help-0

[alpine sable]

5t(4-t) = 0 implies 5t = 0 and 4 - t = 0,

What values of t do you get then? @small holly

[alpine sable]

What have you tried?

[small holly]

so if so then what i did 0(4-0)

which =0

equation becomes 0=0

[alpine sable]

No

From 5t = 0, you get that t = 0

And from 4 - t = 0, you get t = 4

[bitter sage]

Yes I did and I got the wrong answer

[small holly]

t=4?

[alpine sable]

From 4 - t = 0, yes

[small holly]

yeah

[alpine sable]

Then put in those values in the function

https://gyazo.com/2c617f349eacd858f0de797919a14911

[alpine sable]

Expand the squares and use pythagorean identity

[small holly]

i dont even get whatever is happening

[alpine sable]

Put in t=0 and t=4 in the original function

[smoky harness]

"The intelligibility of the existent world does not imply that and every part of it obeys the laws of logic ; but, unless at least two further conditions were fulfilled it would still be an unintelligible chaos to the scientific investigator.

The laws might be too numerous or too complex for us to unravel ; they might be such that it is practically impossible for us to isolate any one phenomenon from all the rest even to a first degree of approximation ; or again, our situation in nature might be so unfortunate that our sensations came to us in such an order that they failed to reveal the laws which really are present in nature.

The scientist who assumes that nature is and will always remain intelligible must therefore assume that nature obeys other laws in addition to those of logic
172
477
523
513
513
218
EXCURSION 2

Use the following table of connectives to format your answer.

~ negation: 1
\ / disjunction: 2
/ \ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9"

[alpine sable]

h = 20•0 - 5•0^2
and
h = 20•4 - 5•(4)^2
Makes sense? @small holly

[terse grotto]

is infinity a number

im trying to prove a point to someone

[smoky harness]

Anyone know about truth table table of connectives thing?

Use the following table of connectives to format your answer.

~ negation: 1
\ / disjunction: 2
/ \ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9"

[upper pebble]

no

[wary stream]

Is there a specific question with this?

[smoky harness]

"The intelligibility of the existent world does not imply that and every part of it obeys the laws of logic ; but, unless at least two further conditions were fulfilled it would still be an unintelligible chaos to the scientific investigator.

The laws might be too numerous or too complex for us to unravel ; they might be such that it is practically impossible for us to isolate any one phenomenon from all the rest even to a first degree of approximation ; or again, our situation in nature might be so unfortunate that our sensations came to us in such an order that they failed to reveal the laws which really are present in nature.

The scientist who assumes that nature is and will always remain intelligible must therefore assume that nature obeys other laws in addition to those of logic
172
477
523
513
513
218
EXCURSION 2

Use the following table of connectives to format your answer.

~ negation: 1
\ / disjunction: 2
/ \ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9"

Truth Table of Logical Negation. The negation of a statement is also a statement with a truth value that is exactly opposite that of the original statement. For instance, the negation of the statement is written symbolically as. ~ P or ¬ P \large{\neg P} ¬P. ~ P or ¬ P {\neg P} ¬P is read as “not P.”

[small holly]

and so those are the t values right?

[smoky harness]

definition, p → q is false if, and only if, its hypothesis, p, is true and its conclusion, q, is false. It follows that the negation of "If p then q" is logically equivalent to "p and not q."

that negation

[wary stream]

I already know that information. I don't understand what the question wants

[smoky harness]

It's a riddle

[alpine sable]

Those are t-intercepts

[smoky harness]

We been stuck on for like 10hrs

Want me to send the whole riddle

https://cdn.discordapp.com/attachments/866737142915137587/867055868884549662/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867055969959149578/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056115195969576/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056458130915358/unknown.png

Any ideas?

[novel coral]

You have to find 7?

[smoky harness]

?

[novel coral]

There's no connective assigned to 7

[smoky harness]

then I'd think so yeh

[novel coral]

I guess you'd have to solve this

Something to fill in the blanks that satisfies it

That's my guess

[smoky harness]

thanks

[novel coral]

Np

[smoky harness]

do u know how to do it

[novel coral]

Not sure I'm still learning this stuff

Idk if what I have even makes sense

[smoky harness]

I c

[novel coral]

Sorry it looked interesting so I wanted to give it a shot but that's the best I got, good luck

[rich basin]

for (C)

this is my equation for (c)

$\int_{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int_{\frac{3}{4}}^{2}\left(x^{2}-4x+4\right)dx$

[ocean seal]

BorutoEyePower

[smoky harness]

The numerical value of excursion in Pythagorean Numerology is: 2

[wary stream]

Use the law of cosines to find one of the missing angles then law of sines for the rest

[cursive sorrel]

How to use law of cosines?

I am confused there

[wary stream]

Do you know the equation?

[cursive sorrel]

Yes I do

[rich basin]

Would anyone be able to pelase help me with my question

[rich basin]

this

[wary stream]

Then plug in the known values and find the angle

[cursive sorrel]

There is two variables

[wary stream]

There shouldn't be, if you set it up correctly

[cursive sorrel]

I don't know any of the angles

[wary stream]

That's what you're finding

[cursive sorrel]

So when I do cos C/c and CosA/a there are two variables

c and a

[wary stream]

What is the law of cosines?

[cursive sorrel]

Nvm

Got ir

[dark lotus]

yes its b)

[kind helm]

you just made me realise that pythagorean theorem is basically the law of cosines

wtf

[topaz scaffold]

I used Pythagorean theorem to derive it

[gaunt magnet]

Can i get help

[topaz scaffold]

I can try

[gaunt magnet]

ok thanks

[topaz scaffold]

Just send the question next time, no need to ask

[gaunt magnet]

will you just plug 3/5 for cos(x)

and then just solve this

[topaz scaffold]

Does it tell you what x is?

[gaunt magnet]

nope

[topaz scaffold]

There's not enough information here

You can find x but it doesn't give you anything about theta

But if you want to find 3/5 you use the inverse cosine not the regular cosine

Also keep in mind that it's periodic

[gaunt magnet]

Ohh

[topaz scaffold]

Assuming it's in radians it'll be $\approx 0.927 \cdot 2\pi n$, $n\in \mathbb{Z}$

[ocean seal]

RipeOrange

[gaunt magnet]

I think they want me to use the compund angle formula or double angle formula

[topaz scaffold]

Even if you expand it tho, you get everything in terms of theta

And they don't provide enough information to solve for theta

Kinda like saying solve 4x

And also btw y = 6

And x is positive

[gaunt magnet]

I think my teacher wants me to use the compund angle formula or double angle formula to develop a formula for the question

and i get cos(3x)

[topaz scaffold]

So θ = x?

[topaz scaffold]

Just realized I missed an answer here, oof

[brave edge]

Can someone help wit this one

[topaz scaffold]

That looks like a test question my dude

[cobalt geyser]

Can Some one explain me what to do here ?

[gaunt magnet]

do u get answer

[cobalt geyser]

their slopes are equal

[gaunt magnet]

3/4 pi and 7/4 pi

[topaz scaffold]

Please don't post in an occupied channel

[gaunt magnet]

is this occupied

[cobalt geyser]

negative reciprocals of one another

[topaz scaffold]

Yep

[cobalt geyser]

yea now i do thank you

[wicked plover]

hello, I need some help

[topaz scaffold]

Plug it into the future value equation

I have no idea what the equation is but it's somewhere out there

[alpine sable]

p(1+r/something)^t

[wicked plover]

Ohhh

[nimble meteor]

pls help I have to graph these parametric equations.

[remote heron]

what do these equations look like in a table?

can you think of any periodic behavior that might happen with these equations? what might be good numbers to plug in

[nimble meteor]

I mean like ig trial and error could work but like I am learning how to eliminate parameters

so like

yeah

[remote heron]

hmm

so maybe we can solve one in terms of t

which one do you want to solve

[nimble meteor]

probably x

so I got (x/3)^1/3

[remote heron]

,w solve for t: x=3(sin(t))^3

[nimble meteor]

= sint

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by jan Niku#2119

[remote heron]

,w graph y=arcsin( (x^(1/3) )/( 3^(1/3) )

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by jan Niku#2119

[remote heron]

you didnt solve the full way

assuming youre allowed to use inverse trig functions

[nimble meteor]

so just to clarify I can't graph that manually right?

[remote heron]

if you are familiar with these you could graph this

[nimble meteor]

like how would I know the inverse sin of the cube roots tho?

ok that's besides the point sorry just curious

[remote heron]

oh, idk

approximately

[nimble meteor]

gotcha

[remote heron]

you can get the shape

[nimble meteor]

don't I have to plug that in

for y though

[remote heron]

into the y equation yea

but you want t alone, iirc

so need arcsine is all

what do you get?

[nimble meteor]

this person explained it like this

I have no idea how he even was able to apply pythag identity

bc even if you seperate sin^3

[remote heron]

interesting

[nimble meteor]

its sin^2 (sin)

and like that as a fractional exponent

[remote heron]

im pretty dumb with this stuff tbh

thats a cool solution though

[nimble meteor]

would be (x/3)^1/6 right

[remote heron]

well i bet its a standard solution but its cool to me

? what makes you think that

you can think of it like

the upper number becomes the exponent

the lower one becomes the root

then $x^\sfrac{2}{3} = \cbrt{x^2}$

damn i was hopin cbrt was a thing

$x^{\sfrac{2}{3}} = \sqrt[3]{x^2}$

[ocean seal]

jan Niku

[nimble meteor]

pls correct me if I"m wrong but isn't that how its evaluated?

[remote heron]

i cant really read it

[nimble meteor]

about as clear as I can get it

[remote heron]

I think its more like

\begin{align*}
x &= 3 \sin ^3 t \
\frac{x}{3} &= \sin ^3 t \
\left( \frac{x}{3} \right) ^{\frac{1}{3}} &= \sin t \
\left( \left( \frac{x}{3} \right) ^{\frac{1}{3}} \right) ^2 &= \left( \sin t \right) ^2 \
\left( \frac{x}{3} \right) ^{\sfrac{2}{3}} &= \sin ^2 t
\end{align*}

[ocean seal]

jan Niku

[remote heron]

is that what you wrote? sorry

[nimble meteor]

nah

I wrote ((x/3)^1/2)^1/3)

Ijust don't get how you went from the first to second step

ohhh wait

you just basically squared

ohhh

ok sry that makes sense

ok thx

[remote heron]

np

[hoary fiber]

anyone out here from India who can help me with 12th grade state board math?

[river hearth]

I need help

Ive tried to solve but I cant figure them out

[nimble meteor]

ask question

I have no idea but just ask in case people can help

[silk coral]

<@&286206848099549185>

[alpine sable]

<@&286206848099549185>

hi all this is probably a dumb question but

how can i figure out relative max with the critical point

u find max of relative point

[pearl marlin]

irational roots exists in pair

[alpine sable]

yes

so -1/56?

[pearl marlin]

b-c/ade = 1/de(b/a-c/a)

[alpine sable]

wym?

im very confused by this prob

i do not know :/

[pearl marlin]

you are working in multi variable hmm

[alpine sable]

yeah

multi var calc

[pearl marlin]

waht points you get?

[alpine sable]

wym?

[pearl marlin]

by taking partial derivatives

[alpine sable]

oh

i got 49 49 0

as critical pt

[pearl marlin]

do you try to visulize this in 3d graph?

[alpine sable]

in desmos?

[pearl marlin]

in geo like calculator

[alpine sable]

i tried yeah

[pearl marlin]

ok what D you get/

values of D?

[alpine sable]

i get a circle??

i must be doing this wrong

[pearl marlin]

in 3d it is not

https://www.geogebra.org/3d?lang=en

plot in this

[alpine sable]

ok yeah i see

its a plane

how can i get values from this graph

[pearl marlin]

lets try this algebracily

what is value of D?

[alpine sable]

wym by D?

[alpine sable]

what does fxx(ab) and f(yy) mean

[pearl marlin]

double derivative of f wrt x (partial

[alpine sable]

ah ok

double derviatve of x is -2

same for y

-2

so thats 4

fxy is just second derivative then right

so its option b

bc D is 8

[hoary fiber]

its not a specific doubt
in the class that i go to they haven't started teaching us math..... at all
n i have boards in a few months
so i need to learn literally everthing

[nimble meteor]

do you have a syllabus?

[pearl marlin]

check the value of z

[alpine sable]

its 0

[hoary fiber]

ya

[pearl marlin]

where are you putting this ?

[alpine sable]

into the answer

so i know the coordinate for z is zero

[nimble meteor]

send>

[hoary fiber]

basically i need to do all the chapters in the 12th textbook

[hoary fiber]

k
1min

[pearl marlin]

put x=49 y=49 in 98x+98y -x^2-y^2

[alpine sable]

yeah so i get

4996

[pearl marlin]

now try this

[pearl marlin]

still dont know this is correct

[alpine sable]

4802*

sorry

mind fart

[pearl marlin]

,w 98(49)+98(49)-(49)^2-(49)^2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by learn4math#9125

[hoary fiber]

this is book 1

[alpine sable]

so is that the z coordinate then?

@pearl marlin

is it (49,49,4802)

[pearl marlin]

try this

[nimble meteor]

I may be able to help with trigonometric functions

[alpine sable]

4802 as z coordinate?

[nimble meteor]

and pair of straight lines...I'm not sure what that menas linear functions?

and vectors I know some

[alpine sable]

omg it worked

tysm

[nimble meteor]

line and plan I'm not sure what means

@hoary fiber

[pearl marlin]

no see z= 98x+98y-x^2-y^2

[pearl marlin]

you are calculating z

[alpine sable]

yess

tysmm

i didnt realize that

i thought we were setting it equal to zero

oops

do u have good resources for lagrange multipliers

[pearl marlin]

for practice questions or theory part?

[hoary fiber]

k
thanks

[solid sorrel]

I'm doing some practise questions for stats and this one seems wrong:

The median is larger/smaller than the mean.
The largest/smallest value gets the smallest rank.```

I'm assuming that in ranks, the mean and median are always the same.

But as for which value gets teh "smallest" rank... Smallest rank means LOWER NUMBER (rank 1) or the "last rank", highest number?

[velvet condor]

:/

[alpine sable]

https://cdn.discordapp.com/attachments/757546773790064670/867270758110330891/unknown.png

[smoky harness]

72
477
523
513
513
218
EXCURSION 2

---

Use the following table of connectives to format your answer.

---

~ negation: 1
/ disjunction: 2
/\ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9

[glossy harbor]

(6/10×5/10)+(5/10×4/10)= 1/2

[smoky harness]

72
477
523
513
513
218
EXCURSION 2

---

Use the following table of connectives to format your answer.

---

~ negation: 1
/ disjunction: 2
/\ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9

truth table i tink

[alpine sable]

can you tell me how u got it

[glossy harbor]

1st bracket shows probability of (BB) i.e. Black then black when white is added.
2nd bracket shows probability of (WW) i.e. White then white when black is added

[alpine sable]

wouldnt the probability of (WW) be 4/10 x 3/10?

[craggy dirge]

how would i find the area of the part of a plane 2x + 3y + z = 1 that lies inside the cylinder x^2 + y^2 = 2x

[velvet citrus]

Evaluate the given expression.
P(k, 2)

[placid trellis]

I need help with math

[alpine sable]

@placid trellis

this is a mathematics server

[placid trellis]

i figured it out

[alpine sable]

ok

how do i prove that $\zeta{(s)}=\sum_{n=1}^{\infty}\frac{1}{n^s}$?

[ocean seal]

jswatj

[gaunt magnet]

hi this free

i got root15/7

[alpine sable]

tan(x+x)

[ocean seal]

The following error occured while calculating:
Error: Undefined function arcsin

[ionic jewel]

its literally just the definition of the function

reimann zeta function

[gaunt magnet]

,w sin(x)= -1/4

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Usman#0988

[rough zodiac]

5^-2

how do u do that?

[pearl marlin]

$\frac{1}{5^2}$

[ocean seal]

learn4math

[rough zodiac]

wut

[alpine sable]

Oh am I intruding, apologies.

[pearl marlin]

$\tan 2x = \frac{\sin 2x}{ \cos 2x}$\ \ =$\frac{2\sin x.\cos x}{\cos^{2}x-\sin^{2}x}$\ \ = $\frac{2(\frac{-1}{4}).\cos x}{\cos^{2} x -\frac{1}{16}}$

[ocean seal]

learn4math

[pearl marlin]

you need to find just $\cos x$

[ocean seal]

learn4math

[rough zodiac]

what is 2^-2

i mean

5^-2

is it 10?

1?

[ionic jewel]

its 1/5^2

[pearl marlin]

do you know how to adjust negative powers?

[rough zodiac]

what does that mean

;-;

[pearl marlin]

https://learn4math.blogspot.com/2021/04/some-important-formulas-quadratic.html

check 4th point

[gaunt magnet]

so now i need to solve it

and ill get

ill find cos x

[pearl marlin]

$ \cos x= \pm \sqrt{1- sin^{2}x}$\\

$ \cos x= \pm \sqrt{1- \frac{1}{16}}$\\

Simple $ \cos x= \pm \sqrt{ \frac{15}{16}}$\\

But in third quadrent cos is negative so

$\cos x= -\frac{\sqrt{15}}{4}$

[ocean seal]

learn4math

[alpine sable]

how do i write a third degree polynomial

that is ALSO a trinomial

isnt the format ax^3+bx^2+cx+d

how would u make that a trinomial

[gaunt magnet]

ty

[pearl marlin]

Only three terms like ax^3+bx^2+c ,

Provide a is not zero

[alpine sable]

o

ty

[hearty mortar]

hello guys how do i do this question?

Is it something like this?

[vale wigeon]

it says $AB^T$ not $(AB)^T$

[ocean seal]

Ann

[vale wigeon]

this means $(A)(B^T)$

[ocean seal]

Ann

[pearl marlin]

First find B transpose

[vale wigeon]

you're late

[hearty mortar]

oh i see thanks a lot

[rich basin]

I got the answer for (a) to be y = 1/20 * x + 26

$y=\frac{1}{20}x\ +26$

[ocean seal]

BorutoEyePower

[rich basin]

but apparantly it is not the right answer

And i am really confused why it isn't the right answer

[pearl marlin]

What are your corrdinates of A and B?

[rich basin]

so i made A to be (0,26)

and B to be (100,18)

[pearl marlin]

A IS not right

[rich basin]

i mean A (0,21)

[pearl marlin]

A=(-60,21)

[rich basin]

and then be (100,26)

it still won't change my answer

[pearl marlin]

Why x coordinate is zero in A, A is not on y axis

[rich basin]

Isn't it on the y axis?

[pearl marlin]

Can you check y axis is in centre

[rich basin]

based on it relative to the y axis it should be 21 high

Like it should be 21 vector

like the vector for this is 21

[pearl marlin]

And what about x axis?

[rich basin]

it should also be the same

you can't have negative length

[pearl marlin]

But can have negative corrdinates

[rich basin]

i looked at the answer

and the answer has a bit of explanation because it is an odd question

the answer for this is similar to mine but not exactly

it is y-26 = 1/20 (x-40)

which is x - 20y + 480 = 0

[pearl marlin]

Try to calculate with (-60,26) and (100,26) ,if it give you wrong answer then we will look into this

[rich basin]

@pearl marlin why do they have the same y coordinates

[pearl marlin]

B ia not right

[rich basin]

and also the answer can be wrong as well

i know b is wrong

i corrected it later

(100, 26)

for b

and a should be (0, 21)

the amswer had a similar answer in finding the gradient

[pearl marlin]

What is answer?

[rich basin]

here

[rich basin]

another form

wait but they made the A coordinates to be (-60, 21)

and b (40,26)

[pearl marlin]

You have to find the equation of line corrdinates are sufficient to use

[rich basin]

I think I manage the answer

but now this one is the one that i'm confused with in C

this is my equation for (c) $\int{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int{\frac{3}{4}}^{2}\left(x^{2}-4x+4\right)dx$

[ocean seal]

BorutoEyePower

[rich basin]

$\int{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int{\frac{3}{4}}^{2}\left(x^{2}-4x+4\right)dx$

[ocean seal]

BorutoEyePower

[pearl marlin]

C?

[rich basin]

part (c)

$\int_{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int_{\frac{3}{4}}^{2}\frac{3}{4}^{2}\left(x^{2}-4x+4\right)dx$

[warm wren]

@rich basin the problem is you moved A to the Y axis making the problem much harder than it is, just make yourself a favour and leave A where it is

you'll notice that the slope is 1/20 just like you have it

in order to find b you check how high up AB is at x = 0

to do that you know that (x-21)/(0- (-60)) = 1/20 so you have x-21 = 3 and x = 24 so you have y = 1/20 x + 24, which is the same answer they gave you, since y-26=1/20 (x - 40) simplifies to that

[rich basin]

@warm wren Yeah i understand, didn't think the y axis would mean much

[ocean seal]

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

[warm wren]

it doesn't really, even when moving it you can still find the correct answer, but you have to take it into account afterwards when trying to find b :p

[rich basin]

that is my equation for (c), but when i get the answer it is apprantly wrong

this is the graph of the prolbme

[pearl marlin]

Okk integrate parabole from 0 to 2

[rich basin]

but what about the line?

[pearl marlin]

Then subtract the area of line from 3/4 to 2

[rich basin]

isn't my answer that?

except for the 3/2^2

[pearl marlin]

What is in second integration

Seems not the equation of line

[rich basin]

$\int_{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int_{\frac{3}{4}}^{2}\left(4x^{2}-4x+4\right)dx$

[ocean seal]

BorutoEyePower

[pearl marlin]

From where this 4x^2-4x +4 come?

[rich basin]

mybad, the actual equation is

$\int_{0}^{\frac{3}{4}}\left(x^{2}+1\right)dx\ +\ \int_{\frac{3}{4}}^{2}\left(x^{2}-4x+4\right)dx$

[ocean seal]

BorutoEyePower

[rich basin]

which i got 1.54166666667

[pearl marlin]

I solve this with some other way

[rich basin]

I managed the get the right answer, that was the actual right answer. I spent the entire day having bad thoughts because of this question

okay thanks

I looked at the answer and my answer and we have different answers

so in this i made x^2-4 therefore x needs to be greater or equal to 0

but then that is when me and the answer split, the answer bounds it between -4 and 2

while i bounded it between -4 and root(6)

i mean 0 and root(6)

[ionic jewel]

i think the answer is wrong

[rich basin]

@ionic jewel the answer did actually integrate with boundaries 2 and -4 with integrand root(y+4)

[thorn tapir]

root 6 is more than 2

[ionic jewel]

ah they just did it in terms of y then

also right

did you not get the same answer?

ohhh

[thorn tapir]

so it will cut off at 2

[ionic jewel]

yours is lower

[rich basin]

no i did not get the right answer

[ionic jewel]

you need to take the absolutely value of the stuff in your integral

[rich basin]

yeah i did, but still not the right answer

[ionic jewel]

,w integral from 0 to sqrt(6) of abs(x^2-4)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

hmph

[rich basin]

,w 4 * root(6)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by BorutoEyePower#4998

[ionic jewel]

wait

[rich basin]

that is apparantly the answer

[ionic jewel]

,w integral from -4 to 2 of sqrt(y+4)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

yeah there we go

now time to figure out what's wrong with the other version

oh

2-

[rich basin]

but i am confused why is it different from my answer

[thorn tapir]

your graph should look like this

[ionic jewel]

,w integral from 0 to sqrt(6) of 2-(x^2-4)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

✅

[thorn tapir]

the x = sqrt(y+4) one I mean

[rich basin]

Wouldn't it bound at the y axis

[ionic jewel]

you need to do too function minus bottom function @rich basin , the top function how you did it is y=2

see my Wolfram soln

[thorn tapir]

yeah y= 0 and y = 2

[rich basin]

okay i get it now, thanks that really helped alot.

And also i don't get the intuition with using y

[ionic jewel]

it's the same thing but sideways

you will need to learn how to do it though

[rich basin]

Okay, so it is basically the same with but instead of x with the y

and if you flip it, you get the same thing with x

[ionic jewel]

it's from y = -4 to 2 between the y axis and the function

which is the same area

[thorn tapir]

wait, y= -4?

[ionic jewel]

yes

[rich basin]

and also with the question right, didn't it say it is bounded by the y axis?

[ionic jewel]

the y intercept is -4

[rich basin]

How come the answer is going pass the y boundary

[ionic jewel]

and the upper bound is 2

hence -4 to 2

[thorn tapir]

OH Y AXIS

I'm stupid

no ok

[rich basin]

yeah i get it now

[thorn tapir]

letme redo the graph

[ionic jewel]

yes but that's just how the integral works, like how the normal integrals are naturally bounded by the x axis

[rich basin]

it is a coincidence for it to be unable to parse negative valuse as well as it bound edto the y axis right?

[ionic jewel]

just know if you are doing the functions in the y direction it's right minus left not top minus bottom

[rich basin]

@ionic jewel what happens if we get a +-

[thorn tapir]

this would be correct

[ionic jewel]

two integrals, presumably

[rich basin]

like this question

[ionic jewel]

although i think usually people just use the primary root

[rich basin]

so you make y the subject in this

[thorn tapir]

draw the graphs it's always easier that way

[rich basin]

so my strategy for probably when i see +-, i would just evaluate it by turning it back into a square

[ionic jewel]

this one is perfectly easy without turning sideways but yea

the integrals are

[rich basin]

it would just be twice right, like an even function

no

the y at 4 is blocking it

[ionic jewel]

,w integral from -2 to 2 of 4-x^2 dx = integral from 0 to 4 of sqrt(y) dy

[rich basin]

i'm confused now

[ionic jewel]

shoot

[thorn tapir]

lol

[ionic jewel]

[rich basin]

i am right now visualising the +- root(y) the same as x on the x plane

[thorn tapir]

this is your area that needs to be evaluated

[rich basin]

Nah i'm not getting it the connection with the question by visualising it like

[rich basin]

I am trying to make x the subject

root(y) =. x

[thorn tapir]

do it then

you do know how to find the area ofrectangle right?

tell me the area of the rectangle i sent

[rich basin]

i don't know what rectangle

[thorn tapir]

look at this

[rich basin]

that would be integrate with boundaries of -2 and 2 with 4- x^2

but then making y would be challenging, and i don't know what would it be

[thorn tapir]

that's just the unshaded region inside the box i drew

ok lemme show you

[rich basin]

why would that be?

[thorn tapir]

i subtracted the two areas to get our intended region

if your variable of integration is x

[rich basin]

I get it, but how would it relate to the y

[thorn tapir]

the area is always bounded by x axis usually

what y

[rich basin]

I get how to do the y now

I mean making x the subject

and then integrating with the base of y

[thorn tapir]

oh then

[rich basin]

so this is might thought proecess of how i would interpretate solving y

so i basically visual it like an x

but then flipped

substituting the y like an x

[thorn tapir]

look at the right half - the two parts is equal due to symmetry wrt x axis

[rich basin]

the y= 4 becomes x = 4

root(y) becomes root(x)

and then making it between the boundaries of 0 and 4

[thorn tapir]

damn

[rich basin]

because you can't have negative values

times it by 2 as well

because you finding absolute value

[thorn tapir]

yeah that way works, whatever floats your boat

[rich basin]

But does this thinking process work in all scenarios

[thorn tapir]

but there could be problems, especially if you're given both type of curves in a single graph

if you're watchful you should be fine though

[rich basin]

This made my day, thanks

Just encountered that problem just then with this thinking style

[thorn tapir]

do you get why we have the f(x)dx for us to integrate? just asking

[rich basin]

yeah

if you are trying to F(x)

if F`(x) = f(x)

then dx is the small infidestimal thing you are trying to multiply

[thorn tapir]

you can use the same concept for y axis, It's literally the same

[rich basin]

visualising it like a rectangle

and the integrate s is basically a sum

[thorn tapir]

can you tell me why it's a rectangle

[rich basin]

as you approach from x1 to x0 in which x1 and x0 are points on the graph

it would form a rectangle on the graph

and that distance between x1 and x0 as it approaches to each other is dx

[thorn tapir]

it's only a rectangle because dx is small enough

[rich basin]

yes, the rectangle is because dx is small

[thorn tapir]

to be treated as a line segment

yeah

[rich basin]

It is basically like folding up a sheet

[thorn tapir]

that's what you need

[rich basin]

as you fold a sheet you get closer to forming a line like shape

[thorn tapir]

when you integrate wrt y

take a point on the graph

and move up so

the value of y changes by dy

Right?

now,

[rich basin]

yeah

[thorn tapir]

what should be the length of the rectangle?

[rich basin]

it should be dy

[thorn tapir]

the f(x) whre you started with

[thorn tapir]

that would be width

[rich basin]

yeah f(x)

[thorn tapir]

and then book

boom*

you have your rectangle

integrate it over your limit

you don't need to think about making x axis as y axis

flipping everything

while you do this

it's just the same thing as you do in x anyway

[rich basin]

What do you mean by making x axis as y axis

[thorn tapir]

this

read back

[rich basin]

you mean from y axis to x axis

I think i'm starting to get the way you are heading, this was something that i had in the back of my mind

[thorn tapir]

area of rectangle stays the same

so you don't have to think about visualising it like x

it confuses you when you have multiple graphs

[rich basin]

Okay, I think I get it now. Thanks alot

[thorn tapir]

man i thought i would fail to put it in a comprehensible way

i'm terrible at turning my thoughts into words sometimes

[rich basin]

It was fine since i had this kind of understanding before

[lyric wadi]

How to solve this using similarity?

[barren bramble]

How do I Prove: if x^4+4 is/is not a prime number.

[lyric wadi]

sorry sir i asked the question first

[thorn tapir]

I can give a hint

RP and BQ are used in 2 pairs of triangles

First pair - APR and ABQ

Second - PRQ and QBC

use this fact

The RP/BQ ratio is going to help you

[lyric wadi]

Well AR/AQ = PR/BQ so it wil equal to 4/6 = PR/BQ

So is PR = 4 BQ = 6?

[thorn tapir]

noo don't assume that

it could be 8 and 12 instead

you don't know for sure

[lyric wadi]

So

[thorn tapir]

you're just 2 steps away - look at the pair PRQ and QBC

[lyric wadi]

cross multiplication?

[thorn tapir]

uh no

[thorn tapir]

those two are similar triangles right? you yourself wrote it

now what can you infer?

[lyric wadi]

oh so the solution should be

RQ/QC = PR/BQ

is that right?

and then i solve for QC

[thorn tapir]

NICE

you got it

😎👍

[lyric wadi]

really? wait

so what is PR/BQ?

is it 4/6?

[jaunty crane]

whats the answer if a-1(a+6)

[alpine sable]

find it yourself, follow bodmass or smth

expand -1(a + 6)

but wait its not a equation lol

[thorn tapir]

yes

[lyric wadi]

tysm appreciate it! 👍

[thorn tapir]

so RQ/QC is also 4/6

you're welcome 😎

[obtuse cove]

would anyone know how to solve this for x

I'm essentially trying to find a slope of 0.7 from this function so i can connect it to another function with making a smooth transition between the slopes

<@&286206848099549185>

this is the original function, it's a decaying sin function

[thorn tapir]

damn, this is nasty

[obtuse cove]

yes...

I might be able to just use technology to cheat but algebra looks more fancy

[thorn tapir]

lol true but

I'm actually scared to even attempt this

[alpine sable]

same

[vale sapphire]

Perhaps some complex number tomfoolery could do it

oh god why is there an exponential inside of an arctangent this is all wrong

[shadow mango]

Can someone please tell me what this would mean in terms of relations?

[odd scroll]

hallo

[smoky harness]

Hi anyone good at longish riddles? I'll pay

[alpine sable]

if you got a question

[smoky harness]

no homework

[alpine sable]

you can just ask it

[pearl marlin]

Composition of relations

[smoky harness]

https://cdn.discordapp.com/attachments/866737142915137587/867055868884549662/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867055969959149578/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056115195969576/unknown.png https://cdn.discordapp.com/attachments/866737142915137587/867056458130915358/unknown.png

The answer is found in excursion 2
The page number riddle here forms the actual question

hints

[shadow mango]

oh alright...thanks!!

[alpine sable]

is this even math

[smoky harness]

"The intelligibility of the existent world does not imply that and every part of it obeys the laws of logic ; but, unless at least two further conditions were fulfilled it would still be an unintelligible chaos to the scientific investigator.

The laws might be too numerous or too complex for us to unravel ; they might be such that it is practically impossible for us to isolate any one phenomenon from all the rest even to a first degree of approximation ; or again, our situation in nature might be so unfortunate that our sensations came to us in such an order that they failed to reveal the laws which really are present in nature.

The scientist who assumes that nature is and will always remain intelligible must therefore assume that nature obeys other laws in addition to those of logic
172
477
523
513
513
218
EXCURSION 2

Use the following table of connectives to format your answer.

~ negation: 1
\ / disjunction: 2
/ \ conjunction: 3
-> implication: 4
<-> equivalence: 5
( opening bracket: 8
) closing bracket: 9"

https://avalonlibrary.net/ebooks/Rudy Rucker - Infinity and the Mind The Science and Philosophy of the Infinite.pdf
look through pages 275-291 i think the main hint is in there

table of truth is maths

and logic

[small holly]

how do i do a?

[uneven garnet]

Find t as h=0

[alpine sable]

Would I put 4x-65+4x-65+2x-4=180

[pearl marlin]

Sin x

[rich basin]

yeah jsut realised

[true crystal]

Those are lengths not angles

[alpine sable]

So how would I setup that?

[true crystal]

Do you know the midsegment theorem ? If not go check it

[rich basin]

I am rather confused how to do this? Is it possible to use substitution

make u = cosx

and du/dx = sinx

sub in du/dx

[true crystal]

There is easier

[rich basin]

u/ 1 + du/dx * dx

[true crystal]

If not the numerator then the...

[rich basin]

I am stuck at this point

[smoky harness]

The answer is found in excursion 2
The page number riddle here forms the actual quesyion

[rich basin]

$\frac{udx^{2}}{dx\ +\ du}$$

[ocean seal]

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

[shell widget]

Try the substitution u = 1 + sinx

[rich basin]

that would be negative du/dx

so it would -du/u

[true crystal]

du = cos(x)dx

[rich basin]

what would you do with the du?

i subbed in the du/dx for cos

[true crystal]

Yeah so you get du/u

[rich basin]

you mean negative du/dx

[true crystal]

sin'(x) = cos(x)

[rich basin]

yeah

okay

but then what would you evaluate du/u down to?

[true crystal]

Do you know ln(x)

[rich basin]

yeah

the derivative of that would be 1/x

[true crystal]

that is it

[rich basin]

what

[true crystal]

you should know the integral of du / u

[rich basin]

I don't understand it intuitively

[true crystal]

Do you understand integral of 1/u * du

[rich basin]

no

what happened the dx

[true crystal]

The dx canceled

(du / dx)* dx

since cos(x) = du / dx

[rich basin]

but wouldn't you need the du/dx

because the top part is the du/dx of the inside function

[true crystal]

By substitution you get (du / dx ) * dx / u right ?

[rich basin]

yeah

[true crystal]

You can cancel something

[rich basin]

yeah

[true crystal]

So that you just end with only one variable

[rich basin]

but i feel like it won't be satisfactory to turn into ln(x)

[true crystal]

it is ln(u)

[rich basin]

yeah ln(u)

[true crystal]

You just do the the integral with another variable

That is subsitution

[rich basin]

like when you differentiate ln(u) it would be du/dx * 1/u

[true crystal]

No since you differentiate respect to u

[rich basin]

dy/du

dy/du * 1/u

[true crystal]

Do you know substitution ? Or you just discover it ?

[rich basin]

i know it already

[true crystal]

Yeah so you end with ln(u) which is ln(1+sin(x))

[rich basin]

okay thanks, i would just do some more research

[true crystal]

Sorry if you didn't get it

[alpine sable]

I still dont understand

[true crystal]

The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long

And you have the length (function of x) of GH and SQ

[alpine sable]

uh

[rich basin]

@true crystal I think i get it now, you are integrating it relative to that variable right?

[true crystal]

Yeah

[rich basin]

so it should be represented as int 1/u * du

[alpine sable]

Im sorry, im still confused on how to setup the equation @true crystal

[true crystal]

You get rid of all the x and do normal integral just this time it is about u

Which is simplier

[rich basin]

Yeah, i get it now thanks

[true crystal]

the segment connecting the midpoints of two sides of a triangle

What is it in our case ?

[alpine sable]

GH?

4x-65

[true crystal]

yeah

is parallel to the third side and half as long.
What is it here ?

[alpine sable]

?

RG?

[true crystal]

The triangle is the big one

so 2x-4

[alpine sable]

I'm sorry if I'm not understanding this, thank you for your patience

Okay so

SQ

[true crystal]

Don't worry

yeah and it is half as long so you get your answer

Just re-read the sentence

and replace the length of the sides

[alpine sable]

Im so confused

Can you setup the equation for me?

Like how would I solve it

[true crystal]

GH / SQ = 1/2

this is what the definition says

re-read the sentence

"half as long"

[alpine sable]

4x-65
2?

[true crystal]

What is 2 ? x ?

[alpine sable]

W h a t

Ohh

Im dividing by 2

idk

Im so confused im sorry

Im trying to understand

[true crystal]

no prob

[rich basin]

this is my equation

$\int_{\frac{\pi}{4}}^{\frac{5\pi}{4}}\left(\sin x-\cos x\right)dx$

[ocean seal]

BorutoEyePower

[rich basin]

but it is not the right answe

[glass lichen]

yeah cause you neglected the rest of the interval

[rich basin]

so it should be pi/4 to 2pi ?

[glass lichen]

No, on the rest of the interval cosx>sinx

[rich basin]

but it will only be greater than sinx once it is greater than 5pi/4

[rich basin]

so 0 to pi/4

i mean 0 to 5pi/4

[glass lichen]

no

So either you can do the 3 integrals, or leverage the graph and notice it's 2 of the integral you calculated, just the 2nd one is sliced up

[rich basin]

i mean 0 to pi/4 + 5pi/4 to 2pi

[glass lichen]

yes

[rich basin]

but why does it have to be greater than sinx?

[glass lichen]

what?

you're computing area b/w 2 curves.. so you need top - bottom

if the top and bottom change, you have to change the integrand

[rich basin]

@glass lichen What is the problem with changing the integrand?

[glass lichen]

it becomes a different integrand...

[rich basin]

you can just use that integrand and then change the integrand to suit the other intervals

but doesn't it count as between the curve during the intervals of pi/4 to 5pi/4

@glass lichen unless you mean we want 3 integrals

[glass lichen]

sinx>cosx on [pi/4,5pi/4]

[glass lichen]

I said that, yes

or leverage the symmetry in the regions

[rich basin]

like 3 integrals for the three intervals

such as 0 to pi/4

pi/4 to 5pi/4

[glass lichen]

yes

[rich basin]

5pi/4 to 2pi

because there is a negative

[glass lichen]

that's what I was saying, however it's easier to just compute $2\int_{\frac{\pi}{4}}^{\frac{5\pi}{4}}(\sin(x)-\cos(x))\dd{x}$

[ocean seal]

Mosh

[rich basin]

@glass lichen is that to count both positive and negative

like between the intersection of the x axis

as well as the curves

[glass lichen]

If you read what I've been writing.....

[rich basin]

I'm trying to understand why you multiply it by 2

[glass lichen]

I said you can leverage the regions and notice on [0,2pi] you get 2 of the regions from [pi/4,5pi/4]

[rich basin]

@glass lichen okay

[alpine sable]

Whats the Definition of p value and its uses

[atomic nymph]

guys i feel so stupid, how do you get from the one on the left to the one on the right?

[novel siren]

rationalize the denominator by multiplying by sqrt3/sqrt3

[alpine sable]

Hey that's against the rules I asked here first

[atomic nymph]

mb i thought u were done

also, you didnt really ask a question

[alpine sable]

Alright no problem I don't think anyone knows the answer anyways

[atomic nymph]

statistics is confusing xD

[alpine sable]

Do it yourself, you have asked like 10 questions on the same principle since yesterday

[thorn tapir]

multiply by sqrt(3) on both numerator and denominator

[exotic mortar]

Can someone share the answers?

[lofty abyss]

If cscθ > 0 and sec θ < 0, what quadrant is θ in

[exotic mortar]

^

[alpine sable]

@lofty abyss draw it out on a unit circle?

[nimble meteor]

pls help me graph this parametric equations by eliminating the parameter?

I was able to find out how the graph looks but I don't konw how they got it

[shell widget]

maybe squaring both sides of both equations and then adding them might help

i think

[flat widget]

(-x^3)^2

Answer please 🥺

Lol i know it's a dumb one but I'm not sure what the answer is

I knew it

Thx kind stranger

[dense frost]

hello everyone

tells me to find a vector parallel to the line ax + bc = c which sits on a plane

i end up finding (c/a)i - (c/b)j (or with the signs swapped)

the solution multiplies this vector I found with a*b

why is that

is my answer still correct? what step am I missing?

[wide gyro]

2/3 can be represented as 10/15 and 1/5 can be represented as 3/15

10/15 + 3/15 is just adding the numerators

so 10+3 / 15

since they have the same denominators you can do that

and decimal addition is pretty easy so i think you can do that

@alpine sable

[alpine sable]

@wide gyro and b)?

please

[wide gyro]

are those decimals?

i dont know what 2 comma 47 means if your assignments means 2.47

its decimal

is it a decimal

[alpine sable]

need to simplify?

[wide gyro]

no

12.6 is 12.60

[alpine sable]

ok thanks

[wide gyro]

understand?

so 12.60 + 2.47

add 12 and 2

which is 14

and then the decimals

[alpine sable]

<3

[wide gyro]

.60 and .47 which s

60+47 = 107

whichs 1.07

so 14+1.07

15.07

you can just do addition

if your 13+ you should know this

pretty easily

[alpine sable]

❤️

[flat widget]

I messed up here, and i don't know where. Help 🙏

The right answer is (-Infinity; 0,5]

[teal epoch]

When you multiply negatives in this case (-6) you switch the inequality sign

[pearl marlin]

Change the inequality

[ocean seal]

Nonexisty

[flat widget]

Ok, is it the same when u divide?

[teal epoch]

Yes

[flat widget]

Ok thx

[ocean seal]

Nonexisty

[teal epoch]

fixed

[gray fulcrum]

waht is 1+1

[gaunt magnet]

hi

i got

1/3pi and 2/3 pi

am i correct

[minor heath]

nope

just let tan theta be a variable

[dawn wraith]

Treat it as a quadratic

[minor heath]

sorry, channel occupied

[gentle atlas]

oh mb

[gaunt magnet]

,w $3tan ^2 θ+tanθ−2=0$

,w 3tan ^2 θ+tanθ−2=0

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Usman#0988

[alpine sable]

,w 3.3

,w 3x3

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by gustavas#4706

[alpine sable]

thats cool

[gaunt magnet]

i posted the wrong question

this

[minor heath]

theres two more solutions for that

remember, theta is between 0 and 2pi

sorry channel occupied

[gaunt magnet]

4/3pi and 5/3pi

[minor heath]

ok thats all the solutions

[gray isle]

you should expect 4 solutions

[minor heath]

he just named the 2 additional solutions

he had the 2 others earlier

[gaunt magnet]

ye i did get 4 solutions

[gray isle]

oh,

[agile coral]

ok maybe this is too advanced for me to understand but my friend who likes numbers is always telling me some extremely specific fact, often about prime numbers like "every prime that is 4n+1 is a sum of two squares" or "every even number is a sum of two primes"

so my question is literally why do we care and why does that matter at all

all mathematicians making these things just for fun or is there an application to knowing specific primes are a sum of squares

[indigo jetty]

these kind of properties are used frequently in cryptography

[ancient bear]

This is the first time I have an integral like this and I'm not sure what to do here

These are the properties I know

[unique hatch]

you're gonna have to set u=the numerator

then do u=substitution

exactly what bob said

[ancient bear]

also, can I move the numerator down since sin^-1(x) = (sin(x))^-1?

[buoyant meadow]

Hi, i seen this explication in a site:

The Distributive Axioms are that x(y + z) = xy + xz and (y + z)x = yx + zx.
These equations are true for all numbers x, y and z.

My question is, why not do the some first and multiply then?

[unique hatch]

in this case the -1 tells you that its arcsin, so basically the angle that when you take its sine, it gives you that value

[ancient bear]

so i cant

okay

Ill go ahead with the substitution

curious as to how do you see that

habit?

neither the lecture nor the book showed an example like this

oh yeah, I understand the notation

I was just wondering if moving it down was legal

because (sin x)^2 = sin^2 x, right?

so it occured to me, nevermind

[unique hatch]

if the -1 is outside of the brackets

then u can move it down

[ancient bear]

okay

[unique hatch]

but if its between sin and x then its arcsin

[alpine sable]

b) ?

[buoyant meadow]

now i know

lol, took a while to understand

[rocky dock]

can someone help me complete this

im trying to graph ans im using y = -7x - 6 but im having a hardd time because the graph cuts off

and it seems like if i go the other direction there is no whole number...? idk'

[true crystal]

(0, -6) and (-2, 8) works

[rocky dock]

it did, interesting

@true crystal on desmos that point showed up as decimals

not whole numbers

[gray dove]

@rocky dock use mathway

[kindred lion]

Is this channel free rn?

[night gust]

Yes

[kindred lion]

Can someone solve this one? Derived the expression but couldn't get the sum right

[true crystal]

general term 4 * 1/(2k-1) * 1/(2k+1), k >= 1 and probably telescopic sum

or 4 / ((2k+1)*(2k+3)), k >= 0 if you like

[kindred lion]

Ah okk