Problem in exam | Mathematics | Page 1

exotic shoal Jun 21, 2023, 5:02 PM

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I need the other measurements from this triangle

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fossil breach Jun 21, 2023, 5:02 PM

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exam? sus

ruby nymph Jun 21, 2023, 5:02 PM

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is this an exam?

exotic shoal Jun 21, 2023, 5:02 PM

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It was from the exam

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But it's over yes

ruby nymph Jun 21, 2023, 5:02 PM

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ok

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is lengths of AB and CD all you are given?

exotic shoal Jun 21, 2023, 5:03 PM

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Yes

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Nothing more

fossil breach Jun 21, 2023, 5:03 PM

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if you notice that ABD ~ DBC

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well ABD ~ ADC ~ DBC and similarity is transitive

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if you just call some length here x then you can most likely use proportionalities and pythag to solve for x

exotic shoal Jun 21, 2023, 5:05 PM

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I don't think ABD and DBC share any similarities with each other because they're not an isosceles triangle

ruby nymph Jun 21, 2023, 5:05 PM

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ABD is right

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?

exotic shoal Jun 21, 2023, 5:06 PM

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Wdym right

ruby nymph Jun 21, 2023, 5:06 PM

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angle

exotic shoal Jun 21, 2023, 5:06 PM

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B has a right angle, so does D

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But not the line that cuts through D

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The line that cuts through D has a right angle on B

exotic shoal Jun 21, 2023, 5:07 PM

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fossil breach if you just call some length here x then you can most likely use proportionaliti...

We've not done this before

fossil breach Jun 21, 2023, 5:07 PM

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weird that it was on the exam, then

exotic shoal Jun 21, 2023, 5:07 PM

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Would you show me the steps?

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I'll try to comprehend myself

fossil breach Jun 21, 2023, 5:08 PM

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ok lets call BD = x

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then AD = sqrt(64 + x^2)

exotic shoal Jun 21, 2023, 5:09 PM

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Wait

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Yes ur right

ruby nymph Jun 21, 2023, 5:10 PM

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prove the triangles similar then use similarity to find sides

fossil breach Jun 21, 2023, 5:10 PM

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^

exotic shoal Jun 21, 2023, 5:10 PM

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ruby nymph prove the triangles similar then use similarity to find sides

I don't understand

fossil breach Jun 21, 2023, 5:10 PM

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prove that the 3 triangles in the diagram are similar?

exotic shoal Jun 21, 2023, 5:11 PM

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I don't go to an English school what does similar mean

fossil breach Jun 21, 2023, 5:11 PM

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same angles

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proportional sides

exotic shoal Jun 21, 2023, 5:11 PM

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Ohh

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No they're not similar triangles they have 90° angles

fossil breach Jun 21, 2023, 5:11 PM

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they are in fact similar

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to prove similarity you just need 2 same angles

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the right angle is 1 of them

exotic shoal Jun 21, 2023, 5:12 PM

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Then how would I get the other 2?

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Sorry am confused

fossil breach Jun 21, 2023, 5:13 PM

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wha

exotic shoal Jun 21, 2023, 5:13 PM

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No

fossil breach Jun 21, 2023, 5:13 PM

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exotic shoal Then how would I get the other 2?

look at the medium triangle and the big triangle

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they both have angle A

exotic shoal Jun 21, 2023, 5:14 PM

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fossil breach look at the medium triangle and the big triangle

The medium triangle is ABD and the big one is ACD?

fossil breach Jun 21, 2023, 5:14 PM

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yes

exotic shoal Jun 21, 2023, 5:14 PM

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Yes

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How do I get A

fossil breach Jun 21, 2023, 5:14 PM

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you dont

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just notice that they both have it as their angle

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they are also both right triangles

exotic shoal Jun 21, 2023, 5:15 PM

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Correct

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How would this information help me

fossil breach Jun 21, 2023, 5:15 PM

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so ABD is similar to ADC

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you can run the same justification with the small triangle and the big triangle

exotic shoal Jun 21, 2023, 5:15 PM

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Ooooooooohhhh

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Yeaah

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How do I proceed?

ruby nymph Jun 21, 2023, 5:16 PM

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fossil breach you can run the same justification with the small triangle and the big triangle

.

fossil breach Jun 21, 2023, 5:17 PM

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so this will most likely convince you that all the triangles are similar

exotic shoal Jun 21, 2023, 5:18 PM

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I understand

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But how do I solve the problem?

fossil breach Jun 21, 2023, 5:18 PM

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now you can use proportional sides

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remember that we called BD x and AD = sqrt(64 + x^2)

exotic shoal Jun 21, 2023, 5:19 PM

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Yess

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But we're still missing one of the measurements

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Oh wait

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Let me try

fossil breach Jun 21, 2023, 5:19 PM

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you know that the legs of ABD are in the same ratio as the legs of ADC

exotic shoal Jun 21, 2023, 5:21 PM

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AD^2 = (64 + x^2)
AC^2 = (9 + DA^2)

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Am i in the right direction

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This looks messy

fossil breach Jun 21, 2023, 5:23 PM

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yes it looks like there's a simpler way

exotic shoal Jun 21, 2023, 5:23 PM

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Yeah?

fossil breach Jun 21, 2023, 5:23 PM

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well I was thinking AB/BD = AD/CD

exotic shoal Jun 21, 2023, 5:25 PM

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That makes sense

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But we're still missing variables

ruby nymph Jun 21, 2023, 5:25 PM

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wdym

exotic shoal Jun 21, 2023, 5:25 PM

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We only have 2 known variables

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And 2 unknown

fossil breach Jun 21, 2023, 5:34 PM

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fossil breach well I was thinking AB/BD = AD/CD

8/x = sqrt(64+xx)/3
this is definitely getting ugly

exotic shoal Jun 21, 2023, 5:34 PM

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Still stuck lmao

ruby nymph Jun 21, 2023, 5:34 PM

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i got some weird stuff

fossil breach Jun 21, 2023, 5:34 PM

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24 = xsqrt(64 + xx)
576 = x^2(64 + x^2)

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ok thats a quadratic

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easily solvable

exotic shoal Jun 21, 2023, 5:35 PM

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fossil breach 8/x = sqrt(64+xx)/3 this is definitely getting ugly

Why 8/x?

ruby nymph Jun 21, 2023, 5:35 PM

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BD/AB

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wait

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no

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AB/BD

fossil breach Jun 21, 2023, 5:35 PM

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that is in fact what i said in the message i replied to

exotic shoal Jun 21, 2023, 5:36 PM

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oh

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I'm dumb

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Fuck

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Where does the sqrt(64+xx) come from

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Shouldn't it be 8/x = AD/3

ruby nymph Jun 21, 2023, 5:38 PM

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fossil breach well I was thinking AB/BD = AD/CD

cuz we defined AD as sqrt (x^2 + 64)

exotic shoal Jun 21, 2023, 5:39 PM

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Ahhhh

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My lack of sleep is showing

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Is the equation correct?

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What did I do wrong?

ruby nymph Jun 21, 2023, 5:45 PM

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you didnt do sqrt of (x^2+64)

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and you also didnt distribute the x to the 64

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in that scenario

exotic shoal Jun 21, 2023, 5:48 PM

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What does the sqrt of (x^2+64) do

ruby nymph Jun 21, 2023, 5:48 PM

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wdym what does it do

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it is the value of AD

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in terms of x if x = BD

exotic shoal Jun 21, 2023, 5:49 PM

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ruby nymph it is the value of AD

The value of AD is 64 + x^2

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Wait

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Ur right

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Now?

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ruby nymph Jun 21, 2023, 5:50 PM

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No

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The x has to be on the outside

exotic shoal Jun 21, 2023, 5:51 PM

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The both Xs right

ruby nymph Jun 21, 2023, 5:51 PM

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Or you have to multiply both by x^2

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AD is in sqrt

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BD is not

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So when you multiply

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You either transfer the x inside the sqrt and do sqrt(x^2)(64 + x^2)

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Or

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You keep the x outside and do x * sqrt (x^2 + 64)

exotic shoal Jun 21, 2023, 5:53 PM

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ruby nymph You either transfer the x inside the sqrt and do sqrt(x^2)(64 + x^2)

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So like this

ruby nymph Jun 21, 2023, 5:54 PM

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That works

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Now multiplying it out what do you get

exotic shoal Jun 21, 2023, 5:54 PM

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ruby nymph That works

I got a question

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So in an equation

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When you multiply something does it apply to everything or only once per side

fossil breach Jun 21, 2023, 5:55 PM

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like, if you have a = bc
then 2a is not (2b)(2c)

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it's 2bc

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once per side

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however if you have addition a = b + c

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then you would multiply everything

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2a = 2b + 2c

exotic shoal Jun 21, 2023, 5:56 PM

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Oh

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And division once per side too

fossil breach Jun 21, 2023, 5:56 PM

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well

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a = b/c
becomes
2a = 2b/c

exotic shoal Jun 21, 2023, 5:57 PM

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Makes sense

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My stupid ass

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How difficult is this question

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For college mathematics

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Even tho I'm in HS

ruby nymph Jun 21, 2023, 5:58 PM

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For college

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This is easy

exotic shoal Jun 21, 2023, 5:58 PM

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😐

ruby nymph Jun 21, 2023, 5:59 PM

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Assuming your HS taught you how to prove triangles are similar and factor expressions

exotic shoal Jun 21, 2023, 5:59 PM

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Nope

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I did not get taught this

ruby nymph Jun 21, 2023, 5:59 PM

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Interesting

exotic shoal Jun 21, 2023, 5:59 PM

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Might've missed a class or two

ruby nymph Jun 21, 2023, 5:59 PM

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You should get taught in geometry

exotic shoal Jun 21, 2023, 6:00 PM

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This is the first time I was doing this problem

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Yeah we have geometry

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Not this shit tho

exotic shoal Jun 21, 2023, 6:01 PM

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exotic shoal

Could I just do -64 to bring it to the left

ruby nymph Jun 21, 2023, 6:01 PM

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I would square it

exotic shoal Jun 21, 2023, 6:01 PM

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So, 8+X?

ruby nymph Jun 21, 2023, 6:02 PM

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To get rid of square roots so

exotic shoal Jun 21, 2023, 6:02 PM

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Help

ruby nymph Jun 21, 2023, 6:02 PM

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(24)^2 = x^2 (64 + x^2)

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Since square roots are taking it to power of 1/2

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We want power of one

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So we take to the power of 2 to do that

exotic shoal Jun 21, 2023, 6:03 PM

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How I do this

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By * sqrt?

ruby nymph Jun 21, 2023, 6:04 PM

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Do what

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Get rid of square root?

exotic shoal Jun 21, 2023, 6:04 PM

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ruby nymph (24)^2 = x^2 (64 + x^2)

This

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Yeah, what you wanted to do

fossil breach Jun 21, 2023, 6:04 PM

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fossil breach 24 = xsqrt(64 + xx) 576 = x^2(64 + x^2)

i already said that lol

ruby nymph Jun 21, 2023, 6:04 PM

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For example sqrt(a)^2

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= a^1/2^2

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= a ^ (2 * 1/2)

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= a^1

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= a

fossil breach Jun 21, 2023, 6:05 PM

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there's also sqrt(a^2) = a^2^(1/2) = ??? somehow absolute value gets introduced = |a|

exotic shoal Jun 21, 2023, 6:05 PM

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fossil breach 24 = xsqrt(64 + xx) 576 = x^2(64 + x^2)

I gotta take a moment to understand this

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Now i did

exotic shoal Jun 21, 2023, 6:09 PM

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ruby nymph = a^1/2^2

I don't understand this

ruby nymph Jun 21, 2023, 6:09 PM

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Just remember that taking the square of a square root cancels the square root

exotic shoal Jun 21, 2023, 6:10 PM

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Is taking the square root calculating it

ruby nymph Jun 21, 2023, 6:10 PM

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Wdym

exotic shoal Jun 21, 2023, 6:10 PM

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√9

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So it's 3

ruby nymph Jun 21, 2023, 6:10 PM

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Yea

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But for things that can’t be simplified that easily

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Sqrt(x) = Sqrt(73)

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Squaring both sides

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x = 73

exotic shoal Jun 21, 2023, 6:11 PM

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Yeap

exotic shoal Jun 21, 2023, 6:11 PM

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ruby nymph = a^1/2^2

But what is this?

ruby nymph Jun 21, 2023, 6:12 PM

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For any number a

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Taking the square root of a

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Then squaring that

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Results in a

exotic shoal Jun 21, 2023, 6:13 PM

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Oh yeah

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But why do you do that

ruby nymph Jun 21, 2023, 6:13 PM

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To show you the cancellation of the sqrt

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In your example

exotic shoal Jun 21, 2023, 6:14 PM

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How else would you solve something that has a √ in it?

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Other than to, cancel it

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Could you do ÷ √?

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And you're left with a

ruby nymph Jun 21, 2023, 6:15 PM

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Yea

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But that is the same thing

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Also cancelling

exotic shoal Jun 21, 2023, 6:16 PM

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So 4 = √9X / ÷ √
√4 = 9X

fossil breach Jun 21, 2023, 6:17 PM

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square root is not dividable like that

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it's a function

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not a number

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that makes as much sense as dividing by +

ruby nymph Jun 21, 2023, 6:18 PM

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exotic shoal Could you do ÷ √?

I thought you meant sqrt (a)

exotic shoal Jun 21, 2023, 6:18 PM

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fossil breach square root is not dividable like that

So what is the correct way to bring it to the other side

fossil breach Jun 21, 2023, 6:18 PM

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wdym by bring it to the other side

exotic shoal Jun 21, 2023, 6:19 PM

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So for the example 4 = √9X what do i have to do to get √4 = 9X

fossil breach Jun 21, 2023, 6:20 PM

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you dont

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that is not a valid step

ruby nymph Jun 21, 2023, 6:20 PM

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That’s not equal

exotic shoal Jun 21, 2023, 6:20 PM

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I see

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Another question if I had √9X it would be the same 3X right

ruby nymph Jun 21, 2023, 6:21 PM

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If it’s over only the 9

exotic shoal Jun 21, 2023, 6:22 PM

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If it's over both?

ruby nymph Jun 21, 2023, 6:22 PM

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No

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3 sqrt(x)

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We can’t guarantee x is a perfect square

exotic shoal Jun 21, 2023, 6:22 PM

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3 * √X?

ruby nymph Jun 21, 2023, 6:22 PM

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Yea

exotic shoal Jun 21, 2023, 6:22 PM

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Damn aight

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I'm pretty dum

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Well thanks for the help guys

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I wish to improve my math 😐

ruby nymph Jun 21, 2023, 6:23 PM

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You are all good?

exotic shoal Jun 21, 2023, 6:29 PM

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😃

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I got another question

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So if I have ab + 7 = 7a + b

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And i multiply by 2

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Is it 2ab + 14 + 14a + 2b

ruby nymph Jun 21, 2023, 6:32 PM

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2ab + 14 = 14a + 2b

exotic shoal Jun 21, 2023, 6:32 PM

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Yeah so by everything

ruby nymph Jun 21, 2023, 6:32 PM

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Yea

exotic shoal Jun 21, 2023, 6:32 PM

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And if I had

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√x = 5

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Could I do ^2

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And have X = 25

ruby nymph Jun 21, 2023, 6:33 PM

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Yea

exotic shoal Jun 21, 2023, 6:33 PM

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Is it the same with

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Nvm

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Thanks 👍🙏

ruby nymph Jun 21, 2023, 6:34 PM

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Np

exotic shoal Jun 21, 2023, 6:42 PM

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+close

#Problem in exam