

Looks like you're learning exponents here

[trail cairn]

yes

[limpid turret]

When it says "how many times stronger" it's basically asking for the ratio

[trail cairn]

im still in grade 8 and this is like hard

[limpid turret]

As an example "10 is 5 times larger than 2"

To find the ratio (in my example), just divide: 10/2

So to find how many times stronger magnitude 7 is to magnitude 5, you do
(magnitude 7) / (magnitude 5)

[trail cairn]

1.4

[limpid turret]

Nah that's 7/5

"magnitude 7" is a number with 7 orders of magnitude

(i.e. 7+1 digits)

[trail cairn]

im not sure

what do i do

then

[limpid turret]

magnitude 7 will be estimated to just 10^7

and magnitude 5 estimated to 10^5

That's what you need to do

[trail cairn]

Yeah?

[limpid turret]

yea

[trail cairn]

What do I do

I’m lost

[limpid turret]

^

[trail cairn]

Do I

Divide

[limpid turret]

yup

[trail cairn]

7/5

=1.4

[limpid turret]

You divide "magnitude 7" by "magnitude 5", not "7" by "5"

[trail cairn]

How do I do that

[limpid turret]

^

[limpid turret]

^

That is, let "magnitude 7"=10^7

And "magnitude 5"=10^5

[trail cairn]

is it 100

[limpid turret]

good work

[trail cairn]

so question 1 is 100

do you want to do number 2

question 2'

[limpid turret]

sure

what are your thoughts?

Notice any similarities to the first problem?

[trail cairn]

i like the way you teach

[limpid turret]

Thanks. Been tutoring for a long time now

[trail cairn]

um

no

[limpid turret]

In one sentence, try to tell me what was problem 1 was asking

[trail cairn]

find how many times stronger the magnitude was

[limpid turret]

Yeah

[trail cairn]

between 7 and 5 earthquake

[limpid turret]

I'll make it a little more precise "How many times stronger is a magnitude 7 and than magnitude 5"

[limpid turret]

Ah yes. You beat me to it. Nice

[trail cairn]

haha thanks i cant beat you

so its a surprise i did

A magnitude 7.4 was recorded in the Solomon Islands in April 2014. Earlier that
month, a magnitude 7.7 earthquake was recorded near the coast of Northern Chile.
How much stronger than the Solomon Islands earthquake was the Chilean
earthquake? Give your answer to the nearest whole number.

[limpid turret]

Again here, try to tell me what it wants, in one sentence

[trail cairn]

How many times stronger is a magnitude 7.4 and than magnitude 7.7?

[limpid turret]

beautiful

Well done

[trail cairn]

thanks

[limpid turret]

err. actually got the numbers backwards

But don't feel bad. It got me too

[trail cairn]

its wrong

[limpid turret]

"How much stronger than the Solomon Islands earthquake was the Chilean earthquake?"
The wording here was a little confusing. It basically asking how many times stronger was chilean than solomon

[limpid turret]

So you need to switch your numbers here

[trail cairn]

oh i see

my bad

sorry

[limpid turret]

No worries. Like I said, I made the same mistake

[trail cairn]

thanks for correcting me

so how do we start question 2

[limpid turret]

Question 2 is asking "How many times stronger is magnitude 7.7 than magnitude 7.4?"
Question 1 asked "How many times stronger is magnitude 7 than magnitude 5?"
So ask yourself how you solved question 1

[trail cairn]

ok

um

is it 10 times bigger

[limpid turret]

Not quite.

[trail cairn]

0.3

[limpid turret]

Answer this for me: How did you solve question 1?

[trail cairn]

we were finding how much times stronger the maginute was

[limpid turret]

That's what question 1 was asking. I'm asking how you solved it

Explain the process to me that gave you 100 for Q1

[trail cairn]

um i divided it

[limpid turret]

divided what

[trail cairn]

10^7 and 10^5

to get 100

[limpid turret]

yeah

And how did you choose the numbers 10^7 and 10^5?

[trail cairn]

because magnitude 7 will be estimated to just 10^7
and magnitude 5 estimated to 10^5

for question 2 is is 10^7.4?

idk

[limpid turret]

mhm

Yeah you have it right

It's the exact same idea in Q2

[trail cairn]

so its not 10^7.4

[limpid turret]

Is what 10^7.4?

[trail cairn]

question 2

is it 10^7.4? divide bt 10^7.7

[limpid turret]

close

Very close

[trail cairn]

idk

[trail cairn]

yeah ik

but i dont know how to work it out

[limpid turret]

You almost had it here. Just look at how the numbers are ordered here, and compare it to how you ordered the numbers in Q1, where you did 10^7 / 10^5

[trail cairn]

so like 10^4 and 10^7

[limpid turret]

where'd you get 4 and 7 from?

[trail cairn]

the question

idk what im doing

[limpid turret]

No worries

Your magnitudes were 7.7 and 7.4

[trail cairn]

im just typing randomnumbers

[trail cairn]

yes

it is

[limpid turret]

If your magnitudes were 4 and 7, this would have been correct

[trail cairn]

thats what i meant but i wrote 10^4 and 10^7

[limpid turret]

what's what you meant?

[trail cairn]

i meant the magnitude was 4 and 7

but iwrote it as that

10^4 and 10^7

[limpid turret]

Ah. But magnitudes are 7.7 and 7.4, not 4 and 7

[trail cairn]

i just took 7 away and left 4

in 7.4

ok so what do we do now

[limpid turret]

You don't need to do this.

Just keep it as 7.7 and 7.4

So it's 10^7.7 and 10^7.4

[trail cairn]

yh i know

[trail cairn]

what is

[limpid turret]

You almost had it right here, just had the numbers switched

[trail cairn]

10^7.4and 10^7.7

is that correct

[limpid turret]

Depends how you divide them

[trail cairn]

i dont know what to di

do

[limpid turret]

What did you do with 10^5 and 10^7 in Q1?

[trail cairn]

divide

[limpid turret]

yup

So we do the same thing here

Q1 and Q2 are the exact same problem

Just using 7.7 instead of 7 and 7.4 instead of 5

[trail cairn]

0.50118723362

is that correct

[limpid turret]

close, you divided in the wrong order

[trail cairn]

really

1.99526231497

better now

to the nearest whole number is it 2

[limpid turret]

Looks great

well done

[trail cairn]

do you want to do 3

[limpid turret]

posting here again to bring it closer

sure let's do 3

[trail cairn]

is thats 10^6.7 divide by 10^6.2

[limpid turret]

yup

You're seeing the pattern

Good work

[trail cairn]

yh

[limpid turret]

Much faster that time

[trail cairn]

but im still not 100%

[limpid turret]

https://tenor.com/view/personal-record-frozone-my-best-record-my-record-my-own-record-gif-21812333

[trail cairn]

let me work it out

haha

[limpid turret]

Well you got Q3 correct, instantly. So I hope that helps.

[trail cairn]

is it 3

3.16

[limpid turret]

yup

[trail cairn]

becuase it said 2 decimal

[limpid turret]

Oh

good catch

yes that's 100% right

Student surpasses the master

[trail cairn]

haha

for the first time

can we do question 4

Use the logarithmic values for the animals’ weights in Example 37 to find how much
heavier than a shrew is a tree kangaroo, to the nearest thousand.

[limpid turret]

sure sure

share example 37

[trail cairn]

Example 37^

^^

um anything else

[limpid turret]

your log weights are the right column here

So use those

[trail cairn]

ok

[limpid turret]

Those are basically your magnitudes likes we've dealth with in questions 1-3

[trail cairn]

do we use the body weight or log weight

[limpid turret]

Q4 is asking you to use the logarithmic values

[trail cairn]

so log weight

10^0.40 divide 10^3.90

??

=0.00031622776

[limpid turret]

close

[trail cairn]

0.000

idk

[limpid turret]

You understand the concept, but got the numbers backwards

Gotta read the problem very carefully

[trail cairn]

10^3.90, 10^0.40

[limpid turret]

How much heaver than a shrew is a tree kangaroo?

[trail cairn]

??

[limpid turret]

They say it in a weird way to try to mix you up. Gotta be careful. This question is the same as "how many times heavier is a tree kangaroo than a shrew?"

[trail cairn]

3,162.278

is that the answer

[limpid turret]

looks good

[trail cairn]

lets do number 5

If the sound of a normal conversation is 60 decibels, and the sound of a train going
through a tunnel is 90 decibels, how much louder is the sound of the train than a
conversation?

[limpid turret]

Do you recall the definition of a decibel?

[trail cairn]

Here is example 39

isnt it like a ratio

of a unit

or istensity

[limpid turret]

No worries, we'll use example 39 to walk through the provlem

[trail cairn]

i thought we might need it

60-90

[limpid turret]

Let her figure it out

[raw jetty]

ok

[trail cairn]

i already saw it

but its ok

um

is it -30 or 10^3

[limpid turret]

you wanna do larger - smaller, not smaller - larger

[trail cairn]

30

soz

[limpid turret]

They write this

but do this

[trail cairn]

is it wrong

[limpid turret]

No

[trail cairn]

nvm

[limpid turret]

It's subtle because of the word from

60 from 110

You have 110, and you take away 60 from it

make sense?

[trail cairn]

yh

[limpid turret]

Okay so that was step 1

[trail cairn]

yes

[limpid turret]

step 2 next

[trail cairn]

so 30 divide 10

20

[limpid turret]

Looks like you subtracted

[trail cairn]

opps 3

so 10^3

[limpid turret]

perfect

yup

[trail cairn]

whats next

[trail cairn]

10^3=1000

lets do 6

The sound of a vacuum cleaner is 80 decibels and someone whispering is 20 decibels.
How much softer is the sound of someone whispering than the sound of a vacuum
cleaner?

[limpid turret]

ooh interesting

[trail cairn]

so 80-20

= 60

60divide 10

[limpid turret]

They're going with softer instead of stronger. But you should be able to use the same process

[trail cairn]

=6

so 10^6

1000000

thats it

[limpid turret]

good work

done

https://tenor.com/view/oddish-fainted-faint-gif-22681020

[trail cairn]

i have answered a question can you please check of its right

[limpid turret]

This is my confirmation (and a medal for a job well-done)

[limpid turret]

Oh you mean here?

[trail cairn]

thanks

can you check if its right

and if its wrong can you tell me so i can know how to fix it

[limpid turret]

a

b

c

d

e

f

[trail cairn]

damn

all wrong

[limpid turret]

I can't tell what you got for c and f

[trail cairn]

can we do it togather

[limpid turret]

You got a correct

[trail cairn]

can we do it together

lets do b

[limpid turret]

you were doing sale price - original price

[limpid turret]

Use this to find b

[trail cairn]

$60.00 - $52.00=8

[limpid turret]

You're doing a right now, but sure. Let's do a first just to be safe.

[trail cairn]

im so dumb

[limpid turret]

nw

[trail cairn]

lets do b

$250.00 -$185.00=65

[limpid turret]

(If you write a dollar sign, that triggers the TeXit bot)

[trail cairn]

oh

what is the next step

[limpid turret]

Divide this by sale price original price

[trail cairn]

Divide 65

By 250

[limpid turret]

I made a mistake

Divide by the original price

[trail cairn]

250

=0.26

What next?

[limpid turret]

Multiply by 100 to make it a percent

[trail cairn]

26%

ill do the other by myself please check if their right after im done

5000.00- $4700.00= 300

300 divide 5000= 0.06 x 100= 6%

is that right

no

really

[limpid turret]

300 divide 5000

,w 300/5000

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[trail cairn]

check now

please

[limpid turret]

looks good

[trail cairn]

$3.80 -$2.90=0.9

[limpid turret]

,w 3.8-2.9

[ocean seal]

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[kindred anchor]

🫡

[trail cairn]

2.90 divide by 3.80=0.23 x100= 23%

[limpid turret]

did it backwards

[trail cairn]

0.23

2.90 divide by 3.80=0.23 x100= 24%

this right

[limpid turret]

,w (3.8-2.9)/3.8*100

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[limpid turret]

Maybe round to 24%

[trail cairn]

$29.75 -$24.50=5.25

[limpid turret]

,w 29.75-24.5

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[trail cairn]

5.25divide by 29.75=0.17x100 = 18%

???

[limpid turret]

5.25 divided by 5.25?

[trail cairn]

haha

sorry

[limpid turret]

,w 5.25/29.75 * 100

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[limpid turret]

Looks good

[trail cairn]

thanks

[limpid turret]

Again, I'd round to 18% tho

[trail cairn]

ok

$12.95 -$10.00=2.95

2.95 divide by 12.95=0.22 x100=22%

[limpid turret]

,w (12.95-10)/12.95*100

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[limpid turret]

Did you consider what you should round it to?

[trail cairn]

23?

$79.99 -$65.00=14.99 , 14.99 divide by 79.99=0.1868x100=19%

[limpid turret]

,w (79.99-65)/79.99*100

[limpid turret]

Do you know when to round up vs down?

[trail cairn]

yes

but i got confused

wether i should

[limpid turret]

oops hold on, I wrote the wrong query

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[limpid turret]

Yes, you got it right

You rounded up correctly

[trail cairn]

19%

$29.99 -$19.99=10

10 divide 29.99=0.33 x100= 33%

[limpid turret]

,w (29.99-19.99)/29.99*100

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[limpid turret]

Seems like you understand it, @trail cairn

[trail cairn]

yh thanks to you

i got linear relation questions can we do them after i finsh my table

[limpid turret]

I'm off to bed actually

[trail cairn]

oh ok

[limpid turret]

ded

[trail cairn]

by have a good sleep

thanks for everything

[limpid turret]

np

[trail cairn]

nw ill be back tomorrow for more questions

hehe

[lone heart]

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[alpine sable]

anyone know why this is wrong?
intersects are at (0, 1) (𝜋/8, 0.92) (𝜋/4, 0.71) (3𝜋/8, 0.38) (𝜋/2, 0)(5𝜋/8, −0.38)

[ruby current]

rounding error? your answer is close

[peak bough]

I was thinking the same

[limpid turret]

Hard to say why it's wrong without seeing your work.

[peak bough]

Tried and got 1,0331859094 as the answer (not rounded off)

[alpine sable]

i thought i rounded correctly, the original answer was 1.032798585

[limpid turret]

I'm on nibble mobile so can't calculate, but if it looks rounding close, I'd suggest not to round until the very end.

[peak bough]

Did you round off at any point before calculating the final answer?

[limpid turret]

But if you got here, i doubt you did

[ruby current]

,w riemann sum cos(x) x = 0 to 3pi/4 6 intervals

[alpine sable]

no

[ocean seal]

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[alpine sable]

its all on my calculator

[ruby current]

more digits gives 1.033185909351051

[peak bough]

If you use these numbers to this accuracy, you get your result of 1.032798585. So it is a rounding error

[peak bough]

That's not the problem

[alpine sable]

wdym?

[peak bough]

The problem is that you round something like cos(π/8) off to 0.92 instead of keeping it as at least the same accuracy as you want in the end

[alpine sable]

thats the value i was given

"The x y coordinate plane is given. A curve and 5 rectangles are graphed. The curve starts the point (0, 1), goes down and right, crosses the x-axis at x = 𝜋/2, and ends at the approximate point (3𝜋/4, −0.71). The x-axis from x = 0 to x = 3𝜋/4 is divided up into 6 subregions, each of which becomes the base of a rectangle with width 𝜋/8. The rectangles that extend up from the x-axis intersect the curve at their top left corners at the following approximate points (0, 1) (𝜋/8, 0.92) (𝜋/4, 0.71) (3𝜋/8, 0.38). The rectangle that extends down from the x-axis intersects the curve at its bottom left corner at the point (5𝜋/8, −0.38)."

[peak bough]

Hmm. Okay I see now. If you are allowed a calculator, which I assume you are, maybe the points are just given as control points to make sure you have the right values when evaluating something like cos(π/8) yourself with a calculator?

Because if you are supposed to use the approximations given in the coordinates of the points, then your answer should be correct

[alpine sable]

so I would have to plug in every x value for cos(x)?

[peak bough]

Yeah

[alpine sable]

wow thats tedious

[peak bough]

(cos(0) + cos(π/8) + cos(π/4) + cos(3π/8) + cos(π/2) + cos(5π/8)) ∙ (π/8) should give you the right answer

1.0331859094 here is the result if you don't wanna do it yourself

You just have to round it off to the correct accuracy

[alpine sable]

its correct, tysm

.close

[lone heart]

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[olive citrus]

does anyone know where i can learn how to make most of the important logic gates using And, Or, and Not?

[lone heart]

@olive citrus Has your question been resolved?

[lone heart]

@olive citrus Has your question been resolved?

[modern sedge]

https://logic.ly/demo/ here you can build your own gates. I would recommend you to start with something like an adder, than a whole calculator and then maybe a small computer. Tutorials for adder, calc and even computers are on youtube.

[olive citrus]

.close

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[frank tree]

how do i start this i don't understand the problem

[echo socket]

Basically you need to rewrite the expression so that the trig functions have 2theta's as inputs instead of just theta

First I'd suggest expanding $(\sin{\theta} - \cos{\theta})\cos{\theta}$

[ocean seal]

A Lonely Bean

[frank tree]

ohh okok

[frank tree]

so cosθsinθ-cos^2θ

what about the one with the fractions

[frank tree]

what's next to this? do i use the identity for cos^2θ

[echo socket]

cosθsinθ is just sin(2θ)/2

And yes recall that cos(2θ) = 1 - 2cos^2(θ) meaning cos^2(θ) = (1 + cos(2θ))/2

[frank tree]

what how

[echo socket]

sin(2θ) = 2sinθcosθ
sinθcosθ = sin(2θ)/2

[frank tree]

ohhh

okok

so

sin (2θ)/2- (1+cos (2θ))/2

[echo socket]

Yeah

[frank tree]

what now

[echo socket]

That's it

[frank tree]

oh

yea there's 2θ

[echo socket]

(sin(2θ) - cos(2θ) - 1)/2 would look nicer btw

[frank tree]

what do i do with the fraction?

[echo socket]

You mean 2sqrt(2)v^2/g?

[frank tree]

yea

[echo socket]

Well there's no theta so just leave it

[frank tree]

ohhhhh

OH OK I GET IT

is it just to somehow make the problem complex?

but there's really nothing to do with it?

[echo socket]

Yeah it stays

Unless you can express v with theta

Which I doubt

[frank tree]

oki oki thank youu

.close

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[keen folio]

I need help

[keen folio]

#3 pls

I need help

[vale wigeon]

have you made progress thus far?

[keen folio]

No

I used to know how to do it I think

But I forgot

[echo socket]

I'd recommend rewriting cscx as 1/sinx and isolating the sine

[vale wigeon]

if the equation were written as 1/sin(x) + 2 = 0 would you know how to proceed?

[keen folio]

yes

Bring the 2 to the other side

Ok

I was able to rewrite it as

Sinx=-1/2

Wait

Now do I just look to the unit circle for answers?

7pi/6 & 11pi/6

Is that right??

[vale wigeon]

yeah, sure.

[keen folio]

Really??1!

[vale wigeon]

do you doubt any part of this process?

[keen folio]

Yes

[vale wigeon]

ok, which one?

[keen folio]

Wait nvm

I figured it out

Thx

What about question 4

Do I factor out cos?

[echo socket]

Yes

cos squared preferably

[keen folio]

Ok

And then I solve for the individual factors = to 0?

@echo socket

[echo socket]

Yes

[keen folio]

How do I solve cossquaredx = 0

Wait can’t I just break that down into 2 more factors

(Cosx)(cosx)

[echo socket]

cos^2(x) = 0 <-> cos(x) = 0

[keen folio]

Ohhh

Thx

So cos is = to 0 at pi/2 and 3pi/2

Thx I think I got it

[vale wigeon]

^ this symbol exists...

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[keen folio]

No

[lone heart]

@keen folio Has your question been resolved?

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[fierce zenith]

I don’t really know if I need help but is this correct

[long iris]

if you're talking about the last one, then yes

[fierce zenith]

So the last one Is correct

?

Ok good to know

[long heath]

all correct

nice bruh

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[pseudo fjord]

sqrt of x reflected across the x axis

[last ether]

What about that

[pseudo fjord]

is it

y=sqrt of -x

[last ether]

That's reflected across the y axis

[pseudo fjord]

really?

[last ether]

Yes

[pseudo fjord]

ohh

so its on the outside of the sqrt

right?

[last ether]

Yes

[pseudo fjord]

is this basically memorization

or is there smthin that applys

[last ether]

Uhh kinda if you're lazy

It's just more understanding what's going on

[pseudo fjord]

oh

[last ether]

Reflecting across the x axis changes y-values

[pseudo fjord]

ye

[last ether]

Reflecting across the y axis changes the inputs

But that's because of how the image itself is reflected

[pseudo fjord]

oh alr i see

also

[ionic jewel]

How can i do solve the question number 2

[last ether]

#❓how-to-get-help

Bro

[pseudo fjord]

bro

[last ether]

This is the second time you've done this

[pseudo fjord]

time him out

[last ether]

I'm not a mod lol

[pseudo fjord]

oh

anyways

what i was saying

when solving polynomial inequalities how do you graph your answers

[last ether]

Depends

Sometimes you shade it in

Sometimes you use a number line

[pseudo fjord]

like for -x²-8x-15 less than or equal to 0

[pseudo fjord]

ye number line

[last ether]

There are rules

https://www.mathwarehouse.com/number-lines/graph-inequality-on-number-line.php

[pseudo fjord]

like ik the answer is -3 and -5

[last ether]

The answer isn't -3 and -5 if you're dealing with an inequality

[pseudo fjord]

but how do u graph it on a numebr line

[last ether]

_ _

[pseudo fjord]

x=-5 and x=-3

[last ether]

No it's $-5 \leq x \leq -3$

[ocean seal]

$e^{\text{Umbraleviathan}}$

[last ether]

Just read this

[pseudo fjord]

dont go

ill ping u if i dont get smthing

[last ether]

Maybe

[ruby current]

your time is mine

[last ether]

Dman

Me sitting my bored ass in AP macroeconomics

[ruby current]

enjoy dude

took that course :p

[pseudo fjord]

ok im back

so u

its not hard to graph

but idk how u got -5 <x<-3

@last ether

[ocean seal]

Hehehehaw

[last ether]

Function analysis

I found the zeroes and used their multiplicity

[ruby current]

a polynomial passes through roots with odd multiplicity and bounces off roots with even multiplicity

use this along with the end behavior determined by the leading coefficient of the polynomial to see where it is positive

[pseudo fjord]

O

is it the same thing as

-3>x>5-5

does it matter how u write it

[ruby current]

the roots are key here because they are the points at which the polynomial may possible change sign

[last ether]

Since $-x^2 -8x - 15 = -(x+5)(x+3)$ and the leading coefficient, $-1 < 0$, I can safely use function analysis and understand that the parabola is greater than and equal to 0 when $-5 \leq x \leq -3$

[ocean seal]

$e^{\text{Umbraleviathan}}$

[last ether]

Perhaps you haven't learned about multiplicity of zeroes

[pseudo fjord]

nope

can u show me the graph of that inequality on the number line

i wana see if i got it right

[last ether]

And then label the number line "x"

[pseudo fjord]

yea that

is that it for polynomial inequalities

[last ether]

Any inequality

[pseudo fjord]

cuz on some graphs

i see that have positive and negative symbols

where did they get that from

[last ether]

That's a sign analysis

That's for intervals

[pseudo fjord]

so do i need that?

[last ether]

Maybe

Depends on your curriculum

[pseudo fjord]

wdym

[last ether]

Depends on what your teacher wants

[pseudo fjord]

o

[last ether]

I didn't need to use it since I understand function behavior

Maybe you need it

[pseudo fjord]

ye im guesing we do

where do u put the intervals

[last ether]

Depends on the context

[pseudo fjord]

the problem we just did

@last ether

[ocean seal]

Hehehehaw

[last ether]

You would do it based on the zeroes

[pseudo fjord]

can u show me

[pseudo fjord]

?

why is -5 = -3 positive

when its negative

so everything out of the shaded part is negative

@last ether

[ocean seal]

Hehehehaw

[pseudo fjord]

hello?

@last ether

[ocean seal]

Hehehehaw

[pseudo fjord]

@last ether

[ocean seal]

Hehehehaw

[pseudo fjord]

hello

<@&286206848099549185>

.close

[lone heart]

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[alpine sable]

Hi!

[alpine sable]

im trying to figure out how to use my scientific calculator for a quadratic equation and it is being difficult >:(

when I put my numbers in and ask for the answer, it doesn't give me what the answer is on my homework

[ruby current]

what are you trying to do?

[alpine sable]

a quadratic equation

using this

[gray isle]

are you using sufficient parentheses to get the calc to do the operations in the order you want?

[alpine sable]

these are the calculators i have

[alpine sable]

my teacher didnt specify that i needed to

[gray isle]

it's more of a calculator thing

calculators aren't psychic

most try to the best of their ability to follow the order of operations

[alpine sable]

i can use an online quadratic equation calculator, but my teacher says we need to learn it for calculator they give us at the exam

im just stressing about it even though itll be like 7 marks of my exam

[gray isle]

if you are not accurately representing what you have when inputting in the calc, it won't give you the result you desire

can you take a pic of exactly what you're entering

[alpine sable]

yes wait one moment please

[crimson totem]

in calculators its best to find out the discriminant first

[undone holly]

dont use a calculator for quadratic equations bro

[gray isle]

knowing the ordering of operations is key to entering stuff properly

[undone holly]

like i have no problem but still a tip

[crimson totem]

i can use an online quadratic equation calculator, but my teacher says we need to learn it for calculator they give us at the exam

[alpine sable]

so if I go into an exam, ill have a calculator so i cant go online

:(

[undone holly]

we dont get to use calculator 💀

[crimson totem]

+1

honestly it hinders your calculation skills

[alpine sable]

you get a calculator for an exam for quadratic equations? but then again, different situations for different classes

at this point calculators are too op

they can literally do anything

[crimson totem]

specially scientific ones

in india you have to solve this with pen paper

[alpine sable]

when i think abt it, its weird that they give a calculator for any of it since a lot of it is just pure maths

[alpine sable]

im 14 chill 😭

[crimson totem]

im 16

[alpine sable]

shh

[undone holly]

i am also 15

[pseudo ice]

Looks like a bracketing issue here

[undone holly]

10th icse boards @crimson totem

[crimson totem]

cbse

[pseudo ice]

If I remember these calculators, you need to put a ) at the very end of the square root to close it

[undone holly]

nice bro these people too lucky

[alpine sable]

i have to do tha because its a negative

[crimson totem]

exactly

[alpine sable]

oh?

ill see!

[gray isle]

hence why I said

knowing the ordering of operations is key to entering stuff properly

[crimson totem]

wait a min

does the calc return 2 roots?

[pseudo ice]

As in it should be $\sqrt( (-16)^2 \ldots )$

[ocean seal]

chartbit

[crimson totem]

or does take the root as positive

[alpine sable]

i have to enter it once with a - and once with a +

[crimson totem]

$\sqrt{ (-16)^2 \ldots }$

[ocean seal]

Shockshwat

[crimson totem]

better

[gray isle]

here in what you entered, the root is only being applied to the (-16)^2

[pseudo ice]

don’t correct that, as it’s not how it appears in the calc

I deliberately TeXed it that way to illustrate what the calc input looks like

[crimson totem]

yeah the one i sent is the one that should be done but the one u sent is the one being done

[gray isle]

and also make sure that when dividing
you have () around the whole expression you wish to divide

[pseudo ice]

Point being is that you can’t put that into the calc if you get me? See here

[alpine sable]

[crimson totem]

Yeah exactly

[crimson totem]

bruh just get the value of b^2 - 4ac

then root it

you will get the D

[alpine sable]

i dont get any of this 😭

im just stressing so much abt it

i might get a diff teacher for maths

[crimson totem]

what did you not get 😭

[alpine sable]

you guys arguing over brackets

its in brackets because it only does the B right if its negative, if it is in brackets

it will square it differently if its out of brackets

[ruby current]

as soon as you press sqrt, enter another bracket and make it look like this

[ruby current]

brackets are crucial here

[alpine sable]

sqrt?

[ruby current]

$\sqrt{,}$

[alpine sable]

oh

[ocean seal]

tushar

[gray isle]

sqrt is plain text abbreviation for square root

[alpine sable]

ok ill try

error

[pseudo ice]

Alright what’s the quadratic equation you’re working with?

[gray isle]

show what you're entering now

[alpine sable]

the same thing as before except

with another bracket before the 1st one

[gray isle]

image speaks 1000 words

[ruby current]

well you need to close the extra bracket

[alpine sable]

and then an extra bracket before the little symbol before the 2x3

[pseudo ice]

And also this question please? I haven’t seen what quadratic equation you’re working with

It’ll help so that we can figure out what’s happening

[alpine sable]

3x^2-16x+6=0

[pseudo ice]

Thank you!

Alright, and also what you’re entering into the calculator please? Try and show the whole input, taking multiple pictures if necessary

[alpine sable]

here but 2 brackets before the -16
and one before the thing that looks like a little r

[gray isle]

take a pic

[pseudo ice]

As above, please! There may be something that we can spot in a picture that we can’t in words 🫶

[pseudo ice]

Okay thank you so much for that! That helps a lot

First off, be careful with bracketing the numerator and denominator separately

[pseudo ice]

What’s this symbol here you put in?

[gray isle]

that's the fraction symbol

anyway you need () to clearly indicate the denominator

i.e you need () around the
2 * 3

otherwise the calc will first divide by 2 then multiply by 3

also it seems that you ignored

and also make sure that when dividing
you have () around the whole expression you wish to divide

[alpine sable]

so brackets around everything?

[gray isle]

to clearly indicate the order in which operations are to be performed

if needed

$$\blue{(}16 + \zqrt{, } \red{(} {\green{(} -16 \green{)}}^2 - 4 \times 3 \times 6 \red{)} \blue{)} \div \orange{(}2 \times 3 \orange{)}$$

[ocean seal]

ℝamonov

[alpine sable]

i think im going to check in with my teacher

[gray isle]

understanding order of operations is key as mentioned earlier

[alpine sable]

bidmas

[gray isle]

yeh, that

all of my colour coded parentheses serve a purpose in the image above

the green to clearly indicate what's being squared
the red to indicate what the square root applies to
the blue to indicate what is being divided
and the orange to indicate what you're dividing by

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[viscid junco]

i dont understand the mechanism of the first three steps

[viscid junco]

like how did they reversed the double angle formula

[echo socket]

That's, um, not the double angle formula

[mortal trellis]

well they noticed that cos(pi/3)=1/2 and sin(pi/3)=sqrt(3)/2 which fits very well here

and yeah that's the angle addition formula, double angle formula is a special case

[viscid junco]

what about the factor 2 in the beginning

where did it come from

[echo socket]

They noticed that factoring 2 out would make the coefficients (of cos and sin) 1/2 and sqrt3/2

Which both can be rewritten with cos and sin of the same angle

In this case, the angle happened to be pi/3

Here is an example: sinx + cosx

We have 1 as both of the coefficients, right?

[viscid junco]

yes

[echo socket]

Generally you'd want to change the coefficients so that the sum of their squares is equal to 1

That's when you'll be able to write them as sin and cos of some angle

In this case I would factor sqrt2 out

So that the coefficients become 1/sqrt2 and 1/sqrt2

Which are sin(pi/4) and cos(pi/4)

Notice that the sum of squares of 1/sqrt2 and 1/sqrt2 is equal to 1, as I said

That's why I chose them

I also made them equal because the original coefficients were equal

Meaning whatever I factor out, they will stay equal

[viscid junco]

oh ok

what if its something like 5 sin x + 7 cos x

is it impossible

nvm

.close

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[stoic barn]

Let p be an even integer. Can I find a constant C(p), such that given any normalized symmetric p-linear form M on R^d, there exists a normalized symmetric bilinear form Q on R^d that "dominates" M in the following sense:
|M(v) - M(w)| <= C(p)|Q(v) - Q(w)|
for any unit vectors v,w.

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@stoic barn Has your question been resolved?

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[steady basin]

hello

[steady basin]

ive tried to prove that Q is countable

could someone have a look at this plz

[modern topaz]

seems quite right

[fallen verge]

indeed it is

[pseudo ice]

Yep that's the way you generally are to do it!

[steady basin]

yay

[pseudo ice]

[note that there's some repetition in the lists you've made, but that doesn't matter too much tbh]

[steady basin]

imma prove uncountable sets now

using cantors diagonal argument

is that hard?

or trvial?

[pseudo ice]

As in e.g. prove the cardinality of R and N aren't the same? That one isn't too bad tbh

[fallen verge]

not trivial, but easy

[merry depot]

usually pretty straight forward, there's a couple of little details to watch out for, but mostly fine

[modern topaz]

friend me

now

[fallen verge]

easier

[steady basin]

ye

[merry depot]

why?

[steady basin]

so i need to prove that R is uncountable

[modern topaz]

why not

[modern topaz]

^

continuum

[steady basin]

cuz i could be assessed on this

next week

in my exam

[pseudo ice]

I don't think that "why?" was for you, it was for Boki I think haha

[steady basin]

oh

lol

[modern topaz]

[steady basin]

HAHAHAHAHAHAH

@hollow sparrow u hiding?

just cuz its real analysis doesnt mean u stop lurking brother

[fallen verge]

do not ping specific people please

[hollow sparrow]

[hollow sparrow]

Its fine for SA

[steady basin]

mehdi chartbit and I have a special relationship

[hollow sparrow]

Why charbit change the photo of Arthur ?

[fallen verge]

...ok

[steady basin]

ikr

big RIP

[pseudo ice]

Cause I felt like it

Can add why on earth I'm still D.W. to the list of world's unanswered questions

[steady basin]

this thing ive done here

do we call this a 'denumeration'?

[steady basin]

could u answer this for me plz?

[merry depot]

answer my own question?

[steady basin]

^

[steady basin]

^

[merry depot]

sure. that's a word for it

[steady basin]

heres my uncountable proof for the reals

[pseudo ice]

Looking good 😎

[steady basin]

the proof i did earlier to show that Q is countable

would that also be a suitable proof to infer that Q has the same cardinality as the naturals?

ie there wouldnt be a need to show the whole onto and one to one stuff

[pseudo ice]

I mean, the way you did it wasn't one to one [see what I said here], but as before it's easily overcome ("...but if the number already appears in the list, skip it and move on to the next one...")

It would clearly be surjective though at least

[steady basin]

but weve proved that Q is countable

which means that Q has the same cardinality as N no?

therefore

weve always proved that as well

and hence for that to occur, that must mean that Q and N have a bijection

[pseudo ice]

Hmmm, welllll I guess so depending on who you're dealing with, some may want your pairing you did to be bijective, but others may not care as much

Either way, no matter what, it's easy to create a bijection as per above so it's all good, by just pairing them together as per my suggestion! [skip over the repeats]

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[pliant estuary]

shouldnt this part = 1 and not 10/4?

[pliant estuary]

and the whole thing seems odd to me

-10/4*(1 0 0)^T shouldnt be (-3 2 0)^T, am I right?

.close

[lone heart]

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[mild snow]

Alright, so hypothetically this problem should be really easy

[mild snow]

Determine the velocity as a function of position

Is it not v = (5/6)s-1/3?

Ah, nevermind

The relationship isn't linear

.close

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