#precalculus | Mathematics | Page 295

agile gyro Jul 16, 2021, 6:06 PM

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$G(x)=\int^x_1 f(t)dt = F(x)-F(1)$

obsidian monolithBOT Jul 16, 2021, 6:06 PM

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Syst3ms

quick bluff Jul 16, 2021, 6:06 PM

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Yes

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F(1) is constant

agile gyro Jul 16, 2021, 6:06 PM

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And so what you did was say $G'(x) = F'(x)-F'(1)$

obsidian monolithBOT Jul 16, 2021, 6:07 PM

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Syst3ms

quick bluff Jul 16, 2021, 6:07 PM

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Ah

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Got it

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Thanks a lot hype

agile gyro Jul 16, 2021, 6:07 PM

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one final note

quick bluff Jul 16, 2021, 6:07 PM

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Sure

agile gyro Jul 16, 2021, 6:08 PM

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$F : x\mapsto \int_a^x f(t)dt+\lambda$ ($\lambda$ some constant) is a sort of "canonical" look for an antiderivative

obsidian monolithBOT Jul 16, 2021, 6:08 PM

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Syst3ms

sick steppe Jul 16, 2021, 6:08 PM

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when you use lambda over c sully

agile gyro Jul 16, 2021, 6:08 PM

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so, whenever you see something like this, you can immediately go "ah, F's an antiderivative of f, so F'=f$

quick bluff Jul 16, 2021, 6:08 PM

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Okok

agile gyro Jul 16, 2021, 6:08 PM

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sick steppe when you use lambda over c <:sully:651816820122189834>

conventions, conventions

quick bluff Jul 16, 2021, 6:09 PM

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I think I get it

agile gyro Jul 16, 2021, 6:09 PM

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Whenever you're not sure, take an antiderivative and write the integral in terms of it

quick bluff Jul 16, 2021, 6:09 PM

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agile gyro Whenever you're not sure, take an antiderivative and write the integral in terms...

Ok

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Thanks once again

agile gyro Jul 16, 2021, 6:09 PM

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np

quick bluff Jul 16, 2021, 6:10 PM

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Just to verify if I got it, would F'(x) be x^2 . g(x) in the pic I gave?

agile gyro Jul 16, 2021, 6:11 PM

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correct

quick bluff Jul 16, 2021, 6:11 PM

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hype

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And if the upper bound had been x^2 it will become x^4 . g(x^2) . 2x?

agile gyro Jul 16, 2021, 6:14 PM

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yeah, that sounds right

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proper chain rule

quick bluff Jul 16, 2021, 6:14 PM

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And if the upper and lower bounds of an integration is the same it gives 0 right? kek

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Since the area at a single point will be the area of a line which is 0?

agile gyro Jul 16, 2021, 6:15 PM

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yup

quick bluff Jul 16, 2021, 6:16 PM

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Thanks for bearing with me, helped me a lot

agile gyro Jul 16, 2021, 6:16 PM

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F(a)-F(a) = 0 in other words

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np

viscid thistle Jul 17, 2021, 8:05 PM

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anyone know how to do this?

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@everyone

haughty lance Jul 17, 2021, 8:06 PM

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have you tried using the quadratic formula? (if you can't right away, what's stopping you)

viscid thistle Jul 17, 2021, 8:06 PM

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yeah i have

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i switched the sec squared to 1+tan squared and put it in the quadratic formula

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idk what im doing wrong tho it keeps saying im wrong

haughty lance Jul 17, 2021, 8:08 PM

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did you consider the interval when taking the square root?

viscid thistle Jul 17, 2021, 8:08 PM

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i didnt take a square root

haughty lance Jul 17, 2021, 8:09 PM

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how did you use the quadratic formula ?

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there's a portion thats +- sqrt(b^2 - 4ac)

viscid thistle Jul 17, 2021, 8:09 PM

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(tantheta-4)(tantheta+2)=0

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oooooooooooooooooh

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i understand lol

haughty lance Jul 17, 2021, 8:09 PM

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and the plus minus is an issue with trig stuff

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so you could easily end up in the wrong quadrant

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if one doesn't think about it

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but also, you get multiple answers if that's what you want

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depending on context

viscid thistle Jul 17, 2021, 8:11 PM

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yeah, i see

haughty lance Jul 17, 2021, 8:11 PM

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and if it's electronic you might have to account for periodicity

viscid thistle Jul 17, 2021, 8:12 PM

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im not that advanced yet

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lol

haughty lance Jul 17, 2021, 8:12 PM

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i don't know what they want you to put

viscid thistle Jul 17, 2021, 8:12 PM

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just the solution set

haughty lance Jul 17, 2021, 8:12 PM

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oh no that's just the +2πn

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some systems want that

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some don't

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i think ?

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not sure lol

viscid thistle Jul 17, 2021, 8:12 PM

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im pretty sure i got it now thanks bro

haughty lance Jul 17, 2021, 8:13 PM

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cool

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np

viscid thistle Jul 17, 2021, 8:37 PM

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can someone just tell me if they're all correct

summer knot Jul 17, 2021, 8:50 PM

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Yeah, the points should be at the same location.

viscid thistle Jul 17, 2021, 9:06 PM

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great thanks

fossil hazel Jul 18, 2021, 1:40 AM

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Someone help evaluating this integral, exact answer not decimal and with full steps

molten garnet Jul 18, 2021, 2:46 PM

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Is there an easier way of solving this

flint ingot Jul 18, 2021, 2:48 PM

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molten garnet Is there an easier way of solving this

What do you mean by "easier"?

molten garnet Jul 18, 2021, 2:50 PM

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Im currently doing the factor tree for each number

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its too long

flint ingot Jul 18, 2021, 2:51 PM

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Hm,

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I'm not sure if this would be more helpful,

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but I would solve this by writing down the first few primes (1, 2, 3, 5, 7, 11, 13) and try to see which numbers are divisible by them off the bat

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1 doesn't matter,

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2 is quite obvious (even or uneven number),

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each number and its properties

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I suppose it's a little too similar,

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let me see if I can maybe find something else

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Not quite sure if there is another method, sorry

rough carbon Jul 18, 2021, 3:04 PM

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Write all the numbers as prime factors
So (7x5)^4 * (7x2)^6 * …
Then you’ll find that powers of numbers will cancel

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I’m sure that’s what you were doing anyway though

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So I’m not really sure of a shorter way

uncut mulch Jul 18, 2021, 3:06 PM

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Im currently doing the factor tree for each number
these numbers are relatively small and have very few factors, you shouldn't need to resort to drawing a factor tree for these

molten garnet Jul 18, 2021, 3:09 PM

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hmmm

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alright

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thanks

molten garnet Jul 18, 2021, 3:36 PM

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How would apply the law of indices here when there is plus n minus>

uncut mulch Jul 18, 2021, 3:38 PM

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expand it like you would
(a + b)(c - d)

viscid thistle Jul 18, 2021, 11:12 PM

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could someone tell me if i got any wrong

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not confident with question 19

sick steppe Jul 18, 2021, 11:15 PM

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$\frac{7e^{\frac{3\pi i}{5}}}{0.5e^{\frac{\pi i}{5}}}$

obsidian monolithBOT Jul 18, 2021, 11:15 PM

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Mosh

sick steppe Jul 18, 2021, 11:16 PM

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apply power laws

viscid thistle Jul 18, 2021, 11:16 PM

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so 19 is wrong

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are the others?

subtle ore Jul 18, 2021, 11:16 PM

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20 is

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I think you may have read 9pi/8 as pi/8

wintry eagle Jul 19, 2021, 2:10 AM

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Help?

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Anyone

quick bluff Jul 19, 2021, 4:04 AM

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The 9th question

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The answers are given as B and C

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I'm able to prove A wrong and B correct

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But am not sure how to go about solving C and D

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I think I can say that D is incorrect as f(x) is increasing in (0, infinity) and therefore has no upper limit

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Here's what I have written so far

quick bluff Jul 19, 2021, 4:46 AM

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<@&286206848099549185>

fleet yew Jul 19, 2021, 8:09 AM

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Lets put C in simpler words

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For sufficiently large x, the derivative of the function is always smaller than the function

quick bluff Jul 19, 2021, 9:09 AM

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thonk ok

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magnitudes right?

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oh wait f'(x) is always positive

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im still not getting any ideas sully

pliant gyro Jul 19, 2021, 9:15 AM

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wait

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@quick bluff

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bro this question

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is more like u cant probably prove it with absolute method in exam

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but there is a more theoritical way

quick bluff Jul 19, 2021, 9:37 AM

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what is the "theoretical way"?

pliant gyro Jul 19, 2021, 9:38 AM

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look

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first of all lets not bother about that sine term

quick bluff Jul 19, 2021, 9:39 AM

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in the first derivative?

pliant gyro Jul 19, 2021, 9:39 AM

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it wont affect much when we take higher values

quick bluff Jul 19, 2021, 9:39 AM

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or everywhere?

pliant gyro Jul 19, 2021, 9:39 AM

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in every thing

quick bluff Jul 19, 2021, 9:39 AM

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ok thonk

pliant gyro Jul 19, 2021, 9:40 AM

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we basically have to prove f(x)>f'(x)

quick bluff Jul 19, 2021, 9:40 AM

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pliant gyro we basically have to prove f(x)>f'(x)

how did you come to this?

pliant gyro Jul 19, 2021, 9:40 AM

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look at part C

quick bluff Jul 19, 2021, 9:41 AM

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yes, cant it also be possible that f(x) is negative but of a greater magnitude?

pliant gyro Jul 19, 2021, 9:41 AM

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if alpha>1 that means x>1 and modulus will open with a positve sign

quick bluff Jul 19, 2021, 9:41 AM

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pliant gyro if alpha>1 that means x>1 and modulus will open with a positve sign

oh

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oh yeah

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f(x) can't be negative then

pliant gyro Jul 19, 2021, 9:42 AM

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now if it depends on lnx and 1/x

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just look at the rates of increase or decrease of them

quick bluff Jul 19, 2021, 9:42 AM

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ln x increases and 1/x decreases?

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so there will be point where they intersect?

pliant gyro Jul 19, 2021, 9:42 AM

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yep

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precisely

quick bluff Jul 19, 2021, 9:43 AM

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thinkies makes sense

pliant gyro Jul 19, 2021, 9:43 AM

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and for the d part i proved it wrong

quick bluff Jul 19, 2021, 9:43 AM

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im still skeptical about the "sine term removal" you did tho

pliant gyro Jul 19, 2021, 9:43 AM

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nah when terms get lager they become insignificant

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the sine term integral cannot be more than 3 or 4

quick bluff Jul 19, 2021, 9:44 AM

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pliant gyro and for the d part i proved it wrong

well can't i just say f(x) is always increasing in (0, infinity) and therefore it's not possible for it to have an upper limit?

pliant gyro Jul 19, 2021, 9:44 AM

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it is

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but the problem lies in the values like 20 to 80

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mb there f'(x) goes up and comes down again

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we dont know

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and u can think of it from other methods

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too

quick bluff Jul 19, 2021, 9:46 AM

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thonk ok

pliant gyro Jul 19, 2021, 9:46 AM

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im not sayin that my method is the only best method

quick bluff Jul 19, 2021, 9:46 AM

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pliant gyro im not sayin that my method is the only best method

if it's more concrete than my completely theoretical explanation it must be better

pliant gyro Jul 19, 2021, 9:47 AM

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ya i just thought of it while havin lunch

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i did not write it on paper

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you're in allen??

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@quick bluff

quick bluff Jul 19, 2021, 9:48 AM

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Yes

pliant gyro Jul 19, 2021, 9:48 AM

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ask ur teacher and also tell me afterwards

quick bluff Jul 19, 2021, 9:48 AM

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Sure

unique pagoda Jul 19, 2021, 1:39 PM

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1/sqrt(3x-1) = (3x-1)^(-1/2)

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do you see why?

knotty crescent Jul 19, 2021, 1:44 PM

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Could someone help me out with this?

unique pagoda Jul 19, 2021, 1:44 PM

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you can take constants out during differentiation. here you have a constant factor of 1/2

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so d/dx (3x-1)^(-1/2)/2 =
(1/2) d/dx (3x-1)^(-1/2)

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no problemo

near epoch Jul 19, 2021, 5:59 PM

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can someone pls help me do this using conics?

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analog ravine Jul 19, 2021, 6:36 PM

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<@&268886789983436800> why is math so hard aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

somber yew Jul 19, 2021, 6:37 PM

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sully

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Why are you pinging moderators for this

analog ravine Jul 19, 2021, 6:37 PM

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can you make math easy?

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pls

somber yew Jul 19, 2021, 6:38 PM

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I suggest you to not continue off-topic chitchat here. Move to #chill .

unborn blade Jul 19, 2021, 8:01 PM

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1951    4000000
1952    6000000
1953    9000000
1954    12000000
1955    16000000
1956    21000000
1957    26000000
1958    32000000
1959    39000000
1960    47000000
1961    56000000
1962    67000000
1963    80000000
1964    95000000
1965    112000000
1966    132000000
1967    155000000
1968    182000000
1969    214000000
1970    249000000
1971    287000000
1972    331000000
1973    382000000
1974    434000000
1975    480000000
1976    534000000
1977    593000000
1978    657000000
1979    728000000
1980    798000000
1981    870000000
1982    943000000
1983    1023000000
1984    1109000000
1985    1199000000
1986    1295000000
1987    1399000000
1988    1509000000
1989    1623000000
1990    1743000000
1991    1867000000
1992    1999000000
1993    2136000000
1994    2287000000
1995    2443000000
1996    2611000000
1997    2791000000
1998    2979000000
1999    3181000000
2000    3394000000
2001    3612000000
2002    3843000000
2003    4084000000
2004    4340000000
2005    4603000000
2006    4883000000
2007    5178000000
2008    5459000000
2009    5747000000
2010    6060000000
2011    6385000000
2012    6723000000
2013    7075000000
2014    7442000000
2015    7823000000```

how do I derive a formula based on the above data set?
i ended up with  f(x)=2.023*1.136^x, but my instructor said it was incorrect

haughty lance Jul 19, 2021, 11:11 PM

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for sure it's wrong

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but think about why though

unborn blade Jul 19, 2021, 11:30 PM

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i just followed a technique i found on a khan academy vid

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how do u recommend i do it?

unborn blade Jul 20, 2021, 1:56 AM

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haughty lance for sure it's wrong

sry just pinging in case u dont even see this again lol

haughty lance Jul 20, 2021, 2:08 AM

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i mean it's just hard to discern how the dataset and the equation was derived

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if you show what you did it's easier to point out where the misstep was

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like where does 2.023 come form

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i think it's worth revising what function you're trying to use f(x) = ab^x? some growth with a rate? how are you deriving your terms

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and then think about it in simple terms

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dont think of a huge dataset

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what text are you using, it's always good to go back to that

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which video did you use?

unborn blade Jul 20, 2021, 3:26 AM

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haughty lance i mean it's just hard to discern how the dataset and the equation was derived

hey thanks for the response

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https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/constructing-linear-and-exponential-functions-from-graph

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that is the video I used

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i followed the exact procedures as outlined in that video and ended up with the formula I have

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the data set seems to show an exponential function of some sort, which is why i tried to use f(x)=ab^x form

unborn blade Jul 20, 2021, 3:27 AM

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haughty lance what text are you using, it's always good to go back to that

do you mean the instructions of the assignment im working on?

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it basically just asks us to find some sort of data set online that is a function of degree 3 or higher, or an exponential function, or trig function

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and then to formulate an equation based on the data set that roughly models the data

viscid thistle Jul 20, 2021, 3:34 AM

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did i do this correctly

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fleet yew Jul 20, 2021, 11:48 PM

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500cos(30), 500sin(30)

inland flower Jul 21, 2021, 1:01 AM

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anyone know how to find angle?

toxic flame Jul 21, 2021, 1:22 AM

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@inland flower apply the law of cosines

shut timber Jul 21, 2021, 2:24 AM

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Screen_Shot_2021-07-20_at_7.23.59_PM.png

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how would u get the solution

uncut mulch Jul 21, 2021, 2:26 AM

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you could first consider the product of the constant components and eliminate some choices

shut timber Jul 21, 2021, 2:28 AM

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yea but going from just the equation given

toxic flame Jul 21, 2021, 2:32 AM

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shut timber

$4x^3-x^2-28x+7=x^2(4x-1)-7(4x-1)$

obsidian monolithBOT Jul 21, 2021, 2:32 AM

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coycoy

shut timber Jul 21, 2021, 2:32 AM

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toxic flame $4x^3-x^2-28x+7=x^2(4x-1)-7(4x-1)$

how do u get that

toxic flame Jul 21, 2021, 2:33 AM

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factor out x^2 from the first two terms and -7 from the last two terms

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just continue factoring after that

shut timber Jul 21, 2021, 2:34 AM

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oh

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wow

obsidian monolithBOT Jul 21, 2021, 3:24 AM

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Jaba Teresinha

narrow lichen Jul 21, 2021, 3:24 AM

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how do I solve this system of equations?

toxic flame Jul 21, 2021, 3:36 AM

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multiply the top by y and the bottom by -x. then add the two equations.

obsidian crown Jul 21, 2021, 6:16 PM

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Can someone please answer my Pre-Calc question:

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solemn elbow Jul 21, 2021, 9:40 PM

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we cant answer, but we can help

obsidian crown Jul 21, 2021, 10:03 PM

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solemn elbow we cant answer, but we can help

sorry that's what I meant but I solved this already ty

haughty lance Jul 21, 2021, 10:21 PM

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this is some heavy precal...

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feels not american...

grand lotus Jul 22, 2021, 9:11 AM

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obsidian crown

Use D moivres

viscid thistle Jul 22, 2021, 10:38 AM

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${(-1 + sqrt(5))/2}$

obsidian monolithBOT Jul 22, 2021, 10:38 AM

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∂T/ ∂t = α ∇²T

willow bear Jul 22, 2021, 11:14 AM

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did you mean $\frac{-1 + \sqrt{5}}{2}$

obsidian monolithBOT Jul 22, 2021, 11:14 AM

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Ann

slim echo Jul 23, 2021, 12:16 AM

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I'm having trouble understanding how to get my last term

fleet yew Jul 23, 2021, 12:26 AM

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@slim echo divide all terms by 5

slim echo Jul 23, 2021, 12:28 AM

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ok

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I understand what you're saying but still unsure how this leads to my last term

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does the n=20 just mean that whatever term I get when when I get to the 20th term will be my last term

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nvm I was able to figure it out but thank you anyways

lament sandal Jul 23, 2021, 4:07 AM

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did you mean 3x^{2}+2x+5

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o it doesnt work

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:/

viscid thistle Jul 23, 2021, 4:28 AM

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did i do this correctly

dawn kestrel Jul 23, 2021, 5:41 AM

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viscid thistle did i do this correctly

what kind of school activity is this?

viscid thistle Jul 24, 2021, 5:14 AM

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this good?

willow bear Jul 24, 2021, 5:35 AM

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you should not use the letter x for multiplication

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and also you didn't do what was asked:

Write a full sentence to describe the recurrence relation of the sequence

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$a_{n+1} = 3a_n + 1$ is what you meant for the first one

obsidian monolithBOT Jul 24, 2021, 5:36 AM

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Ann

viscid thistle Jul 24, 2021, 5:37 AM

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i had a sentence but i don't think i phrased it correctly

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so i just ended up deleting it

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Every value is 3 times greater, plus one than the previous value.

wary mulch Jul 25, 2021, 9:24 AM

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idk how to approach this sum can anyone help me

echo wagon Jul 25, 2021, 9:25 AM

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You need to find $$\lim_{x \to 0} f(x)$$and set f(0) equal to that

obsidian monolithBOT Jul 25, 2021, 9:25 AM

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Lunasong the Supergay

wary mulch Jul 25, 2021, 9:26 AM

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echo wagon You need to find $$\lim_{x \to 0} f(x)$$and set f(0) equal to that

how to find tat

echo wagon Jul 25, 2021, 9:31 AM

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||hiding so no one sees, but do you know Lhospitals rule?|| @wary mulch

wary mulch Jul 25, 2021, 9:31 AM

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echo wagon ||hiding so no one sees, but do you know Lhospitals rule?|| <@767045318294241301...

S im not good at it

echo wagon Jul 25, 2021, 9:32 AM

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That's probably the easiest way

wary mulch Jul 25, 2021, 9:32 AM

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OK

echo wagon Jul 25, 2021, 9:32 AM

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The only other way I can think of is a little ugly

wary mulch Jul 25, 2021, 9:32 AM

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wats tat

ivory loom Jul 25, 2021, 9:33 AM

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why not just make x=0 though?

wary mulch Jul 25, 2021, 9:33 AM

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ivory loom why not just make x=0 though?

no it wont work

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it will come as 0/0

ivory loom Jul 25, 2021, 9:34 AM

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would it? my brain must not be functioning today xD

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ohh fuck

wary mulch Jul 25, 2021, 9:34 AM

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ivory loom would it? my brain must not be functioning today xD

S

ivory loom Jul 25, 2021, 9:35 AM

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ignore me, my bad

echo wagon Jul 25, 2021, 9:36 AM

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Nvm what I was thinking doesn't work

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Just do ||LH|| if you know it

uncut mulch Jul 25, 2021, 9:37 AM

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does that even end well here?

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i'd probably approach it with the factorisations for a difference of two powers

echo wagon Jul 25, 2021, 9:38 AM

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Oh, I was doing that, then it didn't work put, but I was dumb and only did it for the one power lol

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Yes, that's the other way, but I mean, it's hella messy with an eighth root

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Which I why recommend ||LH||

wary mulch Jul 25, 2021, 9:39 AM

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echo wagon Which I why recommend ||LH||

yea i did it with LH

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i got ans as 1/5

echo wagon Jul 25, 2021, 9:39 AM

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I don't think that's right

wary mulch Jul 25, 2021, 9:39 AM

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is this crct

echo wagon Jul 25, 2021, 9:40 AM

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You didn't use chain rule when differentiating

wary mulch Jul 25, 2021, 9:41 AM

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my teacher didnt teach differentiations yet

echo wagon Jul 25, 2021, 9:41 AM

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Oh, so you aren't supposed to use LH?

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You can't use LH if you haven't done differentiation

wary mulch Jul 25, 2021, 9:41 AM

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ohhh ok

echo wagon Jul 25, 2021, 9:41 AM

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uncut mulch i'd probably approach it with the factorisations for a difference of two powers

I guess you have to do this then

wary mulch Jul 25, 2021, 9:43 AM

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ok

uncut mulch Jul 25, 2021, 9:45 AM

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its actually not that bad

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there's heavy simplification

echo wagon Jul 25, 2021, 9:48 AM

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Multiply the numerator and denominator by
$[(256-7x)^\frac78 + 2(256-7x)^\frac68 + 2^2 (256-7x)^\frac58 + 2^3 (256-7x)^\frac48) + 2^4 (256-7x)^\frac38 + 2^5 (256-7x)^\frac28 + 2^6 (256-7x)^\frac18 + 2^7][(5x+32)^\frac45 + 2 (5x+32)^\frac35 + 2^2 (5x+32)^\frac25 + 2^3 (5x+32)^\frac15 + 2^4]$

obsidian monolithBOT Jul 25, 2021, 9:48 AM

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Lunasong the Supergay

echo wagon Jul 25, 2021, 9:48 AM

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Lol

wary mulch Jul 25, 2021, 9:48 AM

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u kiddin me

echo wagon Jul 25, 2021, 9:49 AM

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You don't have to multiply out manually

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So this comes from factorization

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$x^n - y^n = (x-y)(x^{n-1} + x^{n-2}y + x^{n-3}y^2 + \dots + x y^{n-2} + y^{n-1}$

obsidian monolithBOT Jul 25, 2021, 9:50 AM

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Lunasong the Supergay

echo wagon Jul 25, 2021, 9:51 AM

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So when you multiply out the numerator with the first bracket, you will just get 2^8-(256-7x)

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And in the denominator, you will just get (5x+32)-2^5

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Then with the extra pair of brackets

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You get 7x times second bracket / 5x times first bracket

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Cancelling out the x's gets rid of the 0/0 issue

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And then you can substitute in

wary mulch Jul 25, 2021, 9:53 AM

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echo wagon So when you multiply out the numerator with the first bracket, you will just get...

this is 0

wary mulch Jul 25, 2021, 9:53 AM

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echo wagon And in the denominator, you will just get (5x+32)-2^5

this is also 0

#

0/0

echo wagon Jul 25, 2021, 9:53 AM

#

2^8 - 256 + 7x = 7x

#

5x+32-2^5 = 5x

#

Cancel out the x's

#

Then it won't be 0/0 anymore

wary mulch Jul 25, 2021, 9:54 AM

#

ohk yeaa it is

#

thanks @echo wagon

echo wagon Jul 25, 2021, 9:54 AM

#

👍

#

This will work in general when you have 0/0 with roots like this

#

It just gets uglier the higher the roots are

#

8 and 5 pretty bad already lol

wary mulch Jul 25, 2021, 9:55 AM

#

how did u findout with wat to multiply and divide so fast

uncut mulch Jul 25, 2021, 9:56 AM

#

factorisation identities

wary mulch Jul 25, 2021, 9:56 AM

#

ohhh ok

echo wagon Jul 25, 2021, 9:57 AM

#

obsidian monolith **Lunasong the Supergay**

This

#

I treat the one term as x, and the other as y

#

Then what I need to multiply with is that longass second bracket

#

And do it for the numerator and denominator

wary mulch Jul 25, 2021, 9:58 AM

#

ok

uncut mulch Jul 25, 2021, 9:59 AM

#

could use sigma notation to avoid tedious writing

echo wagon Jul 25, 2021, 10:00 AM

#

But then it doesn't look as crazy lmfao

uncut mulch Jul 25, 2021, 10:03 AM

#

also makes evaluating the limit much easier in this case

echo wagon Jul 25, 2021, 10:07 AM

#

I agreeeeee

tranquil totem Jul 25, 2021, 1:08 PM

#

@uncut mulch that R is awesome... where to find it?

#

the R on ur name

uncut mulch Jul 25, 2021, 1:09 PM

#

old english font

tranquil totem Jul 25, 2021, 1:19 PM

#

can it be found on keyboard?

uncut mulch Jul 25, 2021, 1:20 PM

#

you can get it in something like microsoft word

#

or search for images online

viscid thistle Jul 25, 2021, 7:39 PM

#

𝔸𝔹ℂ𝔻𝔼𝔽𝔾ℍ𝕀𝕁𝕂𝕃𝕄ℕ𝕆ℙℚℝ𝕊𝕋𝕌𝕍𝕎𝕏𝕐ℤ

shut timber Jul 26, 2021, 12:03 AM

#

Screen_Shot_2021-07-25_at_5.03.03_PM.png

#

how to find equation of expoentnial function with only one point

ivory loom Jul 26, 2021, 1:08 AM

#

that doesn't seem like its the entire question, might be helpful to post all of it

fleet yew Jul 26, 2021, 2:27 AM

#

You dont need the equation

#

Just eyeball it

#

And reverse the coordinates of the given point

shut timber Jul 26, 2021, 2:42 AM

#

Screen_Shot_2021-07-25_at_7.42.07_PM.png

#

the answer is ln x/2 , but how?

ivory loom Jul 26, 2021, 3:44 AM

#

To find the inverse of the function, you swap the x and y variables right?

#

since you know its an exponential equation, the inverse would turn out to be logarithmic

#

honestly the easiest way is to just imagine what the graph would look like in your head when you swap the axis and then you can easily identify which ones must not be correct

#

if its easier, imagine the y=x line and mirror the graph to the other side of that line (someone else might be able to explain this better than i can)

shut timber Jul 26, 2021, 4:02 AM

#

ivory loom since you know its an exponential equation, the inverse would turn out to be log...

wait y

ivory loom Jul 26, 2021, 4:04 AM

#

imagine you have the function y=e^x

#

swap y and x

#

x=e^y

#

solve for y
y=ln(x)

shut timber Jul 26, 2021, 4:05 AM

#

yes

#

but this doesnt have eulers number

ivory loom Jul 26, 2021, 4:06 AM

#

eulers numbers?

shut timber Jul 26, 2021, 4:06 AM

#

e

ivory loom Jul 26, 2021, 4:06 AM

#

shut timber

this graph is exponential, right?

shut timber Jul 26, 2021, 4:06 AM

#

yea

ivory loom Jul 26, 2021, 4:07 AM

#

so then whats the problem?

ivory loom Jul 26, 2021, 4:08 AM

#

ivory loom if its easier, imagine the y=x line and mirror the graph to the other side of th...

do u understand this part?

shut timber Jul 26, 2021, 4:08 AM

#

yea

#

reflection across y axis

ivory loom Jul 26, 2021, 4:09 AM

#

no, should be reflection across the y=x line

#

right?

shut timber Jul 26, 2021, 4:10 AM

#

wait yea

#

yea i get that

#

the inverse would have 1,0 instead of 0,1

ivory loom Jul 26, 2021, 4:10 AM

#

ok, now lets go through the options they provide

the first option is linear, is this a possibility for the graph u have visualised?

shut timber Jul 26, 2021, 4:10 AM

#

yea, it cant be it, cuz it should be exponential

#

and the second and fourth options cant be it, becaue x^2 should have a local extrema

ivory loom Jul 26, 2021, 4:11 AM

#

ok, second and fourth option are quadratics, can they be a possibility?

shut timber Jul 26, 2021, 4:11 AM

#

yea

ivory loom Jul 26, 2021, 4:12 AM

#

ok third is logarithmic, does the function u are visualizing look logarithimic to you?

shut timber Jul 26, 2021, 4:12 AM

#

yea ig

ivory loom Jul 26, 2021, 4:12 AM

#

does the point they outline fit on the third option's graph?

shut timber Jul 26, 2021, 4:13 AM

#

no, but the inverse does

#

they give 0,1 , on ln x/2 1,0 exists

ivory loom Jul 26, 2021, 4:13 AM

#

they dont give (0,1)

#

look at the scales

shut timber Jul 26, 2021, 4:13 AM

#

0,2*

ivory loom Jul 26, 2021, 4:13 AM

#

yes

shut timber Jul 26, 2021, 4:14 AM

#

2,0 exists for lnx/2

ivory loom Jul 26, 2021, 4:14 AM

#

then u have your answer

shut timber Jul 26, 2021, 4:14 AM

#

is there any way you can get that without looking at multiple choice

ivory loom Jul 26, 2021, 4:15 AM

#

nope

#

one point is not enough

shut timber Jul 26, 2021, 4:15 AM

#

ah, i see

ivory loom Jul 26, 2021, 4:18 AM

#

you can prove it to yourself that one point is not enough to get an exponential equation, can u think of multiple exponential equations that go through that same point? use desmos graph tool and test around with some numbers

shut timber Jul 26, 2021, 4:20 AM

#

Yea will do

#

I spent a lot time trying to find equation for the graph, looking online

#

Couldn’t find anything

ivory loom Jul 26, 2021, 4:22 AM

#

quick example

shut timber Jul 26, 2021, 4:22 AM

#

Yep

patent beacon Jul 26, 2021, 7:08 AM

#

Acceleration is second derivative of x. Get that, find a(2)

quick bane Jul 26, 2021, 7:09 AM

#

spark tendon Jul 26, 2021, 8:21 AM

#

When a scalar ,k is multiplied with a function f(x), we represent the resultant function as (kf)(x). But when me multiply f(x) with (k+m), where m is also a scalar, which is a better representation of the resultant function : ((k+m)f)(x) or (k+m)f ?

willow bear Jul 26, 2021, 8:30 AM

#

whichever you think looks better aesthetically

#

you could even say (k+m)f(x) since it's unambiguous what's being talked about

#

and likewise kf(x)

viscid thistle Jul 26, 2021, 10:21 AM

#

${\frac{x/x}}$

obsidian monolithBOT Jul 26, 2021, 10:21 AM

#

∂T/ ∂t = α ∇²T

${\frac{x/x}}$
```Compilation error:```! Argument of \frac  has an extra }.
<inserted text> 
                \par 
l.55 ${\frac{x/x}}
                  $
I've run across a `}' that doesn't seem to match anything.
For example, `\def\a#1{...}' and `\a}' would produce
this error. If you simply proceed now, the `\par' that
I've just inserted will cause me to report a runaway
argument that might be the root of the problem. But if
your `}' was spurious, just type `2' and it will go away.```

viscid thistle Jul 26, 2021, 10:21 AM

#

$\frac{x_x}$

spark tendon Jul 26, 2021, 10:21 AM

#

suppose f is a real valued function, then kf(x) is a real number while (kf)(x) is a function ,right?

obsidian monolithBOT Jul 26, 2021, 10:21 AM

#

∂T/ ∂t = α ∇²T
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

willow bear Jul 26, 2021, 10:30 AM

#

@viscid thistle \frac{num}{denom}, also #bots or #latex-testing

viscid thistle Jul 26, 2021, 10:30 AM

#

thank you

#

didnt know how to use it

#

😦

willow bear Jul 26, 2021, 10:31 AM

#

spark tendon suppose f is a real valued function, then kf(x) is a real number while (kf)(x) i...

no, kf(x) and (kf)(x) refer to the same thing. if you want just the function, it's kf.

#

@viscid thistle there is a cheat sheet pinned in #latex-testing if you want to familiarize yourself with the basics of latex for using the bot with

viscid thistle Jul 26, 2021, 10:33 AM

#

ohh k ty

spark tendon Jul 26, 2021, 10:48 AM

#

willow bear no, kf(x) and (kf)(x) refer to the same thing. if you want just the function, it...

While proving set of real valued functions is a vector spaces, kf(x) and (kf)(x) do not refer to the same thing. Maybe I should try asking this doubt in linear algebra channel. I thought this doubt was related to pre-calculus.

willow bear Jul 26, 2021, 10:53 AM

#

(kf)(x) and kf(x) both refer to a number tho

#

that is if you refuse to acknowledge that the former is defined as the latter

viscid thistle Jul 26, 2021, 8:23 PM

#

Write an equation for the parabola with focus (−1,2)and vertex (3,2).

#

for this problem, would I use the horizontal or vertical equation of a parabola

burnt bridge Jul 26, 2021, 8:28 PM

#

viscid thistle for this problem, would I use the horizontal or vertical equation of a parabola

i think it's horizontal

haughty lance Jul 27, 2021, 5:05 PM

#

viscid thistle for this problem, would I use the horizontal or vertical equation of a parabola

try to think why though, try sketching it out

bitter delta Jul 27, 2021, 6:44 PM

#

can anyone help me out with this question, no clue what to do here

viral juniper Jul 27, 2021, 7:27 PM

#

Hello.
Help, thanks!

#

<@&286206848099549185>

tranquil lava Jul 28, 2021, 5:11 AM

#

You ca start by evaluating dy/dx

#

This will give the turning point

#

@viral juniper

viral juniper Jul 28, 2021, 5:13 AM

#

solved it 😓

#

-5, -11 from what i remember

tranquil lava Jul 28, 2021, 5:13 AM

#

okay cool

left sleet Jul 28, 2021, 5:34 AM

#

Hey, can someone help solve this?A rocket makes a one dimensional motion/movement.

g is the gravitational acceleration,
x is the vertical coordinate,
m is the mass,
t is the time.

Assuming that there is no air resistance/friction etc and only gravity affects the motion of the rocket, the force (F) is
F = –mg.
In this situation, the equation of motion (F= ma where a is acceleration) is (attached as a photo).

(1) Find and show the rocket's velocity as a function of time. However, when t = 0, its velocity is v0.
(2) Find and show the rocket’s position as a function of time. However, when t = 0, its position is x0.
(3) When v0 is much greater/a very large number, describe the rocket's motion.

How would you solve this problem? I'm thinking integrate once to get velocity, and twice to get position. It would be great if you could help out!

#

sand dune Jul 28, 2021, 6:41 AM

#

left sleet Hey, can someone help solve this?A rocket makes a one dimensional motion/movemen...

this doesn't belong here

#

don't post in multiple channels to get more attention

viral juniper Jul 28, 2021, 7:20 AM

#

left sleet Hey, can someone help solve this?A rocket makes a one dimensional motion/movemen...

How does this fall into "pre"calculus loool

copper vigil Jul 28, 2021, 9:56 AM

#

left sleet Hey, can someone help solve this?A rocket makes a one dimensional motion/movemen...

x = 1/2 at^2

#

v = at

signal vine Jul 28, 2021, 6:47 PM

#

Anyone able to help me figure out how to go about solving this?

gritty echo Jul 28, 2021, 7:45 PM

#

What does the derivative tells you about a function?

viscid plank Jul 28, 2021, 10:08 PM

#

When de function decrease and increase and the maxims and minimums

sick steppe Jul 28, 2021, 10:09 PM

#

viscid plank When de function decrease and increase and the maxims and minimums

it wasnt an open question, it was a prompt

signal vine Jul 28, 2021, 11:35 PM

#

gritty echo What does the derivative tells you about a function?

The instantaneous rate of change of the function

heavy finch Jul 28, 2021, 11:39 PM

#

If you'd like I can help you with the question

#

it would be helpful if you posted the function itself but if you only want the knowledge, and then to apply it yourself thats better!

sick steppe Jul 28, 2021, 11:42 PM

#

heavy finch it would be helpful if you posted the function itself but if you only want the k...

that... isnt the question

heavy finch Jul 28, 2021, 11:43 PM

#

yep i didn't read it fully sorry

worn crest Jul 29, 2021, 2:19 AM

#

Could someone walk me through these? Going through my review and haven't done these in awhile

#

Synthetic division and stuff

worn crest Jul 29, 2021, 3:43 AM

#

#

I went back to try and solve it, I got this far with part a but I can’t remember how to go from here, or if I did something wrong

#

I used the rational zero theorem, do I have to finish it by using quadratic formula?

#

Alright I did quadratic formula and figured out another zero but I need one more, am I supposed to use that zero I just got and do synthetic division again?

gritty echo Jul 29, 2021, 4:00 AM

#

signal vine The instantaneous rate of change of the function

Right, so if a derivative is negative you know how much is changing with each step right?

signal vine Jul 29, 2021, 4:02 AM

#

Yeah

gritty echo Jul 29, 2021, 4:21 AM

#

So, there you know that if x<2 the derivative is negative, that means that with each step the function goes down right?

wary mulch Jul 29, 2021, 3:04 PM

#

im getting a=1,b=0 but ans is a=1,b=1/2 can anyone help me

willow bear Jul 29, 2021, 3:41 PM

#

show work?

#

@wary mulch

wary mulch Jul 29, 2021, 3:45 PM

#

fully mind calculation

willow bear Jul 29, 2021, 3:45 PM

#

then do it on paper

wary mulch Jul 29, 2021, 3:45 PM

#

ok

#

now im getting the ans

haughty lance Jul 29, 2021, 8:15 PM

#

mind calculation is cool for when you're walking without paper. it's almost always helpful to write some stuff out. even if it's easy, you might see some other properties that you wouldn't notice if it's all calculated by head

jolly raven Jul 29, 2021, 9:18 PM

#

Wouldn't the answer be a > 0 and b = 0

north cloud Jul 29, 2021, 9:21 PM

#

Can anyone help me solve this problem?

Screen_Shot_2021-07-30_at_6.21.07_AM.png

rough carbon Jul 29, 2021, 9:30 PM

#

Work out the modulus of the vector, which is 5
We want a vector with modulus 1, so our vector will be 1/5 of v given

north cloud Jul 29, 2021, 9:56 PM

#

What do you mean by modulus?

#

Do you mean as in this "%"?

viscid thistle Jul 29, 2021, 10:03 PM

#

north cloud Do you mean as in this "%"?

yes I believe so

north cloud Jul 29, 2021, 10:04 PM

#

Why do you need to use modulus in calculating unit vector direction?

sick steppe Jul 29, 2021, 10:09 PM

#

viscid thistle yes I believe so

No....

#

modulus of a vector is the length/norm

viscid thistle Jul 29, 2021, 10:09 PM

#

ahh too used to programming lol

sick steppe Jul 29, 2021, 10:09 PM

#

clearly modular arithmetic has nothing to do with vectors

#

~~bar Z_p scalar fields~~

viscid thistle Jul 29, 2021, 10:09 PM

#

angerysad

#

why not just say magnitude or length, why modulus 😠

#

but yea that makes more sense now that I think about it lol

sick steppe Jul 29, 2021, 10:12 PM

#

cause modulus is technically correct since C is iso to R^2, ie you can express complex numbers as tuples of real numbers

#

and modulus of a complex number is identical to norm of a vector in R^2

#

since both are just pythagorean

viscid thistle Jul 29, 2021, 10:15 PM

#

I see-ish

weak goblet Jul 30, 2021, 5:22 AM

#

Can someone help

#

#

<@&286206848099549185>

gritty echo Jul 30, 2021, 11:31 AM

#

Still need help? What have you tried/where are you stuck

pliant wadi Jul 30, 2021, 1:39 PM

#

My doubt is if cos x = -1/2 , then x could be -60°

uncut mulch Jul 30, 2021, 1:43 PM

#

there are infinitely many solutions to cos(x) = -1/2
but -60° isn't one of them

inland flower Jul 30, 2021, 2:03 PM

#

anyone know how to graph this

uncut mulch Jul 30, 2021, 2:04 PM

#

seems that ← is supposed to be <

#

which part of graphing are you stuck on?

inland flower Jul 30, 2021, 2:05 PM

#

like i dont know where to start/plot

uncut mulch Jul 30, 2021, 2:05 PM

#

do you know how to graph straight lines?

inland flower Jul 30, 2021, 2:05 PM

#

sort of

uncut mulch Jul 30, 2021, 2:06 PM

#

e.g would you be able to graph
y = x/2 + 4?

inland flower Jul 30, 2021, 2:06 PM

#

yes

uncut mulch Jul 30, 2021, 2:06 PM

#

start by doing that

#

seems that ← is supposed to be <
actually its supposed to be < -

#

and restrict the domain for that piece to (-inf, -4)

#

since f(x) only behaves that way for x < -4

inland flower Jul 30, 2021, 2:09 PM

#

so would graph this y = x/2 + 4

uncut mulch Jul 30, 2021, 2:10 PM

#

until where x is -4

#

since those are the conditions being given

#

f(x) = x/2 + 4 if x < -4

haughty lance Jul 31, 2021, 12:56 AM

#

viscid thistle why not just say magnitude or length, why modulus 😠

modulus is in fact normal usage for it

#

as mosh stated. also useful for dividing complex nums

viscid thistle Jul 31, 2021, 5:47 AM

#

Can commutative and associative laws over sum and product of integers be proved?

pulsar geyser Jul 31, 2021, 6:59 AM

#

help

#

how do i get the answer to blank 5 using the information i already put there

trim hemlock Jul 31, 2021, 7:11 AM

#

Is this an exam or some marked quiz?

pulsar geyser Jul 31, 2021, 7:13 AM

#

no its a practice quiz for the finals its not graded

trim hemlock Jul 31, 2021, 7:14 AM

#

Hmm 5points is kind if sketchy

#

Anyway

#

Try to draw the tiles out

#

Draw the hexagon and squares out, fill them in

#

And see whats missing

#

And what kind of shape you can fill in that gap

pulsar geyser Jul 31, 2021, 7:16 AM

#

im pretty sure i have to use the exterior angle of the green shape to get the number opf sides

#

cuz 360/the measure of one exterior angle = the number of sides in a figure

#

i think its 12nvm idk

trim hemlock Jul 31, 2021, 7:18 AM

#

Tho there is still one aspect of the question i dont quite understand, is the green shaded area supposed to be a whole shape?

pulsar geyser Jul 31, 2021, 7:18 AM

#

ok 12 is right

#

i am pro

#

ge

#

yes

#

i think so

trim hemlock Jul 31, 2021, 7:19 AM

#

Hmmm then why was the top corners coloured purple

#

It seems pike the square are supposed to be attaches to the top two sides of the hexagon

#

Thats where im kind of unclear about the problem

pulsar geyser Jul 31, 2021, 7:20 AM

#

its a

#

tessellation

trim hemlock Jul 31, 2021, 7:20 AM

#

Tho but if the green shaded area is supposed to be a whole shape then yeah, 12 seems correct

viscid thistle Jul 31, 2021, 8:59 AM

#

haughty lance modulus is in fact normal usage for it

thinkfold

patent beacon Aug 2, 2021, 3:39 AM

#

@weak goblet
Define important variables. Hint: there's almost always 2.

Write the important equations - they give you a perimeter, so what's the equation for perimeter? They want an area, what's the equation for area?

Then, write area in terms of one variable. Differentiate. Set to 0.

weak goblet Aug 2, 2021, 6:04 AM

#

I still dont understand, is it possible if you could do it for me? That just helps me better if I get a visual or something

#

willow bear Aug 2, 2021, 6:23 AM

#

we don't do problems for you

#

@weak goblet do you still need help?

weak goblet Aug 2, 2021, 6:24 AM

#

Yes I do

willow bear Aug 2, 2021, 6:24 AM

#

are you ok with me taking you through this by having you do it step by step?

weak goblet Aug 2, 2021, 6:24 AM

#

Yes please

willow bear Aug 2, 2021, 6:25 AM

#

okay, the first thing you should ask yourself is: what does the problem ask you to find?

#

i.e. what will the answer look like?

weak goblet Aug 2, 2021, 6:26 AM

#

To find the area of the rectangle?

willow bear Aug 2, 2021, 6:26 AM

#

no

#

you're asked to find the dimensions of the rectangle, i.e. its length and width

weak goblet Aug 2, 2021, 6:27 AM

#

Oh okay

willow bear Aug 2, 2021, 6:27 AM

#

this should have been clear from a careful reading of the problem

#

your answer will look like:

The area of the rectangle is maximized when its length is ___ and its width is ___; this gives it an area of ___.

#

once we fill in the blanks for length and width, the area is (hopefully) easy to find.

#

therefore the quantities we care about are the length and width.

#

do you follow?

weak goblet Aug 2, 2021, 6:28 AM

#

So we have to find the max length and max width?

willow bear Aug 2, 2021, 6:28 AM

#

no

#

it's area that is maximized. not either dimension on its own.

#

we didn't get there yet.

weak goblet Aug 2, 2021, 6:29 AM

#

Oh okay I understand now

#

Whats the next step

willow bear Aug 2, 2021, 6:29 AM

#

when solving math problems, typically you take the quantities you care about and assign them names, yes?

weak goblet Aug 2, 2021, 6:29 AM

#

Yes

willow bear Aug 2, 2021, 6:30 AM

#

so why don't you do that now with the length and width?

#

which names would you like to call them?

weak goblet Aug 2, 2021, 6:30 AM

#

L and W

willow bear Aug 2, 2021, 6:30 AM

#

alright

#

you should write at the beginning of your work:

L := length of the rectangle, in cm
W := width of the rectangle, in cm

weak goblet Aug 2, 2021, 6:31 AM

#

Done ✅

willow bear Aug 2, 2021, 6:31 AM

#

do you understand why i'm having you write this?

weak goblet Aug 2, 2021, 6:31 AM

#

Yes so we can get a variable

#

And then solve for that

willow bear Aug 2, 2021, 6:32 AM

#

no, it's so we can define our variables.

weak goblet Aug 2, 2021, 6:32 AM

#

Thats what I was thinking lol

willow bear Aug 2, 2021, 6:32 AM

#

then you didn't word it properly.

weak goblet Aug 2, 2021, 6:32 AM

#

Yea sorry so whats next?

willow bear Aug 2, 2021, 6:32 AM

#

anyway, ok, now we can get to the actual problem.

weak goblet Aug 2, 2021, 6:32 AM

#

Okay

willow bear Aug 2, 2021, 6:33 AM

#

we care about the area of the rectangle.

#

so we will need to express it in terms of our variables.

weak goblet Aug 2, 2021, 6:33 AM

#

How will we do that?

willow bear Aug 2, 2021, 6:33 AM

#

well do you know how to find the area of a rectangle?

weak goblet Aug 2, 2021, 6:34 AM

#

L•W

#

Length x width

willow bear Aug 2, 2021, 6:34 AM

#

length times width. don't use the letter x for multiplication.

weak goblet Aug 2, 2021, 6:34 AM

#

Okay

willow bear Aug 2, 2021, 6:34 AM

#

but yes. so you just did exactly what was needed. why did you try to ask me?

weak goblet Aug 2, 2021, 6:35 AM

#

What do you mean?

willow bear Aug 2, 2021, 6:35 AM

#

why did you ask me "How will we do that?" as if you didn't know?

weak goblet Aug 2, 2021, 6:36 AM

#

I guess I just didnt think of it and I mightve been doubting myself

willow bear Aug 2, 2021, 6:36 AM

#

mkay...

#

so we have this:

Area of rectangle = LW

weak goblet Aug 2, 2021, 6:36 AM

#

Yes

willow bear Aug 2, 2021, 6:37 AM

#

there is another piece of info we care about

#

the rectangle is enclosed by a border whose length is 36 cm.

weak goblet Aug 2, 2021, 6:37 AM

#

Yes 36cm

willow bear Aug 2, 2021, 6:38 AM

#

look at the diagram to see the shape of the border, and translate the sentence "The length of the border is 36cm" into an equation.

weak goblet Aug 2, 2021, 6:38 AM

#

L=36cm???

willow bear Aug 2, 2021, 6:39 AM

#

no

#

you're saying the length of the rectangle is 36 cm

#

that's not what you're told here

weak goblet Aug 2, 2021, 6:39 AM

#

Oh the total length of 3 sides is 36cm

willow bear Aug 2, 2021, 6:39 AM

#

perhaps i should have said "The total length of the border is 36cm" so as to prevent you from getting confused.

#

yes, so translate that into an equation, will you?

weak goblet Aug 2, 2021, 6:40 AM

#

Total length of border = 36cm

willow bear Aug 2, 2021, 6:41 AM

#

no. make that into an equation in L and W.

weak goblet Aug 2, 2021, 6:41 AM

#

L•w=36cm

willow bear Aug 2, 2021, 6:41 AM

#

what's lowercase w?

#

did you mean L*W = 36cm?

weak goblet Aug 2, 2021, 6:41 AM

#

Yea

willow bear Aug 2, 2021, 6:41 AM

#

this is nonsense.

#

what does L*W represent?

weak goblet Aug 2, 2021, 6:42 AM

#

Length times width

willow bear Aug 2, 2021, 6:42 AM

#

there is a name for that.

#

it's called area.

weak goblet Aug 2, 2021, 6:42 AM

#

I sorry im just really confused

willow bear Aug 2, 2021, 6:42 AM

#

which is not what we're talking about right now.

weak goblet Aug 2, 2021, 6:42 AM

#

Oh okay

willow bear Aug 2, 2021, 6:42 AM

#

you yourself correctly responded with "L*W" when i asked you how to find the area of a rectangle

weak goblet Aug 2, 2021, 6:43 AM

#

Yea I did

willow bear Aug 2, 2021, 6:43 AM

#

so then why do you say L*W again when prompted to express the total border length?

weak goblet Aug 2, 2021, 6:43 AM

#

Oh right oops

willow bear Aug 2, 2021, 6:43 AM

#

try again.

weak goblet Aug 2, 2021, 6:44 AM

#

Would it be a quadratic function?

willow bear Aug 2, 2021, 6:44 AM

#

you're overthinking it.

#

the words "quadratic function" here are extraneous, and should be ignored for now.

#

again

weak goblet Aug 2, 2021, 6:45 AM

#

W^2 *L

willow bear Aug 2, 2021, 6:45 AM

#

width squared, times length???

weak goblet Aug 2, 2021, 6:45 AM

#

I think so??

willow bear Aug 2, 2021, 6:45 AM

#

what kind of physical quantity do you get when you multiply three lengths together?

weak goblet Aug 2, 2021, 6:46 AM

#

L^3

willow bear Aug 2, 2021, 6:47 AM

#

i'm looking for a word here.

weak goblet Aug 2, 2021, 6:47 AM

#

Length cubed

willow bear Aug 2, 2021, 6:48 AM

#

that's called volume.

weak goblet Aug 2, 2021, 6:48 AM

#

Yea

willow bear Aug 2, 2021, 6:48 AM

#

i asked you for the total border length and you reply with a volume?

#

does this not strike you as odd?

weak goblet Aug 2, 2021, 6:49 AM

#

Yea im sorry again, so the total border is 36cm how would I write that as an equation

willow bear Aug 2, 2021, 6:50 AM

#

look at your diagram again, here

#

what is the total length of the solid edges?

weak goblet Aug 2, 2021, 6:50 AM

#

There is 1 length

#

And 2 widths

willow bear Aug 2, 2021, 6:50 AM

#

answer my question.

#

what is the total length of those?

weak goblet Aug 2, 2021, 6:51 AM

#

36

willow bear Aug 2, 2021, 6:51 AM

#

no, as an expression

weak goblet Aug 2, 2021, 6:51 AM

#

L=36

willow bear Aug 2, 2021, 6:51 AM

#

no!

#

why are you insisting that L = 36? L isn't the entire border, is it now?

weak goblet Aug 2, 2021, 6:52 AM

#

36 = L*W^2

willow bear Aug 2, 2021, 6:52 AM

#

why on earth are you MULTIPLYING them!?!?!?!?!?!

#

oka y

#

look

weak goblet Aug 2, 2021, 6:52 AM

#

W^2+L=36

#

Is that right?

willow bear Aug 2, 2021, 6:53 AM

#

why are you insisting on squaring the width?

#

now you're adding an area to a length! this makes even less sense!

#

look. do you claim the perimeter of this triangle is (5 * 7 * 9) feet? because that's what it should be by your logic.

weak goblet Aug 2, 2021, 6:53 AM

#

Im not sure what im supposed to do, sorry about that please help I will listen to what you say now

weak goblet Aug 2, 2021, 6:54 AM

#

willow bear look. do you claim the perimeter of this triangle is (5 * 7 * 9) feet? because t...

No

willow bear Aug 2, 2021, 6:54 AM

#

you should have listened to what i say from the very beginning. that you say you will do so now implies you didn't before, which is a bit disconcerting.

#

okay, so how do you find the perimeter of this triangle? of my triangle?

weak goblet Aug 2, 2021, 6:55 AM

#

Yea It would be 9+7+5

willow bear Aug 2, 2021, 6:55 AM

#

yeah, so you would ADD the sides

#

not multiply them

#

not multiply one side by another and add the third

#

you would add them

#

now back to this

#

https://cdn.discordapp.com/attachments/363224154469826562/871646095309168660/unknown.png

weak goblet Aug 2, 2021, 6:55 AM

#

Yes I would so in my case, I would do width plus width plus length

willow bear Aug 2, 2021, 6:56 AM

#

yes

#

W + W + L

#

now can you simplify this?

#

simplify W + W + L

weak goblet Aug 2, 2021, 6:56 AM

#

2W + L

willow bear Aug 2, 2021, 6:56 AM

#

okay

#

great

#

so after all this blood, toil, tears and sweat, we have:

#

Area = LW
2W + L = 36
Goal: max Area

weak goblet Aug 2, 2021, 6:57 AM

#

Yes!

willow bear Aug 2, 2021, 6:58 AM

#

the thing about our expression for area is that it has two variables, which makes it hard to maximize. maximizing functions of two or more variables is much harder than those of only one.

#

luckily, we have an equation relating our two variables.

#

this will let us isolate one of the variables, and plug the result into the expression for area. which in turn will make the expression for area contain one variable only.

#

do you understand this?

weak goblet Aug 2, 2021, 6:59 AM

#

Yes I understand this part is clear to me

willow bear Aug 2, 2021, 6:59 AM

#

okay, great.

#

now would you be so kind as to follow up on this?

#

take our equation (2W + L = 36) and isolate one of the variables in it.

weak goblet Aug 2, 2021, 7:00 AM

#

So like subtract either W or L

willow bear Aug 2, 2021, 7:00 AM

#

isolate either W or L.

weak goblet Aug 2, 2021, 7:01 AM

#

Okay. Subtract L from both sides

willow bear Aug 2, 2021, 7:01 AM

#

so you've chosen to isolate W?

weak goblet Aug 2, 2021, 7:01 AM

#

Yes

willow bear Aug 2, 2021, 7:02 AM

#

okay

#

so you choose to subtract L from both sides. what does this give you?

weak goblet Aug 2, 2021, 7:03 AM

#

2W=36-L

willow bear Aug 2, 2021, 7:03 AM

#

okay

#

keep going

weak goblet Aug 2, 2021, 7:03 AM

#

What would I do now

fading cedar Aug 2, 2021, 7:04 AM

#

divide by both sides

#

by the coefficient in front of w

weak goblet Aug 2, 2021, 7:04 AM

#

Divide both sides by 2

fading cedar Aug 2, 2021, 7:04 AM

#

yes

willow bear Aug 2, 2021, 7:04 AM

#

would have preferred if you had let shazz2005 figure this out for themselves, tenletters.

fading cedar Aug 2, 2021, 7:04 AM

#

my apologies

weak goblet Aug 2, 2021, 7:05 AM

#

W=18-2L

willow bear Aug 2, 2021, 7:05 AM

#

are you sure?

weak goblet Aug 2, 2021, 7:05 AM

#

Or W=18-L

willow bear Aug 2, 2021, 7:05 AM

#

are you sure dividing 36-L by 2 gives you 18 - 2L? or 18 - L, for that matter?

#

why would the L miraculously stay intact (or, god forbid, get multiplied by 2?)

weak goblet Aug 2, 2021, 7:06 AM

#

18-L/2

willow bear Aug 2, 2021, 7:06 AM

#

yes, so now you have W = 18 - L/2.

willow bear Aug 2, 2021, 7:06 AM

#

willow bear this will let us isolate one of the variables, and plug the result into the expr...

now follow up on this, will you?

weak goblet Aug 2, 2021, 7:07 AM

#

Im not too sure how

fading cedar Aug 2, 2021, 7:07 AM

#

well, now you have an expression for W in terms of L

weak goblet Aug 2, 2021, 7:08 AM

#

Yeah

willow bear Aug 2, 2021, 7:08 AM

#

Area = LW

#

W = 18 - L/2

fading cedar Aug 2, 2021, 7:08 AM

#

^

weak goblet Aug 2, 2021, 7:09 AM

#

Ummm what am I supposed to do now @willow bear

willow bear Aug 2, 2021, 7:09 AM

#

this will let us isolate one of the variables [we did this already!], and plug the result into the expression for area.

weak goblet Aug 2, 2021, 7:11 AM

#

Im still not to sure I understand

willow bear Aug 2, 2021, 7:11 AM

#

plug W = 18 - L/2 into Area = LW

weak goblet Aug 2, 2021, 7:12 AM

#

W=18-L/2

willow bear Aug 2, 2021, 7:12 AM

#

?????

fading cedar Aug 2, 2021, 7:12 AM

#

not quite

willow bear Aug 2, 2021, 7:13 AM

#

well now you just didn't do what i asked you

#

i did not ask you to just repeat the equation W = 18 - L/2.

weak goblet Aug 2, 2021, 7:13 AM

#

Yea what do I plug in

willow bear Aug 2, 2021, 7:13 AM

#

i TOLD you!

#

i told you EXACTLY what to plug in, and what to plug it into!

#

i asked you to replace W with (18 - L/2) in Area = LW !!!

#

i can't understand what part of this is remotely unclear!

weak goblet Aug 2, 2021, 7:15 AM

#

Oh okay so L*(18-L/2)

willow bear Aug 2, 2021, 7:15 AM

#

Area = L(18 - L/2)

fading cedar Aug 2, 2021, 7:15 AM

#

yes

willow bear Aug 2, 2021, 7:15 AM

#

yes

#

finally

#

great

#

this took way more effort than it should've

#

but ok

#

so now you have that

weak goblet Aug 2, 2021, 7:15 AM

#

willow bear this took way more effort than it should've

Sorry

willow bear Aug 2, 2021, 7:15 AM

#

you have A = L(18 - L/2)

weak goblet Aug 2, 2021, 7:15 AM

#

Yup

willow bear Aug 2, 2021, 7:15 AM

#

you can now change it to standard form if you want

#

this will make it more visible that it is in fact a quadratic in L, which is exactly what you were instructed to do

#

even though you did not need to know that, so the fact they said it explicitly should be treated only as a sanity check

weak goblet Aug 2, 2021, 7:17 AM

#

So I change it to standard form?

#

How would I?

fading cedar Aug 2, 2021, 7:19 AM

#

what do you normally do with brackets?

weak goblet Aug 2, 2021, 7:19 AM

#

Remove them

fading cedar Aug 2, 2021, 7:20 AM

#

and how do you do that?

willow bear Aug 2, 2021, 7:20 AM

#

tenletters, do you want to take over?

#

you seem very eager to help

fading cedar Aug 2, 2021, 7:20 AM

#

i suppose

willow bear Aug 2, 2021, 7:21 AM

#

okay then i'm out

weak goblet Aug 2, 2021, 7:21 AM

#

No @willow bear

#

Dont leave pleas

willow bear Aug 2, 2021, 7:21 AM

#

tenletters just said they're going to take over.

#

i have better things to do.

weak goblet Aug 2, 2021, 7:21 AM

#

Oh okay 😢

#

@fading cedar help me you made her leave

fading cedar Aug 2, 2021, 7:22 AM

#

indeed i may have

#

so...

#

need to expand them brackets, no?

weak goblet Aug 2, 2021, 7:23 AM

#

Yes

fading cedar Aug 2, 2021, 7:23 AM

#

and what do you get from that?

weak goblet Aug 2, 2021, 7:23 AM

#

Do I distribute the L

fading cedar Aug 2, 2021, 7:23 AM

#

indeed you do

#

as a(b+c) = ab + ac

weak goblet Aug 2, 2021, 7:24 AM

#

Okay so it would be

fading cedar Aug 2, 2021, 7:25 AM

#

Yes

#

now

weak goblet Aug 2, 2021, 7:25 AM

#

Yes

fading cedar Aug 2, 2021, 7:25 AM

#

do you know what do to get a maximum?

weak goblet Aug 2, 2021, 7:25 AM

#

I do not

fading cedar Aug 2, 2021, 7:25 AM

#

ah

weak goblet Aug 2, 2021, 7:26 AM

#

Please help me out with that

fading cedar Aug 2, 2021, 7:26 AM

#

you're going to need to get the derivative

weak goblet Aug 2, 2021, 7:26 AM

#

Whats that and how

fading cedar Aug 2, 2021, 7:27 AM

#

in a general sense, it is the instantaneous rate of change

#

as in, for a curve, it will give you the exact slope at any given point

weak goblet Aug 2, 2021, 7:27 AM

#

Oh okay

#

How do I find that

fading cedar Aug 2, 2021, 7:28 AM

#

you take the power of the variable, and multiply it to the front

#

and then take away one from the power

#

(in this case anyway)

weak goblet Aug 2, 2021, 7:28 AM

#

So 18^2

fading cedar Aug 2, 2021, 7:28 AM

#

not like that

#

but 18(2)

#

giving you 36

#

https://calcworkshop.com/wp-content/uploads/power-rule-formula.png

#

and when you derive a function, you usually write it as dy/dx

weak goblet Aug 2, 2021, 7:29 AM

#

Oh okay

fading cedar Aug 2, 2021, 7:29 AM

#

with y being the function, and x being the variable

#

so, in this case, dA/dL

weak goblet Aug 2, 2021, 7:30 AM

#

I would now have A=36L-L/2

fading cedar Aug 2, 2021, 7:30 AM

#

you forgot something

weak goblet Aug 2, 2021, 7:31 AM

#

Oh A=36L- L^2/2

fading cedar Aug 2, 2021, 7:31 AM

#

you're forgetting to reduce the power by 1

#

(of the variable)

weak goblet Aug 2, 2021, 7:31 AM

#

L^1

fading cedar Aug 2, 2021, 7:32 AM

#

not quite

#

36l^0

#

and what is anything to the zero power

#

1

#

therefore you get 36 for the first term

weak goblet Aug 2, 2021, 7:33 AM

#

36-L^2/2

fading cedar Aug 2, 2021, 7:33 AM

#

still got the second term to fix

#

remember:bring the power to the front and multiply it, and reduce the power by 1

weak goblet Aug 2, 2021, 7:34 AM

#

36L^0

fading cedar Aug 2, 2021, 7:34 AM

#

2-1=0?

weak goblet Aug 2, 2021, 7:34 AM

#

No

fading cedar Aug 2, 2021, 7:34 AM

#

are you sure

#

so?

weak goblet Aug 2, 2021, 7:34 AM

#

2-1=1

fading cedar Aug 2, 2021, 7:34 AM

#

yes

weak goblet Aug 2, 2021, 7:35 AM

#

36-L^1/2

fading cedar Aug 2, 2021, 7:35 AM

#

still forgot to multiply by the old power

#

should be (-2L^1)/2

weak goblet Aug 2, 2021, 7:36 AM

#

Ohhhh okay so 36-(2L^1)/2

fading cedar Aug 2, 2021, 7:36 AM

#

yes

weak goblet Aug 2, 2021, 7:36 AM

#

Okay

fading cedar Aug 2, 2021, 7:36 AM

#

but what is something over itself?

#

2/2 = ?

weak goblet Aug 2, 2021, 7:37 AM

#

1

fading cedar Aug 2, 2021, 7:37 AM

#

yes

#

so you can simplify to 36-L

#

now

weak goblet Aug 2, 2021, 7:37 AM

#

36-L

#

Got it

fading cedar Aug 2, 2021, 7:38 AM

#

in order to find a maximum or a minimum, you equal the resulting derivative/slope function to zero

#

as when this occurs, the gradient/slope at the point is zero

weak goblet Aug 2, 2021, 7:38 AM

#

Yea it is

fading cedar Aug 2, 2021, 7:39 AM

#

so, knowing that

#

what to do next

weak goblet Aug 2, 2021, 7:39 AM

#

Make one side 0

fading cedar Aug 2, 2021, 7:39 AM

#

yes

#

and then?

weak goblet Aug 2, 2021, 7:39 AM

#

I have A=36-L

fading cedar Aug 2, 2021, 7:40 AM

#

not a = 36-l

weak goblet Aug 2, 2021, 7:40 AM

#

fading cedar and then?

Im not sure…. Use the quadratic formula?

fading cedar Aug 2, 2021, 7:40 AM

#

rather A'(L) = 36 - L

weak goblet Aug 2, 2021, 7:40 AM

#

Okay

fading cedar Aug 2, 2021, 7:40 AM

#

to indicate it's the derived function

#

well, just solve for your unknown

#

and why involve the quadratic formula?

weak goblet Aug 2, 2021, 7:41 AM

#

Idk

fading cedar Aug 2, 2021, 7:41 AM

#

well, 36 - L = 0

#

what is L

weak goblet Aug 2, 2021, 7:41 AM

#

36

fading cedar Aug 2, 2021, 7:41 AM

#

Yes

weak goblet Aug 2, 2021, 7:42 AM

#

Then what next

fading cedar Aug 2, 2021, 7:42 AM

#

well, we had two variables to begin with

#

or, you can check if a function is maximum or minimum

#

by taking it's second derivative/ or drawing the graph

#

(of the original function)

#

the question is about max area is it not?

weak goblet Aug 2, 2021, 7:44 AM

#

Yea we have to find the max area

fading cedar Aug 2, 2021, 7:46 AM

#

well, in this case, since the highest power of the original function is 2

#

(therefore making it a quadratic)

#

there is only 1, turning point

#

and therefore only one value we can attain

weak goblet Aug 2, 2021, 7:47 AM

#

Yea

fading cedar Aug 2, 2021, 7:48 AM

#

if you take the second derivative, the resulting function will be simply 1

#

as all constants go away

weak goblet Aug 2, 2021, 7:49 AM

#

@willow bear told me to write my answer like this. How would I
The area of the rectangle is maximized when its length is ___ and its width is ___; this gives it an area of ___.

fading cedar Aug 2, 2021, 7:49 AM

#

yes that's right

#

just wondering about this question

weak goblet Aug 2, 2021, 7:49 AM

#

So whats the length

#

36?

fading cedar Aug 2, 2021, 7:50 AM

#

as if you do the min/max test using the second derivative

#

it is greater than 1

#

which means it's technically a minimum

#

but lesser than zero is a maximum

#

regardless

#

you now have your value of L

weak goblet Aug 2, 2021, 7:50 AM

#

36??

fading cedar Aug 2, 2021, 7:51 AM

#

yes

weak goblet Aug 2, 2021, 7:51 AM

#

Then what is w

fading cedar Aug 2, 2021, 7:51 AM

#

but the original expression was 2W + L = 36

weak goblet Aug 2, 2021, 7:51 AM

#

Yea

fading cedar Aug 2, 2021, 7:52 AM

#

L = 36

#

2W + L = 36

#

then?

weak goblet Aug 2, 2021, 7:52 AM

#

2*0+36=36

fading cedar Aug 2, 2021, 7:53 AM

#

oh no

#

i just realized what went wrong

#

my apologies

#

we were working with 36 this whole time

#

it should've been 18

weak goblet Aug 2, 2021, 7:54 AM

#

So my length is 18

fading cedar Aug 2, 2021, 7:55 AM

#

A'(L) = 18 - L = 0

#

from this yes

#

yes so solve for W

weak goblet Aug 2, 2021, 7:55 AM

#

Im getting 9 as my answers

#

Answer*

fading cedar Aug 2, 2021, 7:56 AM

#

and if we do take the second derivative (properly this time) we get -1

#

which is lesser than zero

#

and therefore a maximum

#

okok this is better

weak goblet Aug 2, 2021, 7:56 AM

#

So what is my length?

fading cedar Aug 2, 2021, 7:56 AM

#

18, as you stated

#

but solve for W

weak goblet Aug 2, 2021, 7:56 AM

#

Correct than width is 9?

fading cedar Aug 2, 2021, 7:56 AM

#

2W + L (L is 18) = 36

#

yes

#

(36-18)/2 = 9

weak goblet Aug 2, 2021, 7:57 AM

#

Okay

fading cedar Aug 2, 2021, 7:57 AM

#

weak goblet <@183668144404037632> told me to write my answer like this. How would I The ar...

write it like this now

#

i suppose

weak goblet Aug 2, 2021, 7:58 AM

#

The area of the rectangle is maximized when its length is 18 and its width is 9 this gives it an area of

fading cedar Aug 2, 2021, 7:58 AM

#

18*9

weak goblet Aug 2, 2021, 7:58 AM

#

18cm 9cm*

#

Okay

#

162cm

fading cedar Aug 2, 2021, 7:58 AM

#

as for justifying it is a maximum area

#

you could say if the graph of the original function is drawn

#

it is a local maximum due to being a negative parabola

weak goblet Aug 2, 2021, 8:00 AM

#

👍🏼

fading cedar Aug 2, 2021, 8:00 AM

#

which the turning point of the graph (where the gradient of the graph is zero) is the highest point

weak goblet Aug 2, 2021, 8:00 AM

#

Alright

#

Is that it?

fading cedar Aug 2, 2021, 8:01 AM

#

or you could say you took the second derivative, which simply gave you -1

#

and since -1 is lesser than zero

weak goblet Aug 2, 2021, 8:01 AM

#

But I cant have a negative width or length

fading cedar Aug 2, 2021, 8:01 AM

#

the point is a maximum

#

no this is the second derivative

weak goblet Aug 2, 2021, 8:01 AM

#

Ahhh okay

fading cedar Aug 2, 2021, 8:01 AM

#

if it's greater over zero, its a minimum

#

if it's lesser than zero, it's a maximum

weak goblet Aug 2, 2021, 8:02 AM

#

Oh okay thanks

#

Are we done?

fading cedar Aug 2, 2021, 8:02 AM

#

yea that's about it

weak goblet Aug 2, 2021, 8:02 AM

#

Thank you so much for your help today 😊😊 I have one more question but if you cant do it now tomorrow is fine as it is late for me

#

Ill leave it here and if you get a chance please look at it and tell me the steps I will do it tomorrow morning thanks for your help

magic magnet Aug 2, 2021, 11:50 AM

#

why the answer is only A, why not A and E?

echo wagon Aug 2, 2021, 11:53 AM

#

For E, f(2) = 28 but f(-2) = -36

#

@magic magnet

willow bear Aug 2, 2021, 11:55 AM

#

,rccw

obsidian monolithBOT Aug 2, 2021, 11:55 AM

#

magic magnet Aug 2, 2021, 11:56 AM

#

oh okay , i got it, i need to place value for both sides.
i was just plugging negative value on left side.

plush birch Aug 2, 2021, 12:15 PM

#

mhm

amber marsh Aug 2, 2021, 2:33 PM

#

given that this is true:
if log(u) = log(v), then u = v
does it follow that:
if log(u) = -(log(v)), then u = -v
is also true?

sick steppe Aug 2, 2021, 2:35 PM

#

amber marsh given that this is true: `if log(u) = log(v), then u = v` does it follow that: `...

no

#

$\log(u)=\log(v)\iff u=v$

obsidian monolithBOT Aug 2, 2021, 2:35 PM

#

Mosh

sick steppe Aug 2, 2021, 2:36 PM

#

$-\log(v)=\log(\frac{1}{v})$

obsidian monolithBOT Aug 2, 2021, 2:36 PM

#

Mosh

amber marsh Aug 2, 2021, 2:37 PM

#

ooookay, thank you

viscid thistle Aug 2, 2021, 4:12 PM

#

hello one textbook I was reading stated that 6a9 is not a term, why is this?

weak goblet Aug 2, 2021, 8:29 PM

#

weak goblet Ill leave it here and if you get a chance please look at it and tell me the step...

<@&286206848099549185>

weak goblet Aug 2, 2021, 9:21 PM

#

#

Help pleasee

viscid thistle Aug 2, 2021, 9:30 PM

#

You're more likely to get help if you put effort into presenting the problem

#

Instead of sending a crummy photo

viscid thistle Aug 2, 2021, 11:32 PM

#

😳

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but fr I can't read that I have wack eye sight

solid stirrup Aug 3, 2021, 4:48 PM

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sussy

sharp lagoon Aug 4, 2021, 12:40 AM

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how can i approach this question?

Screen_Shot_2021-08-03_at_5.38.53_PM.png

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Most of the examples i can find have denom,

pliant gyro Aug 4, 2021, 1:12 AM

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@sharp lagoon shouldn't it be set of all real no.s

sick steppe Aug 4, 2021, 1:16 AM

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sharp lagoon how can i approach this question?

f(x) is a polynomial

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and all polynomials have a domain of R

sharp lagoon Aug 4, 2021, 2:09 AM

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sick steppe f(x) is a polynomial

ah ok ty

sharp lagoon Aug 4, 2021, 2:17 AM

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sick steppe and all polynomials have a domain of R

how would i write all real numbers in interval notation

sick steppe Aug 4, 2021, 2:20 AM

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$(-\infty ,\infty)$

obsidian monolithBOT Aug 4, 2021, 2:20 AM

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Mosh

viscid thistle Aug 4, 2021, 3:49 AM

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sharp lagoon how can i approach this question?

is dis algebra 1

sharp lagoon Aug 4, 2021, 3:57 AM

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viscid thistle is dis algebra 1

LMAO i’m taking pre cal but that’s the “hw”

viscid thistle Aug 4, 2021, 3:58 AM

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sharp lagoon LMAO i’m taking pre cal but that’s the “hw”

ohh LMAO

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@sharp lagoon im pretty sure the domain is X element of R

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r as in real numbers

sharp lagoon Aug 4, 2021, 4:13 AM

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okok!

sharp lagoon Aug 4, 2021, 4:32 AM

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Ok, this one I know the radical (x-3) would be x>_to 3 but what do i do with the 6 outside

Screen_Shot_2021-08-03_at_9.32.00_PM.png

trim hemlock Aug 4, 2021, 4:33 AM

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the 6 outside does not affect the domain at all

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for x>=3, f(x) is always defined

sharp lagoon Aug 4, 2021, 4:38 AM

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I see,,,

sharp lagoon Aug 4, 2021, 5:05 AM

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what is wrong with my answer

Screen_Shot_2021-08-03_at_10.05.16_PM.png

willow bear Aug 4, 2021, 5:11 AM

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well for one the domain is just R (or (-∞, +∞) if you so desire and/or are required to write)

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but the range is not (-∞, +∞)

sharp lagoon Aug 4, 2021, 5:12 AM

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willow bear well for one the domain is just R (or (-∞, +∞) if you so desire and/or are requi...

OO makes sense

willow bear Aug 4, 2021, 5:12 AM

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sharp lagoon Aug 4, 2021, 5:12 AM

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OH i shouldve used desmo to graph it

willow bear Aug 4, 2021, 5:13 AM

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i mean you didn't need to use desmos specifically but you would've done well to graph it yes

tribal coral Aug 4, 2021, 6:51 AM

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f(x) = ln(10x)e^-x

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How do I prove ln(10x) < e^x for all x

steel venture Aug 4, 2021, 9:37 AM

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start by graphing it @tribal coral

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then think about manipulating the expression ln(10x)e^(-x) into the inequality ln(10x) < e^(x)

lusty veldt Aug 4, 2021, 3:00 PM

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Hello, can I ask where did the 4 and 1 came from?

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steel venture Aug 4, 2021, 3:04 PM

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it's completing the square

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they're on the other side of the equation as well

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if you're wondering why it's 4 and 1 specifically,
it's because x^2 - 4x can be turned into x^2 - 4x + (4 - 4) = (x^2 - 4x +4) - 4 = (x-2)^2 - 4
and similarly
y^2 + 2y = y^2 + 2y + (1 - 1) = (y^2 +2y +1) - 1 = (y + 1)^2 - 1

lusty veldt Aug 4, 2021, 3:20 PM

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Thankyouuu^^

hollow fog Aug 4, 2021, 6:56 PM

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trim hemlock for x>=3, f(x) is always defined

isn't it x >=3 ?

sick steppe Aug 4, 2021, 8:17 PM

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hollow fog isn't it x >=3 ?

that's.. what they wrote

mystic cloak Aug 5, 2021, 1:30 AM

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Screen_Shot_2021-08-04_at_4.16.40_PM.png

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Please prove