#geometry-and-trigonometry

1 messages · Page 327 of 1

main lintel
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did you manage to sketch the situation graphically?

night harbor
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How do i find x from
pi sin2x = 0

upper karma
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pi sin2x? Or do you mean sin 2pix?

night harbor
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Oh i can write this as sin2pix?

upper karma
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No

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You differentiated wrong

night harbor
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How¿

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I just watched sa video on youtube and did the same steps hahahaa

upper karma
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Where does the 2 come from?

night harbor
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Ohh...

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I mustve copied it while listening to the video hahahaha

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So -pisinx?

upper karma
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still wrong

night harbor
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Uhmmm -pisinpix

upper karma
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yes

night harbor
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Soo.. how do i solve for x here?

upper karma
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you know the general solution?
$sin x = sin \alpha\
sin x = sin (n\pi + (-1)^n \alpha)\
x = (n\pi + (-1)^n \alpha)$

somber coyoteBOT
night harbor
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No :(

upper karma
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alpha here = 0
so you have pix = npi
or x = n where n is any integer

night harbor
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So there's no exact value for what x is?

upper karma
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there can be infinite solutions for this. But if you want a principal solution, it has to lie between 0,2pi

round isle
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let's see what you have done so far

night harbor
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there can be infinite solutions for this. But if you want a principal solution, it has to lie between 0,2pi
@upper karma okay thank you sm

upper karma
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I NEED HELP WITH GEO

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<@&268886789983436800>

copper valve
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by pinging mods ur almost asking to get banned

upper karma
#

oh

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I didnt know what was a rule

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I thought mods were like people who help

copper valve
#

mods moderate

upper karma
#

oh

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ahm

copper valve
umbral snow
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(5y - 21) + (6x + 32) = 180

upper karma
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ok

umbral snow
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As they together form that straight line

upper karma
#

That dosnt work

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Thats what happens when I enter that

umbral snow
#

Right, but you know x

upper karma
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(5y - 21) + (6x + 32) = 180

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ahhhhh

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m,hmhmhmhmhm

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ty

royal citrus
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Hey what is formula to find the cross section area of a prism?

soft zodiac
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@main lintel I searched up the golf terms but I’m not sure if I set it up correctly

round isle
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@royal citrus you mean the base area?

silent plank
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the CAST / ASTC mnemonic, tells you which trig functions evaluated in which quadrants are positive

dark sparrow
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here's a simple mnemonic on how to use the "CAST rule":

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don't

main lintel
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@soft zodiac yes, you need to verify if the golfing terms are set up correctly. Now after you give a sketch with known figures and wanted unknown figure I can verify the geometric solution.

upper karma
tropic steppe
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im not sure

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how to find either of those

main lintel
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@upper karma What is an arithmetic sequence?

limpid gust
silent plank
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consider constructing a line through <z parallel to AB and CD

limpid gust
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Im just confused about the entire thing and where to start proving it

silent plank
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refer to above comment

limpid gust
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so z ll to x and y?

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I don't know if I am aloud to draw lines

olive rock
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You can copy it onto a piece of paper and draw it there

silent plank
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(yes you are allowed to draw lines)

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but you'd need to state it in your proof

limpid gust
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Alright it turns out I wasn't supposed to know that

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My teacher said that one was just to see if any of us were ahead but it scared the shit out of me it was on a quiz

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But you are right I was supposed to draw the line

dark sparrow
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WHY ARE YOU YELLING

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have you done problems that go like "sin(θ) = blah and θ is in such and such quadrant, find cos(θ)" before?

dark sparrow
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i mean, sin(x/2) can only be found up to sign if all you have is cos(x)

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but you can use the formula sin^2(x/2) = (1 - cos(x))/2 if sign isn't an issue

upper karma
dark sparrow
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by thinking about what length is & your intuitions about it

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you had a 9-foot plank and you sawed 3 feet off one end, how much is left over?

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@upper karma

glass light
dark sparrow
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triple angle identity

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$\sin(3\theta) = -4\sin^3(\theta) + 3 \sin(\theta)$

upper karma
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Yea my bad

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I had gotten it

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Wasn't doing the think

somber coyoteBOT
zealous crag
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could someone tell me the answer for these ones?

limpid gust
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yeah rotate the picture

earnest echo
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,rotate

somber coyoteBOT
dark sparrow
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we dont give out answers here

upper karma
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Consider a trig ratio

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Note that you have opp and you want adj.

earnest echo
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(looks like a test)

kindred rapids
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Nono...its just a past paper question for homework sent by my teacher...

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I got through btw so it's fine now....

dark jacinth
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could I get some help with this please? I'm very lost

loud fiber
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In your opinion which is harder and why, Trigonometry or Statistics?

sinful tide
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Stats for me

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Trig was just easier for my brain to understand

plain wyvern
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@dark jacinth lovely question. It would have been great if we had such questions to solve for coordinate

dark jacinth
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I'm not sure what you mean

plain wyvern
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I meant we never had questions with so much background and all that. Quite precise find out the line from A to B quick

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Talking about the question, just find out the equation of the line from A to C, points are given

dark jacinth
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I am not sure how to set up the parametric equation

plain wyvern
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I see, wait a min

dark jacinth
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thanks 🙂

plain wyvern
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Once you study it, the question will be really simple to do

silk river
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Can y’all guys help me solve trig equation or do I have to go somewhere else

upper karma
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Post it here

cosmic pebbleBOT
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From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

silk river
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It’s for homework I missed class that day

plain wyvern
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did you do anything? Or just posted it here?

silk river
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Wym did I start working on it

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I got all they was to sin(x)-cos(x)= -1

upper karma
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-2 +- the square root of 124 all over 6 can that be simplified

dark sparrow
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yes
(-2 +- sqrt(124))/6 = (-1 +- sqrt(31))/3

shadow wadi
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Hello fellow mathematicians

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I have a question if somebody would care to explain

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From where in this 364. Second to last expression could i deduce that alfa is only possible to be between pi/2 and 0

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The problem was to prove that the first equation is equal to the last one

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I can deduce that alfa must be smaller than pi because sin alfa must be higher than 0

main lintel
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@shadow wadi About which expression are you talking about

shadow wadi
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This with absolute values

main lintel
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Both the left and the right side (the entire equation)?

shadow wadi
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Well wherever you can extract the condition for alfa

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Ill send you the whole problem

main lintel
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Just a second

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OK, please the whole problem

dark jacinth
shadow wadi
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And i must find from where can i limit the alpha to these values

main lintel
shadow wadi
humble pulsar
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translation?

main lintel
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I'm croatian accidentaly so I can understand it 😄

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He put the translation above the image

humble pulsar
#

oh im blind lol

shadow wadi
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Hahahahah nastavit cemo na engleskom da svi kontaju

main lintel
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It says in the text of the problem that you should assume alpha is smaller than pi/2 and greater than 0. There is nothing to deduce.

humble pulsar
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it's just an induction question

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induction? why did i write induction

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identity*

main lintel
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Aha, you are asking, why they put this constraint?

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@shadow wadi

dark jacinth
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@main lintel any help with my problem?

main lintel
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@dark jacinth Have you solved a)

dark jacinth
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no, thats what I am confused about

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im not sure how to set uo the parametric equation

main lintel
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Do you know to set the coordinate system?

shadow wadi
main lintel
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Well, otherwise you can get negative sin(alpha)

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And on the left side you have sum of squares which is positive

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So you cannot match it.

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They could have maybe allowed alpha to go to PI

shadow wadi
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Isnt sin alpha positive to the pi radians?

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Yeah

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Thats what i was thinking

main lintel
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So your question is why they constrained by PI/2 instead of PI?

shadow wadi
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But they invalidate the equation when cos alpha goes negative

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Yes

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This constrain is just pure torture to me

main lintel
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Why?

shadow wadi
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I cannot look at it without understanding it

main lintel
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The stronger constraint makes it easier to solve

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Aha, you are just wondering why.

shadow wadi
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Yeah but you yourself know that mathematics really rarely cares about ease of solving

main lintel
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Can you show your entire solution on paper to check if the solution does not require PI/2

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If you seem sure, you can post the question to the book author, he should be willing to correct.

shadow wadi
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Yeah bro its really not tidy hahahahha

main lintel
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Although if you are right it is not necessarily the error in the question. THe opposite would be.

shadow wadi
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Book author has been dead for decades i think hahaha

main lintel
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Show the electronic solution then.

shadow wadi
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Just says true.

main lintel
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Check it, perhaps he has a mail address.

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Well how did you prove it?

dark jacinth
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@main lintel do you have any idea on how to solve my problem?

main lintel
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I asked you a question before @dark jacinth

shadow wadi
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Well sin alpha must be positive because of addition of squares on the left side so alpha is 0-pi

dark jacinth
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what was it?

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im pretty sure I answered

shadow wadi
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And if i take that and pull the equation to the end it makes perfect sense

main lintel
dark jacinth
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what do you mean by that?

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like do I know the points?

shadow wadi
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Bro i have a similar one ill try to solve it now and ill hit this group up again i hope youll be here then @main lintel

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Gimme 10 min max to write it nicely

main lintel
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@dark jacinth Do you know where the center of coordinate system is, the x, y and z axis?

dark jacinth
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what do you mean by the center

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I know that A= (0,0,0) and G= (10,12,8)

main lintel
dark jacinth
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GH midpoint is (10,12,4)

main lintel
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@dark jacinth THe center of the coordinate system.

dark jacinth
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im not sure what that is

main lintel
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Do you know to visualize the coordinate system with respect to the points and the object

dark jacinth
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not necessarily

main lintel
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You dont know what a coordinate system is? 3d or 2d? @dark jacinth

dark jacinth
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i do, but im not sure what you're trying to show me

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i need a parametric equation

main lintel
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What is parametric equation?

shadow wadi
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@main lintel

dark jacinth
main lintel
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I mean what is a "parametric equation" in this context is slighly ambiguous.

dark jacinth
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look at a

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thats what im confused about

main lintel
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So you are not sure what a parametric equation is?

dark jacinth
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not in this context

shadow wadi
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Broooo I'm done wolfram alpha also outputs a condition alpha 0-pi

main lintel
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Do you have a book and a course that goes along with these questions, perhaps it has similar example in it @dark jacinth

shadow wadi
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Must be an authors mistake

dark jacinth
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no, this is new

shadow wadi
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Its not the first one he made

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Earlier i encountered many others too

main lintel
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I mean it is not strictly a mistake. It is just that the condition where the equation is true can be loosened.

shadow wadi
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Bro that sentence is on point

main lintel
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Perhaps alpha from 2pi to 3pi is also the solution

shadow wadi
#

Lit

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Hahahahahhahah

main lintel
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Have you considered that?

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Does wolfram alpha state that?

shadow wadi
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2kpi-(2kpi +1 ) is the range

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K- integer

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So 3pi to 4pi

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4pi to 5pi

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And so on

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Function is a repeating one

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Anyways bro you helped me validate my mathematical knowledge so thank you very much @main lintel

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Koji si razred

main lintel
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Završio sam faks davno.

shadow wadi
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Ne seri ahhahahahahha

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Koji

main lintel
#

FER u Zagrebu

shadow wadi
#

E r je sta

main lintel
#

pogledaj na netu

shadow wadi
#

Elektrotehnika i racunarstvo

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Mislio sam il je to il je ekonomija i racunovodstvo

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Koliko ti je sad godina

main lintel
# dark jacinth no, this is new

I think in this context parameterized equation might be an equation of the vector (let's call it r) describing the motion like:
r = 2t i + t ** j** - t k

dark jacinth
#

what do each of the variables represent?

main lintel
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Alternatively you can make a parameterized point like (2t, t, -t)

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t is the parameter, and i,j,k are unit vectors in the coordinate system.

dark jacinth
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how would you use that in the context of my problem

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can you make the equation?

main lintel
main lintel
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Where is this question from if you don't have the related backing course on it?

shadow wadi
dark jacinth
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i've never seen anything like this problem

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its brand new

shadow wadi
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Kako ti je sad na poslu pretpostavljam da radis

main lintel
main lintel
dark jacinth
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its for homework

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and I am very confused

main lintel
#

Have you ever learned about vectors?

main lintel
dark jacinth
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yes, I have

main lintel
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And you know what is i,j,k?

dark jacinth
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no

shadow wadi
main lintel
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Onda ti je to super smjer.

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A šta si iz RS-a ili ?

shadow wadi
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Federacija

main lintel
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Ne znam te detalje.

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A zadaci su na ekavici.

shadow wadi
#

Nije mi zadaca spremam prijemni

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Znam da je za 6 mjeseci al sam trigonometriju radio prije 2 godine zadnji put

main lintel
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@shadow wadi Help Dax, it's a nice excercise.

shadow wadi
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Ill try

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@main lintel to find the shortest path id use calculus basics do a first derivative then equal it to zero and find the value of his position on A-C but I really dont think hes familiar with calculus

main lintel
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First solve a)

shadow wadi
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@dark jacinth

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So basically according to my math skills if you put the coordinate system in point a with x axis pointing perpendicular to ab line and y axis being colinear with ab line parametric equation should sound like this for AC line : y=AB/BC *x

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Note that ab is equal to -(its actual length)

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Because were going down on the y axis

ocean smelt
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Are you mid something or can I ask a question? 😊

shadow wadi
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So the linear function limited to AC is y=kx (k being the parameter) sounding like ab/bc

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Yeah dax is not answering go ahead @ocean smelt

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@dark jacinth b) part requires calculus are you able to do simple derivatives

ocean smelt
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So is there a mathematical way to cut a circle of radius x at other points than its “equator” and find the arc length of the remaining piece?

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(This is for a 2D shape I want to revolve around an axis but I want to calculate the parameters needed)

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As a description you could say I am trying to find the segment needed to cover the topmost 30% of a sphere, does that make sense?

main lintel
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@ocean smelt So you want to make a straight line cut on the circle and calculate the length of the respectivev arc?

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Well you need to start from your condition I guess, you want this arc when revolved around some axis to cover 30% of the sphere.

ocean smelt
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Exactly

main lintel
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First when you say 30% of the sphere do you mean its surface or volume?

ocean smelt
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Surface

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But is it really so easy that i let it revolve < 180°?

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(Thinking out loud now)

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If the revolution goes both ways, ie + & - from the starting point, I should be able to accomplish it

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Right? Say I revolve it only 120°

main lintel
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You will revolve the arc around the axis that goes from the circle center throuh the center of the arc

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You revolve it 180 degrees exact to make the full "hat"

ocean smelt
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I will revolve the arc around the axis that goes through the core of the sphere

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Yeah, and everything less than 180°, done equally both forward and backward will create a hat but a “toppier” one..?

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Like those that chimney cleaners wear 😂, zero ear warmth, that’s what I need

main lintel
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I dont know what you want to achieve

ocean smelt
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I have over done this

main lintel
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You said you want to cover topmost 30% of the sphere by surface.

ocean smelt
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Yup

main lintel
#

That means you want to construct a hat.

ocean smelt
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A hat is all I want indeed

main lintel
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It will be fully covered with a circle at the base of the hat

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Right?

ocean smelt
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I want what is left above the line

main lintel
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OK, you want to know the height at which to cut?

ocean smelt
#

Exactly

main lintel
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I wanted to call it a cap

ocean smelt
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Or well, your graphic covers it! Exactly what I want! 😃

main lintel
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Was pretty sure a cap is a good term, but didnt use it at the end

ocean smelt
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Thank you! 😃

main lintel
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They say that using height (that is h on the above image) the formula for the area is 2*PI*r*h

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And the full sphere area's formula is 4*pi*r^2 @ocean smelt

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If you want to cut it mechanically perhaps might be easier to calculate the length of the arc from the top of the cap to the cutting line.

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So you can use that flexible meter on the surface to determine the cutting spot.

winter depot
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Can someone pm me

upper karma
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<@&268886789983436800> ^^ ( they don't want their questions public... that seems suspicous)

twin heron
#

No using this server to cheat. If you do I will ban you right now.

winter depot
#

I just asked for help

west basin
#

ask here

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we will help you 🙂

upper karma
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well you never really asked your question thonkzoom

winter depot
#

What’s wrong asking for help in pm? I’m not trying cause any problems.

twin heron
#

We just have strict no cheating policies here. It just seems a bit unorthodox for someone to be hush hush about math questions

winter depot
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Oh ok

west basin
#

academic dishonesty is not epic

dense niche
sturdy stream
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can someone please help me out

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?

sturdy stream
dense niche
#

expand it :0?

sturdy stream
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(3x+y)(3x+y)(3x+y)

dense niche
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ohhh

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alright ty!!!

sturdy stream
#

np!

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can someone help me with a?

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how would we know which is the proper value of x?

dark sparrow
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wym

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did you get two possible values?

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check whether your values of x result in positive angles

sturdy stream
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ok i think there are 2 values

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thanks

rose sphinx
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Please check this

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Is this correct ?

round isle
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poor handwriting

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wish I could help

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if you can post a picture of this question from the book, then I can take a look at your math

rose sphinx
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@round isle
The equation of the straight line which passes through the point (−4,3) such that the portion of the line between the axes is divided internally by the point in the ratio 5:3 is

round isle
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is there a diagram with the question?

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you can have two possible orientations of the line

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one with positive gradient and another with negative gradient

rose sphinx
#

is there a diagram with the question?
@round isle no diagram

round isle
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(-4, 3) is in the 2nd quadrant, so you should redo your diagram

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and there are two possible lines as I mentioned

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so, two possible equations

rose sphinx
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Is my solution correct (mathematically , skip diagrams)

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Solution that I found on internet

round isle
#

disregard my previous remark that there are two possible equations. Yes, this solution is correct

rose sphinx
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disregard my previous remark that there are two possible equations. Yes, this solution is correct
@round isle why

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And why is my solution wrong ?

round isle
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you didn't even draw the correct diagram

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the point is in the second quadrant

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not the first one

rose sphinx
#

you didn't even draw the correct diagram
@round isle don't see the diagram

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Is the mathematics wrong ?

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I don't think so

round isle
#

post your picture again

rose sphinx
round isle
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your method is incorrect

rose sphinx
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Why

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@round isle

round isle
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please use the line ratio formula

rose sphinx
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What is incorrect

round isle
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do you know the line ratio formula

rose sphinx
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Yaa

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And used it

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The thing is they took the ratio of 5:3 opposite of what I hv taken

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I don't understand why

hushed spear
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how would i prove that sin(180 - x) = sin(x)?

earnest echo
#

Compound angle identities

north lichen
#

can someone explain why POT is not right angled?

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or is it? I initially thought it was

dusky surge
#

I am also thinking POT is a right angle.

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As T leans towards only to the east, it should be on the x-z plane, and OP is on the y-axis, so it must be perpendicular to x-z plane which T is laying on.
Sorry, I don't know how to explain without the regular Cartesian coordinates x,y,z

north lichen
#

EXACTLY

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some people were telling me it was not right angled

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I was thinking of the analogy of a cone - if you rotate POT around the "N (north) - axis", you get a cone

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and the cross section will be a triangle, half of which will give the right angled POT triangle

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So I could use POT to solve part ii)?

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Why can’t my working out do it though?

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Sorry if it’s messy

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OHHHH I SEE IM SO STUPID ITS COS NOT SINE in the first triangle i drew

dusky surge
#

Reading...

north lichen
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@dusky surge unfortunately that only solved one problem

dusky surge
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My brain's stuck😂

north lichen
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now I still have a sin^2(x) next to the a^2

dusky surge
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Lemme grab my paper

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I used this

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$a^2+d^2=(d \cos{\theta} \cot{\alpha})^2 +(d \cos{\theta})^2$

somber coyoteBOT
dusky surge
#

Oh, I see what's the problem of yours.

north lichen
#

shouldnt it be squared rooted a^2 + b^2

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OH

dusky surge
#

Angle PTM is not θ

north lichen
#

OHHHHHH

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i am sooo stupid

dusky surge
#

That's why it cannot be sinθ

north lichen
#

what a bad diagram though

dusky surge
#

Must be

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Bad diagram

night basin
#

Find a point that is equidistant from the following:

( 3, 12 ), ( 5, -2 ), and y = −4

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? i know i have to use distance formula and parobolas but im confused

onyx cloud
#

@night basin its a system of equations
$\sqrt{(3-x)^2 + (12-y)^2} = n$
$\sqrt{(5-x)^2 + (-2-y)^2} = n$
will be your two first equations

somber coyoteBOT
onyx cloud
#

then for any point, the distance in the x direction to y=-4 will be 0

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since the closest distance is a perpendicular line to y=-4

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so we have

night basin
#

set those two equal?

onyx cloud
#

$\sqrt{(0)^2 + (-4-y)^2} = n$

somber coyoteBOT
onyx cloud
#

so now you have 3 equations

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$\sqrt{(3-x)^2 + (12-y)^2} = n$

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$\sqrt{(5-x)^2 + (-2-y)^2} = n$

somber coyoteBOT
onyx cloud
#

$\sqrt{(0)^2 + (-4-y)^2} = n$

somber coyoteBOT
onyx cloud
#

you're interested in finding x and y. I would start by setting the bottom equation equal to any of the top equations

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it will let you solve for y in terms of x

odd blade
#

How can I find a biggest square root for 225

night basin
#

15

odd blade
#

So it’s 15squre root of 15?

night basin
#

oh

odd blade
#

Trying get this to radicle form

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Just don’t know how to do the 225 square root area one

dark sparrow
#

sqrt(225) = 15

odd blade
#

It’s a perfect square ?

night basin
#

@onyx cloud so $\sqrt{(0)^2 + (-4-y)^2} = \sqrt{(5-x)^2 + (-2-y)^2}$ ?

odd blade
#

I got it thanks

odd blade
#

How in the world do you do this

#

So far I got 21 times 5 x times 6 equal 105 divide 6 equal 17.5

silent plank
#

please describe your work more clearly

odd blade
silent plank
#

that looks like complete nonsense to me

odd blade
#

Oh

#

Sorry I have no clue how you do this

silent plank
#

setup an equation properly

#

wtf is $\frac{x}{21}\frac{5}{6}$ supposed to be?

odd blade
#

I belive I have to mutply and then divide

somber coyoteBOT
odd blade
#

It’s triangle proportionlty

#

At least I think

silent plank
#

what's the product of those fractions supposed to give you?

odd blade
#

So if I cross multiply and divide I get an decimal answer which will be the x

silent plank
#

what's written above is an expression only

#

and tells you nothing about x

#

applying proportionality what you could start with is:
$$\frac{x}{21} \red{=} \frac{5}{6}$$

somber coyoteBOT
odd blade
#

Ok I see I got that so far

silent plank
#

that's not what what you have written on the page

odd blade
#

Like I redid it

#

So do we cross multy?

silent plank
#

don't need to do the full cross multiplication

#

multiplying both sides of the equation by 21 is enough

odd blade
#

I am confused

silent plank
#

21 is a value you could multiply to x/21 to get what you want: x
hence to obtain the value of x, while maintaining equality, you can multiply both sides of the equation by 21

odd blade
#

That’s what I got when I redid my work

silent plank
#

its recommended that you write things on a new line

#

so that the rhs of one equation doesn't get mixed with the lhs of the next equation

odd blade
#

I see

silent plank
#

and doing the full cross multiplication is just making more work for yourself

odd blade
#

It’s the way we got told to do it

#

But the way I did it is right ?

silent plank
#

mathematically correct yes

odd blade
#

Wait I can’t have decimal as my answer

#

Well now I am stuck

silent plank
#

leave it as a fraction

odd blade
#

105/6?

silent plank
#

can be simplified since both num and denom have a common factor of 3

odd blade
#

I got 35 over 2

silent plank
#

if you understand where cross comes from, you'll realise that it results in more work here

#

yes, that is indeed equivalent to 17.5

odd blade
#

I see thanks

silent plank
#

$\frac ab = \frac cd \implies ad = bc$ because:
that's the result you get from multiplying both sides by the product of the denominators $bd$: \
$$bd \times \frac ab = bd \frac cd$$

somber coyoteBOT
silent plank
#

however since your goal here is to get x, you only need to multiply both sides of the equation by 21

#

applying the principle above, by doing the full cross multiplication,
you've effectively multiplied both sides by 6,
only to divide both sides by 6 immediately after

odd blade
#

But there is nothing wrong with doing the long way do

silent plank
#

mathematically no, just very inefficient

somber coyoteBOT
vestal pendant
#

hi

silent plank
#

(and demonstrates average understanding and/or that you're blindly following formulas)

odd blade
#

I think I have to follow the formula or I won’t pass

vestal pendant
#

anyone smart

#

in math

#

i always forget how to get x and y away from each other

silent plank
#

you don't have to follow it exactly every time when fractions are involved

#

as per the ridiculous example abouve

upper karma
#

@vestal pendant this channel looks like it's still occupied, please proceed with a free one.

vestal pendant
#

ok

silent plank
#

where if you have x/1 = 3/2,
you don't need to go through those 2 extra steps and just reach the conclusion that
x = 3/2

#

from the reasoning behind cross multiplication:

multiplying both sides by the product of the denominators,
its just as valid to multiply both sides of the equation by one of the denominators
and if that's all that's required to get the result, that's sufficient

#

or in the case of x/1, that's simply just x

odd blade
#

I am pretty sure my geometry math teacher is picky

#

Thanks do

vestal pendant
#

forgot how to do this

silent plank
#

apply properties of congruent figures

vestal pendant
#

x and y

#

its not that, im confused on how to fidn x and y,

#

or am i dumb

#

lemme try it rq

#

i got this @silent plank

silent plank
#

where are those equations coming from?

#

what are properties of congruent figures?

vestal pendant
#

this is = to that

silent plank
#

wdym by this and that?

vestal pendant
#

lemme make markings

#

sec

silent plank
#

use point labelling

vestal pendant
#

what

#

15x + y = 90

#

cause ots congruent to the right angle

silent plank
#

yes

#

FG is improperly marked with 2 lines

#

you're also missing some important markings

#

what do you know about GW?

vestal pendant
#

o

silent plank
#

which side does that correspond to

vestal pendant
#

gd

silent plank
#

capitals but ok

vestal pendant
#

ye

#

3x-5 = 10

silent plank
#

yes

vestal pendant
#

x = 5

#

15(5)+y=90

#

90-75 = 15

#

y = 15

#

ty

silent plank
#

yep

vestal pendant
#

❤️

odd blade
#

Need an expert to help me with triangle proportianty

upper karma
#

@upper karma first you need to realise that it's every element above this linear function, and the linear function is: y = ax + b

so, y = 3 when x = 0 and y = 0 when x = 6 (as you can see in the graph)

3 = a.0+b = b
0 = 6.a + 3

so, a = -1/2 and b = 3

y = -x/2 + 3 is our line. since we want every element above this one, we need to write it as: y > -x/2 + 3

#

no

#

i'll be busy soon

#

<@&268886789983436800> ok this has gone too far, at #help-8 Sanj9 was already warned over not helping here with graded quizzes, yet this is another time they post it here (now the pic is deleted)

odd blade
#

May I have some asstince on setting this up

#

I just need help setting it up I know how to solve it

silent plank
#

express the missing side of the small triangle in terms of x, applying segment addition postuate

odd blade
#

So since I gotta find both x and y

#

I am first going start with x

#

Can I do 42 divide by 2?

silent plank
#

dividing 42 by 2 won't really help you

#

express the length of that red line in terms of x

odd blade
#

So what can I do

silent plank
#

applying segment addition postuate

odd blade
#

35

#

Because it’s the same length !

#

So the red line is 35

silent plank
#

no

odd blade
#

Oh

silent plank
#

you aren't told anything about it being an isoscles triangles

#

right now we're only focusing on the very left part of the diagram

odd blade
#

I am only given 42 do

silent plank
#

and x

#

right now, without setting up more equations,
you should be able to get an expression for the red line in terms of x,
and then continue from there

odd blade
#

42x?

silent plank
#

no

odd blade
#

I got no clue

silent plank
#

black line has length :a
mango line has length: b
what's the length of the green line?

odd blade
#

A+b?

#

Sorry this my weak spot

silent plank
#

lowercase a but yes

#

basics of addition

#

similar idea for your question

odd blade
#

But Idk what x is

#

Can you show me how to solve it then I can use it as an example to solve my next problom

#

?

silent plank
#

x + red = ?

#

doesn't matter if you don't know what x is

#

thats your end goal

odd blade
#

My end goal is to find x and y

#

40 over x equal 14 over 35

silent plank
#

where are you getting that?

odd blade
silent plank
#

what do x, 40 , 14, and 35 have anything to do with each other?
also you haven't responded to my previous question

#

x + red = ?

odd blade
#

Equal y?

silent plank
#

no

#

focusing only on the left side of the diagram

#

only on this:

#

ignore everything else for the question i'm asking

odd blade
#

I am so confused

silent plank
#

properties of addition...

#

going back to this example

#

if you join a line of length a together with a line of length b,
you'd get the green line of length a + b right?

odd blade
#

Yes

silent plank
#

similarly here, you'd have x + red and you are told that the combined lengths of those segments is 42.
so what I was looking for was simply:
x + red = 42

odd blade
#

Oh I se

silent plank
#

and then:
red = ?

#

and like before apply proportionality and properties of similar triangles

odd blade
#

I am confused can you like show me an example with numbers

#

Like the problom I posted if you can help me solve it I can use it as reference

silent plank
#

x + red = 42
subtracting x from both sides; red = 42 - x

odd blade
#

So

#

42-x?

silent plank
#

would be the length of the segment i marked in red

#

you could setup an equation like before

#

however you could apply:
$$\frac{x}{42} = \frac{14}{14+35}$$
here, which is simpler

odd blade
#

?

silent plank
#

bot lag

somber coyoteBOT
odd blade
#

I see

#

I get the first one

#

So that’s for x

#

How in the world do we figure out y

silent plank
#

properties of similar triangles

#

corresponding sides will be in the same ratio

odd blade
#

I just replace the x with y-11?

silent plank
#

no

odd blade
#

Y-11 over 40 14/35

silent plank
#

not quite

odd blade
#

Hmm

silent plank
#

what's the side length of the right side of the larger triangle?

odd blade
#

The 45+14

#

35

silent plank
#

35 + 14 yes

#

hence applying ratio of corresponding sides:
$$\frac{y-11}{40} = \frac{14+35}{35}$$

somber coyoteBOT
odd blade
#

Thanks

#

Wait ramnov

#

Last question

#

What do I do if I don’t have the whole length ?

#

Take look at that example

silent plank
#

you're given that the whole length is x

#

and you can use that to set up an equation

#

solving that will get you the value of x

odd blade
#

So I got x over10

#

And 15 over 24

silent plank
#

you're not applying your ratios properly

odd blade
#

Oh I see

#

Is it 10/15=x/33

silent plank
#

no

odd blade
#

Wait 33/15

silent plank
#

write out full equations

#

also still doesn't lok right

odd blade
silent plank
#

that's incorrect

#

why are you using 33?

odd blade
#

You mean I have to use 24?

silent plank
#

what you use depends on everything else being used

odd blade
#

Replace the 33 with 24?

silent plank
#

no

#

x/10 is the ratio of one of the longer sides to its corresponding shorter side

#

hence what its equal to would have a similar setup

odd blade
#

The shorter side is 15 and 24

silent plank
#

wdym and 24

#

it can't be both 15 and 24

odd blade
#

Oh

#

Wait

#

I add

#

15 and 24

silent plank
#

yes

odd blade
#

And it’s 39

#

Over 15

#

!

silent plank
#

yes

odd blade
#

Yyeyegsgs

silent plank
#

x/10 = 39/15

odd blade
#

I start to get it now

#

What do I do about the y in middle do to find y there is no corresponding

silent plank
#

don't pick random values just because they're there

odd blade
#

I see the pattern now

silent plank
#

from similar triangles, 2y-3 corresponds to the line its parallel to
(the line with length 33)

odd blade
#

And 24 is parlele to 26?

silent plank
#

where's 26 coming from?

odd blade
#

It’s the z

#

X

silent plank
#

the only lines parallel here are the lines being marked as parallel

#

(marked by those arrows)

odd blade
#

So it’s 15

#

Instead of the x

silent plank
#

what's it

odd blade
#

2y-3over15 equal 24over33

silent plank
#

write full equations and the context in which you're using values

#

ugh use () and / instead of the word over

#

hard to read af

odd blade
#

I just use a picture

silent plank
#

incorrect

odd blade
#

It is ??

#

I see the 33

#

It’s 10 instead of 33

silent plank
#

don't pick random values just because they're there

odd blade
#

10 is parallel to 15

#

Ye I see because 33 dosent have a parralel

silent plank
#

you're not using the word parallel properly

odd blade
#

Oh

#

Paraelel is the one across from it right

silent plank
#

the only lines parallel here are the lines being marked as parallel
(marked by those arrows)

#

specifically the lines with lengths (2y-3) and 33

odd blade
#

I see

#

So those 2 are correct

#

10 and 15?

#

Because look at the arrow

silent plank
#

depends on how you're setting up your equation,
write the whole thing

odd blade
silent plank
#

still no

odd blade
#

Where is incorrect

silent plank
#

try describing in words what your ratios represent

odd blade
#

So the 10

#

Shoes half part of the large side

silent plank
#

depends on your intentions

odd blade
#

I am trying find y atm

upper karma
#

how can I do this

silent plank
#

(2y-3)/10 is the ratio of 2 adjacent sides of the small triangle
15/33 is the ratio of one of the sides of the small triangle and another side of the large triangle
setting them equal to each other doesn't make sense

odd blade
#

I see

#

So that why 15 and 33 are not correct

#

They are other sides

#

Then what whould it be

silent plank
#

there are multiple options

#

do you have highlighters?

odd blade
#

What are one of those

#

Not on me atm

silent plank
#

or multicoloured pen
or snipping/editing tool on the computer

odd blade
#

I got a pencil

silent plank
#

it may help if you colour/shade the edges of the small triangle,
and larger triangle

odd blade
#

I just don’t know where to place the numbers since the y is in the middle

silent plank
#

well (2y-3) is the length of a side in the smaller triangle right?

odd blade
#

Like in the middle ye

silent plank
#

33 is the corresponding length of the larger triangle

odd blade
#

So it matches up with the 2y ye

silent plank
#

the ratio of the two: (2y-3)/33
will have the same ratio as the lengths of another smaller side and its corresponding longer side

odd blade
#

But the question is where is one of those 2 numbers

silent plank
#

well you have 2 options for the smaller sides

#

both of which were initially given

odd blade
#

What were those

#

I gotta pick from 15 10 24

silent plank
#

10 or 15,
the other sides lengths of the smaller triangle

#

24 is not the side length of a triangle

odd blade
#

So 24 is not in this equation at all

silent plank
#

i didn't say that

odd blade
#

So there could be a possibility

silent plank
#

it 'could' be depending on your choices

#

if you chose the 10, the corresponding side in the larger triangle will have length x which you found to be 26
if you chose to use the 15, the corresponding side will have length (15+24)

odd blade
#

I see

#

I get it now

#

If we choose the 15

#

It be 15+26

#

Wait no so how will I set it up then

#

I got the 39/33

#

What is below the y

silent plank
#

repost the image

odd blade
silent plank
#

why are you adding 15 and 26?

odd blade
#

I meant 24

silent plank
#

still no

odd blade
#

The 39 is in wrong place ?

silent plank
#

its not about whether one value is in the wrong place

#

its about the relative positions of everything

odd blade
#

Can you post how it whould look like I think now I am confusing my delft

silent plank
#

well (2y-3) is the length of a side in the smaller triangle right?
33 is the corresponding length of the larger triangle
the ratio of the two: (2y-3)/33
will have the same ratio as the lengths of another smaller side and its corresponding longer side

odd blade
#

Self and over complicating it

silent plank
#

pink/purple = green/red = mango/blue

#

alternatively you could also do stuff like
pink/mango = purple/blue
pink/green = purple/red
etc

odd blade
#

15 and 15+24

upper karma
#

bruh mango more like papaya

silent plank
#

identify which sides correspond to each other and set up the appropriate ratios

upper karma
#

mango is more yellow

silent plank
#

well here that's the colour of my gmo mangos

odd blade
#

What does corospomding mean

#

I still don’t get it can you show me an example with like the numbers like you did last question

silent plank
#

pink/purple = green/red = mango/blue
replace colours with the indicated side lengths

odd blade
#

Is the y going to be under 33 or across

silent plank
#

wdym?

odd blade
#

Like when we set it up is it going to be below it

silent plank
#

wdym

odd blade
#

2y-3/33

silent plank
#

as long as its consistent with everything else it doesn't matter

#

$\frac21 = \frac21$ is just as valid as $\frac12 = \frac12$

#

it all depends on what you're setting it equal to

#

also please use sufficient parentheses

somber coyoteBOT
odd blade
silent plank
#

no, that would be incorrect

odd blade
#

How will it be set up then

silent plank
#

pink/purple = green/red = mango/blue

odd blade
#

I did that do the pink 2y the purple 33

silent plank
#

*2y-3

#

and for the right side?

#

you had a choice of green/red or mango/blue

odd blade
#

10

silent plank
#

what's that supposed to be for?

vestal pendant
#

x = (60 + 90)

silent plank
#

that would be incorrect.

vestal pendant
#

or would i need to do

#

x = (60+90+30) as thats the 3rd angle

silent plank
#

would also be incorrect

vestal pendant
#

how would i do it

silent plank
#

angle sum on a line?

vestal pendant
#

oh so

#

wait

#

x + 60 = 180?

silent plank
#

yes

odd blade
#

I swear the god if this is not it

#

I am going to kill my self

vestal pendant
#

oh

#

thx

silent plank
#

your ratios are still incorrect

#

also that sort of mentality is not welcome here

#

pink/purple = green/red = mango/blue

odd blade
#

Sorry

silent plank
#

green = ?

odd blade
#

Green is 15

silent plank
#

red = ?

odd blade
#

15+24

silent plank
#

green/red = ?

odd blade
#

Which is 33

silent plank
#

what's 33?

odd blade
#

The purple

#

33

silent plank
#

i didn't ask for the purple yet

#

green/red = ?

odd blade
#

33

#

39

#

I mean

silent plank
#

those are two different values

#

neither of which is the value of green/red

odd blade
#

39

#

Oh

#

What is it then

#

Because green is 15

silent plank
#

the numerical value of green/red can be obtained by substituting green and red with the numerical values you just stated

odd blade
#

Can you please show me with with numbers

#

Then I can do another example I just need a reference

silent plank
#

if $\green{\text{green} = 15}$ and $\red{\text{red} = 15+24}$, is it not clear that:
$$\frac{\green{\text{green}}}{\red{\text{red}}} = \frac{\green{15}}{\red{15+24}}$$

somber coyoteBOT
odd blade
#

How can I have 15 twice

silent plank
#

wdym

odd blade
#

It says green

silent plank
#

and...?

#

15 is the numerical value of the length of the green line

odd blade
#

Oh I seee

silent plank
#

...

odd blade
#

So the bottom it he 33

silent plank
#

just like how (2y-3) is the value of the length of the pink line
33 is the length of the purple line
and you didn't seem to have an issue with those two

#

$\frac{2y-3}{\text{"blank"}}$???

odd blade
#

So I am right 33 goes below the 2y

silent plank
#

*2y-3

odd blade
#

Ye

silent plank
#

if the other position and values of everything else remain the same, then yes

odd blade
#

Yessss thank you

somber coyoteBOT
upper karma
#

is this correct?

merry gorge
#

Anyone here to help me

#

?

round isle
#

why don't you label that picture

#

the answer pops up

hoary trellis
west basin
#

volume of a trapezoidal prism

umbral snow
#

Area of the trapezoid multiplied by the length

upper karma
#

Heya, would anybody be willing to jump into my dms and help me with just a little bit of geometry?

west basin
#

you could just post it here

#

and well help

upper karma
west basin
#

looks like you already got some decent working for the first part

#

(3x+8)*2=2x+24

#

just solve for x

#

and substitute back into 3x+8

upper karma
#

Ok but it would all cancel out right?

west basin
#

what do you mean>

upper karma
#

Oh hold on I think I’ve got it

west basin
#

you can solve for a nice solution

upper karma
#

So the answer to 24 would be 12 + 8?

west basin
#

6+8

#

x = 2

upper karma
#

I got x = 4

west basin
#

thats wrong

upper karma
#

Oh ok thanks

west basin
#

you can basically do all them the same way

upper karma
#

Thanks a ton that’s really helpful

west basin
#

2(3y-5)=4y+2

#

for 25

#

and for the solution you want 1/2 the length of HJ

upper karma
#

I was doing 25 but I think I did something wrong

west basin
#

yes

#

you did

#

you need to subtract 4y from both sides

#

not add

#

so its 2y=12

upper karma
#

okie thx

#

Yikes I got -35 + 1 for question 26

west basin
#

7z-1=2(4z-3)

#

z = 5

#

not negative 5

upper karma
#

Thanks your the best

west basin
#

np

upper karma
#

Ok last question I promise but I don’t understand 3-5

west basin
#

mid segment is half of the base

#

the base is the line parallel to the midsegment

#

for for 3 its legit just 26/2

upper karma
#

But how do we know it’s half of 26?

west basin
#

because its the mid segment

#

and its half the base

#

and the base is 26

upper karma
#

So what am I dividing by for 4?

west basin
#

multiplying by 2

#

instead

#

lmao

upper karma
#

Ah ok that makes sense

west basin
#

and for 5

#

its the midsegment so

#

it divides the sides it touches in half

upper karma
#

So x is also 6?

west basin
#

yes

upper karma
#

Ok thank you sm for helping me tonight I really wouldn’t have been able to do it without you

west basin
#

im sure you could have

#

but np

oak stag
#

yall I need so much help😭

#

Inverse variation and hyperbolas

#

My teacher did not explain it well. He's great usually but I had no idea what he was on about today

#

I'm going to send through some questions

#

Ignore highlight, that's just something the previous owner of the textbook did

dark sparrow
#

,rccw

somber coyoteBOT
dark sparrow
#

so the unspoken assumption here is that unit cost varies inversely with number of boxes produced?

oak stag
#

yep!

#

I have a, b and c

#

(although a I was iffy on)

#

D is my main problem atm. Hyperbolas make no sense to me skdjfk

upper karma
round isle
#

what do you need help with?

upper karma
round isle
#

well number 1 asks you to plot points

#

so, I suggest you do that

#

position vector is just a vector that goes from the origin to the given point

upper karma
#

I don't get it

round isle
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what grade are you in?

upper karma
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9th

severe hinge
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Bruh

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@upper karma Just plot from (0,0) to the given coordinates

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That’s where your vector ends

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In this case, vector is just a line

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Just draw a line connecting the points

upper karma
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anybody remember how to prove brahmaguptas formula given herons formula? I'm tutoring someone, and that's a question and I don't remember how

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I'm also really tired and don't feel like deriving it rn

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if nobody remembers I'll just go ahead and derive it

upper karma
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nvm ima just go ahead and derive it myself

severe hinge
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Lol

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Sorry

upper karma
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It's fine, I was just being lazy, and couldn't find it online

severe hinge
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Yeah I didn’t know the answer anyway

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I haven’t heard of those formulas

brittle gyro