#geometry-and-trigonometry

1 messages Ā· Page 296 of 1

upper karma
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Thank you so much šŸ™‚

wraith drum
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I have a question:
Let S be a triangle on a co-ordinate grid with vertices (x_1,y_1),(x_2,y_2),(x_3,y_3) , and Q=(x_q,y_q) be a point inside the triangle. Let R=(x_r,y_q) be a point on triangle S such that x_r is maximum, let P=(x_p,y_p) be a point anywhere on the triangle, and let "theta" be the angle PQR, and the length of the line segment PQ be "d", if the function f(x) is defined such that d=f(theta), then what is this function?

twin prawn
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The way this question is phrased seems to suggest that there's an easy formula for the function, but I'm under the impression that might not be the case after drawing a sketch

wraith drum
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it's okay

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i worked on this for 6-7 hours now

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i want to cry

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https://www.desmos.com/calculator/bukr2zhy17

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that is all i could do

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i managed to work out point R

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and the black bit at the top is the "d" value for the bit b/w P2 and the purple point

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which is point R

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that is correct

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AA theorem is a valid answer

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OMN=RPQ, and MON=PRQ

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angles

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so they are similar

silent plank
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2 pairs of corresponding angles will be equal

arctic vortex
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how much square feet do you need for a chicken

dark sparrow
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thonk wat

arctic vortex
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nvm i figured it out

dark sparrow
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so your animal is a chicken?

arctic vortex
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no i changed it to a horse

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but i dont understand what #2 is telling me

dark sparrow
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how many horses are you building your enclosure for?

arctic vortex
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1

dark sparrow
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okay, so you need an area of 4500 ft^2

arctic vortex
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20250000 ft

upper karma
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not really

dark sparrow
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no

upper karma
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it's not (4500 ft)^2 but 4500 (ft)^2

dark sparrow
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i did not say (4500 ft)^2 and even that AREA would not be equal to a DISTANCE of twenty million feet and change.

arctic vortex
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oh

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418 meters

dark sparrow
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no what the fuck

arctic vortex
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418.1

dark sparrow
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do you not understand the distance between length and area

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feet vs square feet

arctic vortex
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yes

upper karma
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it's the radius of the earth

dark sparrow
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yes as in "yes i do not understand the difference"?

arctic vortex
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no yes i do understand the difference

dark sparrow
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anyway, #2 is asking you to sketch three rectangles which don't have the same dimensions but which each have an area of 4500 square feet

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and to calculate the perimeter for each one

arctic vortex
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ohh

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ok

dark sparrow
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the dimensions can be anything you want so long as the area is right

arctic vortex
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so i just find stuff like x * y and y* z = 4500

dark sparrow
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no. three rectangles, not three lengths.

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for example, you could have a 1 ft by 4500 ft enclosure.

arctic vortex
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oh

dark sparrow
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or a 150 ft by 30 ft enclosure

arctic vortex
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so i could do 2 * 2250

dark sparrow
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sure

arctic vortex
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ok

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wow you are a genius

dark sparrow
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how nice of you to label me a genius for essentially repeating what the problem states, almost verbatim

arctic vortex
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yeah

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well i did these

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shape_2 wont load :(

dark sparrow
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uhhhhhh can you screenshot lmao

arctic vortex
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o ok

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nvm this site is bad

dark sparrow
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if you really want me to make you check your own work

arctic vortex
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yeah

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wait where do i create my rectangles agin

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again

dark sparrow
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wym where

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you're overthinking it

arctic vortex
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?

dark sparrow
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i don't know, is it?

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is the area of this rectangle 4500 square feet?

arctic vortex
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yes

dark sparrow
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then what's the issue

arctic vortex
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also this one

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oh

dark sparrow
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is the area of this rectangle 4500 square feet?

arctic vortex
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yes

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o no nvm

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do i just paste this in

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my #2 question now

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@dark sparrow

dark sparrow
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yes

arctic vortex
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ok

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o yeah i do

dark sparrow
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see how you managed to answer your own question with just a little bit of thinking about it

arctic vortex
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yay

meager rapids
arctic vortex
arctic vortex
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never mind i think it is right

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@dark sparrow can u check my finished assignment

dark sparrow
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4500 feet as its area

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here we go again, with you seemingly still not understanding that FEET are for LENGTH while SQUARE FEET are for AREA

arctic vortex
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ohhhhhh

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ok i will change that

meager rapids
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Someone check my question above qurax

arctic vortex
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i would help you but i dont know the midsegment formula

meager rapids
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Ah ok

arctic vortex
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isnt the midsegment the average between b and c | a

silent plank
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x looks fine
what about your calculations for z

arctic vortex
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here is my assignment @dark sparrow

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can u check it also sorry for ping

dark sparrow
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augh what is this

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is this another thing

arctic vortex
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no

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the same thing

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but its in pdf

dark sparrow
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okay so since when did we require that the dimensions of our enclosure be whole numbers

arctic vortex
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i thought that it wasnt allowed

dark sparrow
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you thought that what wasn't allowed?

arctic vortex
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not having whole numbers

dark sparrow
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why?

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a square with sides 67.1 ft long will enclose the necessary area (even going a couple of square feet over) but have a perimeter of 268.4 feet, which is less than your 270.

arctic vortex
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oh

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ok ill change that and find the smallest

dark sparrow
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i mean good luck ig

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your method is basically guess and check

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which is garbage

arctic vortex
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whats the formula to find it then

dark sparrow
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ah here we go again, the "what's the formula" mindset

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honestly ive had enough of this lol

arctic vortex
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o

upper karma
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Develop some intuition, figure out the formula on your own.

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Doesn’t help you to learn how to eat if the other person is holding the fork.

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Hence, your parents stop feeding you at a certain age.

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So get some muscle

arctic vortex
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ok i will find the formula

upper karma
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ok

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If you need help, just post the question and I’ll help you derive said formula.

arctic vortex
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ok

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i did the formula and i got 67.08 @upper karma is this correct?

upper karma
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For which question

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And which formula did you use

arctic vortex
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p = 2x+2(4500/x)

upper karma
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Is that a question?

arctic vortex
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and to find the smallest perimeter using the area

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square feet*

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and the square feet is 4500

upper karma
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Ok

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welp

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uhh

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Is the area part of a given shape?

arctic vortex
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no

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so like the square feet is 4500

upper karma
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Because if not then the smallest perimeter given the area is a circle

arctic vortex
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and i need to find the smallest perimeter

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and it is a rectangle

upper karma
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Ok then it is part of a given shape

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Where did you get said formula that you used?

arctic vortex
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youtube

upper karma
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B a d

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I mean that’s ok but next time try to derive it

arctic vortex
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ok

upper karma
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So the question is like: ā€˜find the smallest perimeter given x area’?

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And it has to be a rectangle

arctic vortex
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yeah

upper karma
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Ok well...

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If the perimeter you gave is in fact the smallest for the given area, how do you know it’s correct?

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Like how can you trust the formula? Did they explain it?

arctic vortex
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i watched that video

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and i watched another one

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and both of them use the same formula

upper karma
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Ok, did they explain how it worked?

arctic vortex
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no

upper karma
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That’s sad

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What’s the formula?

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I need to know how it works before I am ok using it

arctic vortex
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p = 2x+2y then i did y=4500/x then i removed that x then i did p=2x+2(4500x/)

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then i did p=2x+900/x

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then i did p=-900/x^2

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9000*

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then i did x^2=4500

upper karma
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thonkzoom so their formula is just formula for a perimeter then

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Which is self explanatory

arctic vortex
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yes

upper karma
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And given one side it’s a series of algebraic manipulations to find the other... not too hard then

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Do you have a picture of the shape?

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Or the question

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I’m going to do it and then we compare answers

arctic vortex
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ok

upper karma
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So pictur of question?

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Or just describe it

arctic vortex
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here is the pdf

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#4 and #5

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@upper karma

upper karma
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It gave you the answers, you want to know how it got to them?

arctic vortex
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no those are the wrong answers

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i think its 67.08

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for the size

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can u tell me ur answer then we will compare

upper karma
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they’re the wrong answers thonkzoom ?

arctic vortex
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yea

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i put them myself

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but they are wrong because i did not acknowledge decimals

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so im asking if you could solve it

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and then we will compare

upper karma
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uhH decimals

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perhaps

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What are your dimensions?

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For the rectangle after you gave decimals

arctic vortex
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4500 square feet

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and the smallest was 750 * 6

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of my examples

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but i need to make the smallest

upper karma
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uhh

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Well

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60*75 is pretty dang small...

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But they said incorrect

arctic vortex
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yeah

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67.08 as the length would be 268.32

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@upper karma

upper karma
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hmm

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Yea probably

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Turns out that’s the square root of 4500

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Wow am I a dingus

arctic vortex
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yeah

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wait

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is it wrong

upper karma
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don’t think so

arctic vortex
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bc i just submitted it lol

upper karma
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Well idk m8

arctic vortex
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but i think its right

upper karma
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I do too

arctic vortex
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:D

upper karma
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flonshed sorry

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Today I am a dingus

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Square root ensures all sides same length... long as they don’t give you a side length it’s good

arctic vortex
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yeah

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ok thanks

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:D

upper karma
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šŸ™‚

hollow tiger
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I'm having trouble with this problem:

A right pyramid SABCD (AB = 12) has an inscribed sphere in it with O as its center, and has an altitude of SH. M is the midpoint of AB. The pyramid OHMA has a circumscribed sphere around it, and its radius is equal to the previously mentioned one. Find SA
I feel like I'm so close to figuring it out but I just can't
I can send the geogebra thingy I made for easier presentation: https://www.geogebra.org/3d/evxdqqrj

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(I chose an h that would be close enough to what I did with sliders, I didn't actually find it)

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I figured out that the OAH angle should be 30° and found the radius

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I also have an equation: h^2 = x^2 - 72 (h being the altitude, and x is SA)

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I feel like I need to find the ratio of h and x using the angles or something, but I just can't seem to find how

arctic vortex
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@upper karma what occupation would knowing quadrilaterals be important

upper karma
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In general knowing them will benefit you I guess

arctic vortex
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o ok

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thanks

upper karma
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I mean I use them a lot... but idk really flonshed

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Np

finite vigil
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Hey

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I need help w this

eternal crag
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what have you tried?

upper karma
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@finite vigil don't ghost ^ sadcat

finite vigil
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I don't know how to solve it at all

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someone was just giving me answers

eternal crag
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this is not chegg you lazy cow

finite vigil
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?

upper karma
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That's not an honest thing at all

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It will affect yourself negatively, mind your actions.

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someone was just giving me answers
Damn

finite vigil
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ik

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can someone help me tho

upper karma
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I'm partly glad thay you decided to try understand instead of blusting it and pass the homework with a hole of knowledge

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$s=r\cdot \theta$ where $\theta$ is on radians

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@finite vigil

somber coyoteBOT
upper karma
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Pretty much it

finite vigil
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I have no idea

upper karma
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On what?

finite vigil
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Like

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How to do it

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could u walk me through it

upper karma
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@finite vigil you have the radius, you have $\theta$ on angles, all you have to do is put it in radians

somber coyoteBOT
upper karma
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And plug it into the formula above

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To put into radians basically, you should blatantly know what 90° is on radians, if not, $90° \cdot \frac{Ļ€}{180°}=$your desired $\theta$ on radians

finite vigil
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Ahh

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I don't know

somber coyoteBOT
upper karma
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You don't know what? All good now? @finite vigil

vale herald
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@finite vigil copy and paste the question

finite vigil
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ok

upper karma
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Don't do it wtf

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Are you really gonna post your pictures with no context again and i still don't know what you did on the one before?

vale herald
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yo Hannah

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do u know what the question is asking for?

finite vigil
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no

upper karma
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...

vale herald
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so its asking for

finite vigil
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Idk I'm fucking stupif

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kms

upper karma
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Are you really gonna post your pictures with no context again and i still don't know what you did on the one before?
.

finite vigil
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......

upper karma
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I'm out.

finite vigil
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I'm sorry..

vale herald
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uh its asking for the angle for this side

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the answer is already there

finite vigil
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....

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I'm gonna fail...

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Fuckk

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My Dad is gonna be so pissed at me

upper karma
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i feel bad

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yall finna help her or

eternal crag
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i don't think they have the correct attitude to accept any help other than be guided through completely

upper karma
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@eternal crag so that means you cant help

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like how yall gon start helping

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and if she doesnt understand

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you just give up

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what part would attitude be put into that

eternal crag
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are you stupid or don't know how to read? al3dium gave a formula, she replied "I don't know", al3dium then ask for clarification on what she doesn't understand, to which she then replied: "idk i'm fucking stupif" and "kms"

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what the fuck are we suppose to do?

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you tell me

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should al3dium try to clear any confusion without knowing what the confusion is?
should al3dium just give the answer?

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that doesn't mean i can't help, that means i'm unwilling to, i think the other party is not trying hard enough because she refuse to tell us what she doesn't understand

upper karma
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someone should ask

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rather than saying

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"im out"

eternal crag
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someone should ask
al3dium did, and he is not going to do it again

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i don't know what to tell you

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are we suppose to chase people to work hard?

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nobody has the time to do so, helpers don't get paid here

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either they're going to do some think on their own and show some efforts, or there is no point to continue

wind imp
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i feel like if you do not wish to help, that's perfectly fine! however, i would say that insulting people and vehemently arguing against helping might be more the opposite of helpful and could prove detrimental to the atmosphere, especially if someone else is happy to try and reach out/be understanding

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yeah i got mad respect for yall i think it's a really cool thing that you're doing (and people can def be hard to interact with sometimes)

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oof that sucks

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also i missed a comment and would like to add that if anyone feels bad they could consider helping instead of expecting others to do it for them?

wind imp
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uh that was not at you at all, that was in response to the person who kind of started the end of the above conversation which made me realize i wasn't exactly very fair in my first message. now i admit i probably shouldn't have said anything in the first place. so i apologize for making this more messy than it already was

upper karma
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Yea

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What do u need

gloomy slate
upper karma
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@gloomy slate

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Ok

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Yes just search up a bunch of theorems

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And watch YouTube videos

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Or use google

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Pretty easy

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@gloomy slate

gloomy slate
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oh nice thanks man

upper karma
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...

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Nice advice lol

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Use cosine law

gloomy slate
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lol

fading zinc
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hey

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if nobody is in the middle of a question

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Id like to ask one

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Im not quite sure how I calculate the perimeter of this shape

mossy plinth
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How do you simplify,
tan(2t+pi) ?

upper karma
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Use the fact that $\tan(u+kπ)=\tan(u), k\in \bZ$

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@mossy plinth

somber coyoteBOT
mossy plinth
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wait, so 2t = u in this case, whereas k = 1?

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so tan(2t+Ļ€) = tan(2t)?

upper karma
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@mossy plinth yes.

mossy plinth
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Oh, thanks.

upper karma
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Np.

wraith drum
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@mossy plinth if you want, you could use double angle tangent

fading zinc
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what happens if i rotate a shape 180 degrees?

upper karma
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@fading zinc just think about it

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pretty much common sense

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or idk

glacial haven
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if you rotate a shape 180 degrees then it’s rotated 180 degrees

upper karma
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yep

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exactly

glacial haven
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not much to say

finite sky
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In this question, it is asking which lines are parallel

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but im confused why isnt the 68 equal to 64?

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I feel it might be a textbook mistake

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cause answers are

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DE ll GF ( alternate angles are equal)
DG ll EF ( alternate angles are equal)

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:/

silent plank
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only DE || GF

finite sky
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Maybe textbook has mistake

silent plank
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<DGE and <FEG are alternate angles but aren't equal thus DG and EF aren't parallel to each other

finite sky
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okay

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thANKS mr

hollow tiger
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hey um
I'm kinda having trouble with this equation
I feel like I know how to start but I have no idea what to do next šŸ¤”

cinder portal
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let sin(x) = a, cos(x) = b

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you might see something familiar

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if you don't, ping me

hollow tiger
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@cinder portal yeah that's the thing, I did something similar to this and got a simpler(?) equation, but I don't really see what to do next šŸ¤”

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now I have this:

2a/b = b^2 * (1 - (a/b)^2) * (9(a/b)^2 + 4 * (a/b) - 3)

royal edge
upper karma
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What is this

arctic vortex
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can anyone help me with some geometry questions??

upper karma
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Sure

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Just post

arctic vortex
#

k

upper karma
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What have you tried

arctic vortex
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i dont know how to get the measure of triangles

upper karma
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Angle BDC

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Im giving you a hint

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AB is parallel to DC

arctic vortex
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i still dont get it

upper karma
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Properties of angles and parallels?

arctic vortex
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no how to get bdc by parallel lines

silent plank
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do you know how to identify stuff like:
alternate angles, (interior/exterior variants)
corresponding angles
vertical angles

upper karma
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no how to get bdc by parallel lines
Opposite sides of a parallelogram are always parallel

arctic vortex
#

yes

upper karma
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How are <ABD and <BDC called?

arctic vortex
#

triangles

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180 degrees

upper karma
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<means angle

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Are they vertical, alternate, corresponding...?

arctic vortex
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wait

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its 25

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@upper karma

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is it

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alternate angles

upper karma
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Yes

arctic vortex
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ok thank god

upper karma
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Any properties of alternate angles?

arctic vortex
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this one too

silent plank
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do some angle chasing, see what you can determine

upper karma
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What does isosceles trapezoid mean?

arctic vortex
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70

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its 70

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right

upper karma
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Do you even need our help

arctic vortex
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e=55 f=125 i=125 g=55 and 70

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yes

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io do

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wait is it 70

upper karma
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Yes

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"g=55"

arctic vortex
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yay

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no g=55 and 780

upper karma
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which g?

arctic vortex
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g=125

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but its 55 and 7

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70

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what about this one

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i dont understand it with the diagonals and variables

upper karma
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There are 2 variables

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You know that diagonals in a rectangle have the same length

arctic vortex
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yeah

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so 7x-6=3x+43

upper karma
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Yes

arctic vortex
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its 12.25

upper karma
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,w 7x-6=3x+43

somber coyoteBOT
arctic vortex
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yes

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but how do i find 3x+5

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because it would be infinite

upper karma
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Wut

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To find y you will need Pythagoras

arctic vortex
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a2+b2?

upper karma
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it says solve for x

arctic vortex
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yea

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i dont know how

upper karma
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rounded to one decimal place

arctic vortex
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i know the diagonals are 12.3

upper karma
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Aight then we done

arctic vortex
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but what about 3x+54

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3x+5*

upper karma
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That's useless

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The problem asks for x

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that's the size of AB
it doesn't ask you to solve AB

arctic vortex
#

what

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oh

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but it says solve for x

upper karma
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its 12.25

arctic vortex
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the answer

upper karma
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Yes

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Actually 12.3

silent plank
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the "diagonals" aren't ~12.3

silent plank
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you equated the two diagonals and solved for x to get a rounded value of 12.3

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what do you know about the diagonals of a rhombus?

arctic vortex
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oh wait

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i need to use a2+b2=c2

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16.76

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16.8

upper karma
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Are you even thinking about those problems or you are immediately posting them?

arctic vortex
#

16.8*4

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im immediately posting them then im solving them

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67.2

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?

upper karma
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...

silent plank
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don't round until the end

upper karma
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im immediately posting them then im solving them
@arctic vortex
don't do that

arctic vortex
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ok

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i will n-ot

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not

upper karma
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use your head

arctic vortex
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ok

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wait for a rhombus are all sides equal

silent plank
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rounding prematurely will lead to inaccurate answers

arctic vortex
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oh ok

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67

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67.02

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not rounding 16.76

silent plank
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using 16.76 is still rounding

arctic vortex
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what how

silent plank
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try not to round at all

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(until the end)

arctic vortex
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oh

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i think my teacher wants me to round

silent plank
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round at the end

arctic vortex
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ok

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if i do that then i get 67

silent plank
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you shouldn't

arctic vortex
#

rounding at the end?

silent plank
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yes

arctic vortex
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but i get 67 if i round at the end

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if i dont tehen i get 67.2

silent plank
#

specifically the length of a side is sqrt(281)
and you should enter 4*sqrt(281) into your calculator for the perimeter

arctic vortex
#

67.05

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67.1?

silent plank
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yes

arctic vortex
#

thats the answer correct

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i dont understand this one bc its like the variable one

silent plank
#

how long have you thought on this problem?

arctic vortex
#

3 minutes

silent plank
#

think for a few more

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throw all knowledge you have about parallelograms at it

arctic vortex
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ok

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4.4 repeating is X

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@silent plank i dont know

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because its repeating

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it could equal 35 or 36

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x

silent plank
#

use fractions and/or don't round until the end

arctic vortex
#

ok

#

40/9

#

8 * 40/9

#

35.5 repeating

#

320/9

#

y = 64.4

#

repeating

#

@silent plank

silent plank
#

and round that to 1dp

arctic vortex
#

NO WIAT

#

its 100

#

right

silent plank
#

wdym?

arctic vortex
#

y

#

no nvm

silent plank
#

8x + y = 100
y = 100 - 8x

arctic vortex
#

64.4

#

yeah

#

@silent plank wait its 64.4?

silent plank
#

yes

arctic vortex
charred zephyr
#

ye

#

s

arctic vortex
#

is your name sucette

#

like socket

charred zephyr
#

is your name kurax

#

like durex

arctic vortex
#

no like kurax

#

but can u help me

charred zephyr
#

on what

arctic vortex
#

this one

charred zephyr
#

DE = 72 thus EB = 72

#

Then u know what to do

#

DE = 72 thus EB = 72
easy to "prove"

#

ok

arctic vortex
#

yes

charred zephyr
#

did u get the answer

arctic vortex
#

im solving it rn

charred zephyr
#

ok

#

durex u got the answer

placid night
#

am i just being stupid

#

how am i meant to work out PQ?!!!!

azure reef
#

@placid night similar triangles

grave coral
#

similar triangles

#

or Thales

#

whatever

azure reef
#

haha i was first

grave coral
#

xD

placid night
#

oh yeah

#

im just being dumb

#

thanks guys šŸ˜‚

upper karma
upper karma
#

Seems awesome

meager rapids
#

Question asks to find ratio of TAN Z. Is it better if I leave it like that or should I further simplify to 3/4

stone adder
#

Uhh idk, but I think both are fine

upper karma
#

Simplify

#

Always

meager rapids
#

Ok

upper karma
#

Either way they’re equivalent

#

So you should be fine

meager rapids
wind vector
#

that looks about right

#

yes that's correct

meager rapids
#

Ok thanks

wind vector
#

triangle definition of trigonometric functions got me slow

#

unit circle was easiest one to remember

#

but I don't think you should learn unit circle just yet though, since you're just starting out on trig

meager rapids
#

Yeah that’s why I’m practicing rn ahead of time I struggle with this part

wind vector
#

cos Z is 24/30

#

4/5

meager rapids
#

Ah ok

meager rapids
#

I rounded to nearest tenth

silent plank
#

what was your answer?

meager rapids
#

27.4

silent plank
#

oh 1 sec, text so small

#

that's way too big

meager rapids
#

Not sure where I went wrong

silent plank
#

multiple things wrong with that

#

firstly what is h?

meager rapids
#

I just used h to represent missing side

silent plank
#

usually in the context of right triangles, h would be used to represent the hypotenuse
using it to represent something else can only cause confusion

although the question isn't phrased the best way, it seems they want you to find the side indicated by the variable x

meager rapids
#

I think I see where I went wrong I’ll re do and @ when done

#

I tried I’m not sure all I know is you use cos

silent plank
#

only just saw you stuffed your diagram too

#

relative to the 19° angle,
would x be adjacent or opposite to it?

meager rapids
#

Adjacent

silent plank
#

is x touching the 19° angle at all?

meager rapids
#

It’s not

silent plank
#

then it would be the opposite side right?

meager rapids
#

Yeah

silent plank
#

and then apply the proper trig function to find x

meager rapids
#

Ok

versed river
#

no

meager rapids
#

To explain this I need help I know it can’t be sin as im given the adjacent side

versed river
#

so you have an angle, the side adjacent to it, and you want to find the hypotenuse

#

which trig function relates those 3 things?

meager rapids
#

Cos

versed river
meager rapids
#

I’m stuck

silent plank
#

standard process:
location of the two sides relative to the angle you want to use.
which function relates those 3 things

urban egret
#

@silent plank your a beast with math man you are goals

silent plank
#

as mentioned before:

#

although the question isn't phrased the best way, it seems they want you to find the side indicated by the variable x

#

NOT the blank unlabelled side

meager rapids
#

Gotchu

rich mist
#

hello, is someone ready to help right now?

glacial haven
#

sure

#

whats giving you trouble

upper karma
#

||set sec(x)= sqrt(2)||

#

And solve

tropic tide
#

How do you find CDE

upper karma
#

@tropic tide okay

#

Are you familiar with inscribed angle theorem?

tropic tide
#

OK what is that

#

Oh is it that angle at middle is twice at circumference?

upper karma
#

That is vague, but yeah it has to do with that

tropic tide
#

Yea can't visualise it :/

#

In that problem

upper karma
#

Yeah hold up

#

Btw the angle at the center has the same measure as its corresponding measure of the arc

#

Look

#

Click on it

#

Now that part is set up.

#

The visualising part, we will look at this theorem, do you agree that $\angle{CDE}=\frac12 m\angle{CAE}$

somber coyoteBOT
upper karma
#

@tropic tide

tropic tide
#

O I see

upper karma
#

Now

#

Notice that CAE=CB+BAE

#

@tropic tide will you not answer if i don't tag or what?

#

Can you be more participative at least...

#

šŸ‘»

meager rapids
#

@ me

upper karma
#

@meager rapids yes

meager rapids
#

Ok

silent plank
#

show work

meager rapids
silent plank
#

why are you using cos?

upper karma
#

HELP anyone ??

silent plank
#

you've even labelled opp and adj appropriately on the diagram
which trig function relates the angle, the opposite side and the adjacent side?

upper karma
#

can i ask ??

silent plank
#

find an open channel

meager rapids
#

Tan

silent plank
#

yes

meager rapids
#

I got 16.1

silent plank
#

x should be less than 14

meager rapids
#

Ok let me see where I messed up

#

I got 12.2

silent plank
#

rounded to 1dp, yes

meager rapids
#

Aight thanks

fading bramble
#

i see youre supposed to keep it in terms of pi, when you do cos^-1, keep it in exact form then do 2pi- x to get your principle pair

coral dagger
#

can someone check my math

#

I have to simplify the expression: 2(2sin(x)cos(x)) (2cos^2(x)-1)

#

So first I expanded the 2 into 2Sin(X)Cos(X) and got
8Sin(x)Cos(x)*2Cos^2x-1

From there I used distributive property and got
16Sin(X)Cos^3(X)-8sin(X)Cos(X)

But then apparently the answer is 8sin(x)cos^3(x)-4sin(x)cos(x) (I've used x as the variable for theta). Idk what I did wrong?

upper karma
#

how did you get 16?

#

@coral dagger

coral dagger
#

8*2=16

#

like I expanded (8Sin(x)Cos(x)) (2Cos^2 x-1)

#

So first I got

#

16Sin(x)Cos^3x

#

and then expanded into the -1

#

And got -8Sin(x)Cos(x)

#

so combining I got

upper karma
#

i don't get it

#

how'd you get the first expression

#

8 sin(x)

#

how'd you get the 8 in there

coral dagger
#

well the original question was like

#

2(2sin(x)cos(x)

upper karma
#

yes

coral dagger
#

I expanded the two into sin and cos

upper karma
#

what does that even mean

coral dagger
#

so I got

upper karma
#

no stop

#

what does

coral dagger
#

4sin(x)2cos(x)

upper karma
#

blackmarket1156: I expanded the two into sin and cos

#

mean

#

you have

coral dagger
#

I did foil

upper karma
#

$2(2 \sin(x) \cos(x))$

somber coyoteBOT
coral dagger
#

and did distributive property

#

yes

upper karma
#

do you agree that this is equal to

#

$4\sin(x) \cos(x)$

somber coyoteBOT
coral dagger
#

why is it not

upper karma
#

what

coral dagger
#

4sin(x)2cos(x)

upper karma
#

$2(5\cdot10) = 2\cdot5\cdot10 = 5\cdot2\cdot10$

somber coyoteBOT
upper karma
#

but

#

But

#

$2(5 \cdot 10) \neq 2\cdot 5 \cdot 2 \cdot 10$

somber coyoteBOT
upper karma
#

there is no distributive property

#

this is not addition

#

$a(b+c) = ab + ac$

somber coyoteBOT
upper karma
#

$a(bc) = abc$

somber coyoteBOT
coral dagger
#

ohhh

#

Distributive property is an alhebra 1 thing right

upper karma
#

not really? it's just a "math thing"

coral dagger
#

ok I think that’s where everything went down hill

digital perch
upper karma
#

@digital perch which one?

digital perch
#

First part

upper karma
#

cos(27)?

digital perch
#

Yep

#

And sin 60

upper karma
#

Ig you aren't allowed to do it with a calc, and you have to do it with trigonometry, right?

#

Bc the instructions are unclear from what you cut off

digital perch
#

Is it clear now

sleek thistle
upper karma
#

Yeah

sleek thistle
#

am i correct here?

upper karma
#

@sleek thistle how can you not see its occupied...

#

@digital perch is it a test btw

sleek thistle
#

oh you can’t do that? 😳

#

my bad

upper karma
#

No ...

digital perch
#

No it a summer school homework

upper karma
#

Reading rules is what you should do once you enter a server ...

#

@digital perch okay

sleek thistle
#

mhm

upper karma
#

Are you familiar with the unit circle?

digital perch
#

Ah maybe idk

#

No I don't think I have

upper karma
#

Uhh how are you expected to do this? Bc i may not want me to drive you to a new method you don't know

digital perch
#

I just wanna know the basics to solving those questions and I will check in with my teacher for further clarification tomorrow

upper karma
#

Ok

#

Ig i should introduce you the unit circle

digital perch
#

K am ready

upper karma
#

Go watch it first

#

Its clearly occupied.

digital perch
#

am done

#

@upper karma

upper karma
#

Cool

#

The coordinates works like this (cos(x)), sin(x))

#

So you said you wanted the value of sin(60)

#

Look at the unit circle and find where it says "60°"

digital perch
#

yep

#

pi/3

upper karma
#

Now to find the value of sin(60) after you found the 60°, just look at the coordinate

#

No, Ļ€/3 is 60° on radians

#

We are looking at the coordinates

#

The coordinates works like this (cos(x)), sin(x))
@upper karma so you should look at the second one as you are looking for the sine not cosine

digital perch
#

(1/2,square root 3/2)

upper karma
#

Yep

#

But we want sine

digital perch
#

yep

upper karma
#

The coordinates works like this (cos(x)), sin(x))
@upper karma so which one should we take? ^

#

1/2 or $\frac{\sqrt{3}}{2}$

digital perch
#

sin(x)

somber coyoteBOT
digital perch
#

square root 3/2

upper karma
#

Yes.

#

So we know that $\sin(60)=\frac{\sqrt{3}}{2}$

somber coyoteBOT
upper karma
#

And you should leave it like that

digital perch
#

but the question said to solve to the nearest hundredth

upper karma
#

You didn't tell me that ...

digital perch
upper karma
#

Okay well

#

Whatever

digital perch
#

Lol

upper karma
#

,calc (sqrt(3))/2

somber coyoteBOT
#

Result:

0.86602540378444
upper karma
#

@digital perch ^

digital perch
#

yea

upper karma
#

The case on cos(27) is to get an approximation as it is what is asked, by typing it into the calculator

#

,calc cos(27)

somber coyoteBOT
#

Result:

-0.29213880873384
upper karma
#

Approximate correctly and you are done

digital perch
#

ok thanks for you help (man/lady) idk but thanks

upper karma
#

Man lol

#

Np catthumbsup

digital perch
#

have a great day bye

meager rapids
#

I did x=cos ^-1 (4/5)

upper karma
#

Correct but its not x, its theta. @meager rapids

meager rapids
#

šŸ‘šŸ¼

upper karma
#

yes

#

@meager rapids

meager rapids
#

Ok thanks

#

I did x=cos^-1 (6.7/8) and got that

silent plank
#

degrees to 1dp, yes.

meager rapids
#

I did 12/sin18

urban egret
#

@meager rapids your correct

meager rapids
#

Is that good?

silent plank
#

hyp is wrong

meager rapids
#

Hyp is 18

silent plank
#

thats better

#

wdym by "the same"

meager rapids
#

I meant like triangle would be similar by a shortcut

silent plank
#

yes. they will be similar

meager rapids
#

šŸ‘šŸ¼

silent plank
#

the use of "the same" implies congruency, not similarity

#

so use the proper terminology

meager rapids
#

The error would be that he would need to multiply 1.5 to both 8.25 and 18 and then divide them?

#

This person only multiplied it to 8.25 and not 18

#

Right?

silent plank
#

no

#

the error would be with how they setup the ratio

#

the algebraic manipulation being performed was actually fine

#

they should be starting with

#

$\frac{\text{length}}{\text{height}} = \frac{18}{8.25} = \frac{x}{1.5}$

somber coyoteBOT
meager rapids
#

Ok I gotchu

silent plank
#

cross multiplication is excessive

#

you only need to multiply both sides by 1.5

#

no

#

$\frac ab \times c \not\equiv \frac ab \times \frac cc$

somber coyoteBOT
meager rapids
#

Ahhh

#

Ok

#

I got 2.2 for the answer

#

Rounded to tenth

silent plank
#

its not 2.2

#

did you understand what i wrote?

meager rapids
#

I did, I multiplied both sides by 1.5

silent plank
#

no

#

you didn't

#

you multiplied one side by 1

#

which was what i was trying to point out

meager rapids
#

Oh wait I think I understand now

silent plank
#

NO

#

well i mean technically that is mathematically valid though

#

but doesn't help you

#

$\frac{18}{8.25} \times 1.5 = \frac{x}{1.5} \times 1.5 $

somber coyoteBOT
meager rapids
#

Oh that’s much cleaner

silent plank
#

$\frac{18 \times 1.5 }{8.25} = \frac{x \times 1.5}{1.5}$

somber coyoteBOT
silent plank
#

$\frac{18}{8.25} \times 1.5 \neq \frac{18}{8.25} \times \frac{1.5}{1.5}$

somber coyoteBOT
meager rapids
#

So the answer was right before (2.2) I was just setting it up wrong

silent plank
#

no

#

did you understand how to get to:

#

$\frac{18 \times 1.5 }{8.25} = \frac{x \times 1.5}{1.5}$

somber coyoteBOT
silent plank
#

no

#

otherwise you're implying x multiplied by anything is still x

meager rapids
#

Ok new answer is 3.3 now I think I get it now

#

Is that correct now?

silent plank
#

should probably use exact values unless specified

meager rapids
#

Usually it’s rounded just doing some practice to get used to it

silent plank
#

then its fine

dark sparrow
#

what's the question here

#

find the area of the grey region?

#

is there any more information given?

#

such as, do we know the big hexagon to be regular?

upper karma
#

i think it's probably hexagon is regular and semicircles

#

@upper karma do you know how to find the area of a hexagon

#

what is it

#

as opposed to irregular semicircles?

#

..so what's the area

#

uh

#

i am pretty sure that's not the area of it

#

yeah

#

yeah..

#

wait

#

so you already solved it

#

what's the problem then

#

lol

#

what does that even mean

#

"trig" is the study of triangles

#

you just said you broke it up into triangles

#

so you solved it using trig

#

lol

#

yeah no thanks, have fun tho

#

,w define trigonometry

somber coyoteBOT
upper karma
#

this actually fits

#

since equilateral triangles imply something about the angles

#

šŸ™‚

somber coyoteBOT
#

A brief description and guide on how to use me was sent to your DMs! Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

dark sparrow
#

aight so do y'all wanna clown around or do y'all wanna actually solve this problem

upper karma
#

but he said he already solved it

dark sparrow
#

@upper karma the area of a circular sector with radius $r$ and angle $\theta$ is $\frac12 \theta r^2$ (where $\theta$ of course is measured in radians)

somber coyoteBOT
dark sparrow
#

you can do some trigonometry to write down the area of an equilateral triangle as $\frac12 a^2 \sin(\pi/3)$ where $a$ is the side length

somber coyoteBOT
finite sky
#

How to find alpha

#

I know alpha is 50.

#

But i checked answers, and it says
alpha = 50 (co-interior angle, FI ll GH)

#

but its not co-interior..

#

cause 120 + 50 = 170

#

not 180?

#

help?

versed river
#

what about

#

gamma

#

you're forgetting to add gamma

finite sky
#

gamma is 10?

versed river
#

120+50+gamma=180

finite sky
#

Yeah but isnt co-interior

#

just 2 angles?

#

cause co-interior angles on paralell are adding to 180.

#

or do both

#

:/

versed river
finite sky
#

?

versed river
#

you know red and blue add to 180

finite sky
#

oh

versed river
#

so alpha+64+66=180

finite sky
#

Oh!!

versed river
#

you got it now?

finite sky
#

yeah

#

thanks

versed river
#

nw

finite sky
#

I was focusing on

#

120

#

not the top side lol

royal edge
upper karma
#

Yep.

royal edge
#

Thanks

#

Appreciate it

#

How do I convert x^2+y^2+6x-12y+20=0 into standard form?

dark sparrow
#

complete

#

the

#

square

upper karma
royal edge
#

I believe I’ve gotten (x+3)^2+(y-6)^2=5

silent plank
#

something looks off

dark sparrow
#

this looks sus

#

can you show your work

silent plank
#

specifically how did you get 5?

royal edge
#

I have to rewrite my work for it to be legible lol

dark sparrow
#

yes do that

royal edge
#

I believe there was a flaw in my work

#

I got 25

dark sparrow
#

now that's much better

royal edge
#

Thanks guys

royal edge
upper karma
#

Right triangle?

royal edge
#

They didn’t specify

upper karma
#

I see

#

First of all label the tangent points

royal edge
#

Got it

upper karma
#

Show