#Solving for t

195 messages · Page 1 of 1 (latest)

prime python
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So, I solved for t and my answer was 2. My teacher said it was 4 and I don't understand why. Can someone tell me why it should be 4 instead of 2?

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tawdry loomBOT
old hound
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4sqrt(t) = 8 my dude

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When u cancel out the the ts u only have t inside the square root in the left hand side

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not t^2

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This is why it's better to factor the polynomial tbh :p

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Wouldn't have ran into that problem if u solved t(-16t + 64) = 0

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Wait actually

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OK teeeeeeeechnically

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eh nevermind t=4 is more or less right

prime python
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so was I right or wrong to move 16 to the other side and square root it?

old hound
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No that worked too

prime python
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what do u mean by 4sqrt(t) = 8

old hound
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It's valid as long as you know the values inside the square roots will be nonnegative (and acknowledge that it removes t=0 as a solution)

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Well look at your work

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You have sqrt(16t^2) = sqrt(64t)

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Which is 4 sqrt(t^2) = 8 sqrt(t)

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You forgot about the sqrt(t) so assumed the left hand side further simplified to 4t

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Well it does but

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You end up with 4t = 8sqrt(t)

prime python
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so it should be 4t^2?

old hound
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Rather than 4t = 8

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No

prime python
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And then 4t^2 simplifies to 4t

old hound
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no :devastatation

old hound
prime python
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so i only square root t^2 and not the 4?

old hound
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Nooooooooooo

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You square root all of it

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I'm just using the fact that sqrt(ab) =sqrt(a) sqrt(b) when a and b are nonnegative

prime python
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ok

old hound
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to write sqrt(16t^2) as 4 sqrt(t^2)

prime python
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but doesnt taking the square root get rid of the ^2

old hound
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Yes

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However

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You forgot there's another t on the right hand side

prime python
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64t?

old hound
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Yeah

prime python
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wouldnt i square root 64 bc u do the same to both sides?

old hound
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You simplified the equation as 4t =8 because you forgot about the t in 64t

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Yes

prime python
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so what should it be instead of 4t = 8

old hound
prime python
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what does sqrt(t) mean? Swuare root of t?

old hound
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Yeah

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do you get why that is instead of 4t = 8?

prime python
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what does 8sqrt(t) look like written on paper

old hound
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$8\sqrt{t}$ no offense but you spelled it out yourself :p

pliant coralBOT
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992qqoloy

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prime python
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hm ok

old hound
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doesn't sound like you get it dw I'm still here to help diligentClerk

prime python
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how does the square root of 64t simplify to that

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doesnt square root gets rid of the t

old hound
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No

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Why would it?

prime python
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because on the left side

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the square root cancels out a t and then theres one left over

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why doesnt it get rid of t on the right

old hound
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So would sqrt(t^999999999999) only be t^999999999998?

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Oops

prime python
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so then what do I do with that t that stays there?

old hound
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sqrt(t) also goes by t^(1/2)

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Then divide both sides by t^(1/2) and use exponent laws to simplify

prime python
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trying to solve it

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would i do that?

old hound
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sure that too

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Is that a 4 or a t

prime python
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4

old hound
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I mean that you're dividing by

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ok yeah that's part of it

prime python
old hound
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Yup

prime python
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but my teacher said its 4 not 2 square root t

old hound
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Yeah

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Now divide both sides by sqrt(t)

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u can do this just use exponent laws

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t^(1/2) =sqrt(t) by definition

prime python
old hound
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nooooooooooo

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What is a/à ?

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Oops

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a/a

prime python
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1

old hound
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So what is sqrt(t) /sqrt(t)?

prime python
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1

old hound
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yup

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Ur left hand side is right

prime python
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ok so that got rid of the square root

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old hound
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yup

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now use exponent laws again to turn the exponent on t into a 1 hype

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catKing I believe in u

prime python
old hound
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no

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Why is t back on the right hand side

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and t^(1/2) isn't t/2

prime python
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cuz it canceled the square root not the t

old hound
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.....

prime python
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so it canceled the t?

old hound
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The symbol isn't a number

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sqrt(t) is the whole number

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$\sqrt$ doesn't mean anything

pliant coralBOT
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992qqoloy
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

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old hound
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Ok

prime python
old hound
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Yes but for the wrong reason

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t^(1/2) still isn't t/2

prime python
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half of t is t.5 whoch is t/2?

old hound
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what is (x^a)^b for starters

old hound
prime python
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doesnt the explonent mean to multiply a certain amount of times

old hound
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Only for integer values

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for rational values t^(1/a) where a is a positive integer is defined as positive real number x such that x^a = t

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And then t^(b/a) is defined as (t^(1/a))^b

spark trellis
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i got it

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i understand

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math makes me hard

old hound
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lolwat

prime python
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so it would be squarte root of t = 4?

old hound
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no

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t^(1/2) = sqrt(t) = 2

prime python
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so square root of 2 = 4

old hound
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Nooooooooooooo

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Sqrt(2) is approximately 1.44

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Because (1.44)^2 is approximately 2

prime python
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if t to the half is 2 then wouldnt the left be 2?

old hound
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What

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the left is t^(1/2)

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Nothing more to it

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Again for starters

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What is (x^a)^b

prime python
old hound
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No

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How

prime python
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u said nothing more to it

old hound
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Yeah

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Nothing more to the left hand side

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The right hand side is still 2

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You haven't made the right operation to both sides to correctly make t equal to 4

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Your manipulation was incorrect, it was just a pure coincidence that it also got you t = 4

prime python
old hound
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ye

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Again

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Pls answer this time

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What is (x^a)^b

prime python
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(x^a)^b

old hound
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Can you simplify further?

prime python
old hound
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Exponent laws

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Noooooooooo

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Well

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It is correct this time but

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Tha wn'tget you closer to solving for t

prime python
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x^a = x^a

old hound
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OK idk how you dont know this part because they teach it in algebra 1 but

prime python
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and

old hound
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It's x^(ab)

prime python
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i learned square roots in alg 2

old hound
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anyways even if you don't know exponent laws

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What is the inverse of a square root?

prime python
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square

old hound
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Yup

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So do the inverse of square root to both sides to get rid of that square root

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To pu it in rough terms I guess

prime python
old hound
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Yeah

prime python
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ok i got it

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thanks

old hound
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Wait tho you've taken alg 2 and they never did exponent laws? That's weird if so hmmCat

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Actually if they taught you logarithm laws then they should've done exponent laws too

prime python
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maybe they did and i forgot

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but wait

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u said ^1/2 cancels out a square root

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but doesnt a square cancel out a square root

old hound
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No that would get you ^(1/4)

prime python
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but ^1/2 is the same as square root

old hound
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(x^(1/2))^(1/2) = x^(1/2*1/2) = x^(1/4)

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Well yeah

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When you wanna undo division

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You wouldn't do division again would you?

prime python
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but squaring isnt dividing

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its getting rid of it

old hound
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Oh woops I misread as "doesn't a square root cancel out a square root"

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I never said 1/2 cancels out a square root either tho sully

prime python
old hound
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No

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Oml

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You divided by sqrt(t)

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Then used the law x^a/x^b = x^(a - b) with t^(1 - 1/2) to simplify the left hand side

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At least that's what I thought you thought you did but you don't seem to know exponent laws at all devastation

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Sorry but you should seriously consider brushing up on algebra 🙃

prime python
old hound
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I thought you were just crossing out all of the sqrt(t) :facepalm:

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aaaah I'm done seriously re-read a book it is def an alg 1 thing I googled it