#help-49

1 messages · Page 31 of 1

torpid silo
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@wary thorn

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last slate
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Why is the set of all real valued polynomials $\mathbb{P}$ a vector space? What are the vectors? It doesn't have to be linear?

grand pondBOT
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determinate

last slate
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Noobiwan I need to finish this

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.close

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subtle blaze
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It’s a space of functions

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@last slate

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last nebula
midnight plankBOT
last nebula
#

where do I start with this question?

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oh wait nvm I think I got it

raven abyss
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Identify right triangles

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ok 👍

last nebula
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.close

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gritty holly
#

how do you do the following:

midnight plankBOT
gritty holly
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for what values of m will y=mx-8 be a tangent to the parabola y=x^2-5

spring latch
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do you know calculus

gritty holly
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no

spring latch
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alr

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id start by graphing it

gritty holly
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yeah i already did that

final plume
grand pondBOT
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Daddy_314

gritty holly
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k

final plume
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"k

#

"

gritty holly
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yeah i think i know what to do

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mx-8=x^2 -5

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x^2 -mx +3 =0

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cinder path
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hello

midnight plankBOT
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Please don't occupy multiple help channels.

cinder path
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need help for this

lavish venture
cinder path
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i found

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.close

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thorny geyser
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Guys help how do i calculate the f(0,52)

midnight plankBOT
hard zinc
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what module?

thorny geyser
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Supply chain management

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Is there a table i can look at?

main current
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We don't know what f refers to here. We might need more context.

thorny geyser
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This is the task

main current
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Okay so f refers to the normal distribution

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You probably have a table for it somewhere

thorny geyser
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Yes i looked it up online

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But where should i look at the table

main current
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The pdf can be calculated with any calculator, as long as you know the formula

thorny geyser
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Do you know the formula?

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@thorny geyser Has your question been resolved?

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unique cedar
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hi

midnight plankBOT
unique cedar
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is it too small?

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i got the first one right and 36 * 24 = 864 but apperently thats incorrect)

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@unique cedar Has your question been resolved?

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@unique cedar Has your question been resolved?

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@unique cedar Has your question been resolved?

final monolith
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so 864=(36-2*6)*(h-2*9)

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gets you 54

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which makes sense because the post is supposed to be taller than wide and at about a 3:2 ratio

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last nebula
midnight plankBOT
last nebula
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how do I solve this

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like do I do cross multiple with sin(x)

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like how do I single out the x

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to find the angle

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this is my process rn

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but idk what’s next

rose cobalt
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$\arcsin(\sin(x))=x$

grand pondBOT
last nebula
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oh o tysm

last nebula
rose cobalt
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You should write it in this way

sinx = c
Then
x=arcsinc

last nebula
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what?

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sorry I don’t get it

rose cobalt
last nebula
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yes I know

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can you write an example using that equation?

rose cobalt
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$\sin(x)=\frac{\sqrt{3}}{2} \
x=\arcsin(\frac{\sqrt{3}}{2})$

grand pondBOT
last nebula
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but I have to cross multiple?

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I did arcsin (78)

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I got error

rose cobalt
last nebula
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whats RHS?

rose cobalt
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Right Hand Side

last nebula
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no the bottom is

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d=78

rose cobalt
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What’s the value of the number

last nebula
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wdym?

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umbral rampart
#

Wondering if answers are correct

midnight plankBOT
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@umbral rampart Has your question been resolved?

umbral rampart
#

.

crisp oxide
umbral rampart
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flipped diagram upside down and used pythagoras for big cone and small cone then subtracted

crisp oxide
#

I haven’t calculated it but that’s the right method

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formal prawn
midnight plankBOT
formal prawn
#

Is g : R^3 —> R^3
(x,y,z) |—> (1-2t,t,t)
a valid parameterization of C ?

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wintry plover
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Im stuck can skmeone uelp

midnight plankBOT
wintry plover
fiery plover
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is it $\frac{\sin(2x)}{1-\sin^2(x)}$

grand pondBOT
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The Prophet Of The Damned

weak field
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Or x, you ended up with a combination of them throughout your question

dull yoke
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@wintry plover ur on the right track

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just recall what sin(x)/cos(x) is equal to

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keen pebble
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Find the definite integral of y = sec^2 (pi x/2) using the graph. The answer the teacher gave was 3.464 units^2 but I got undefined, so i'm not sure if the question itself is wrong or I did something wrong

raven abyss
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Can you show your work

keen pebble
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if you put x as 1, it's undefined

raven abyss
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Oh I think you’ll need to do the limit as it approaches 1 I think

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Actually I think I’m thinking of something else

keen pebble
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lim (sec^2 (pix/2) when x is approaching 1 is infinity

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or maybe the answer provided is just wrong 🤔

raven abyss
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How did you get the area of 1/X from 0 to 1 then

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I’m pretty sure there’s a value I remember seeing a video or something lol

keen pebble
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I have no idea 😭

raven abyss
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Can I see the original problem

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it’s called a divergent integral

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the one you have I think

keen pebble
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so the limit does not exist?

midnight plankBOT
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@keen pebble Has your question been resolved?

midnight plankBOT
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@keen pebble Has your question been resolved?

small jasper
#

,w integrate (sec(pi*x/2))^2 from 0 to 2pi/3

grand pondBOT
small jasper
#

Looks like it diverges

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tiny gate
#

Have I made a mistake anywhere

midnight plankBOT
tiny gate
#

Nvm

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.close

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toxic flower
#

can someone explain this please? i rearranged to $\frac{dy}{dx} = \frac{y^2 -2xy} {x^2}$ and have $F(t) = t^2-2t$. Im stuck from what to do here. If anyone can help with this, that'd be great

grand pondBOT
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lewis_f04

wild solstice
toxic flower
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??

mortal rain
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Try u=y/x

midnight plankBOT
#

@toxic flower Has your question been resolved?

toxic flower
grand pondBOT
#

lewis_f04

mortal rain
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Then you need to transform dy/dx into the expression of du/dx、u and x

toxic flower
mortal rain
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u=y/x→xu=y
Differentiate both sides with respect of x

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neon dune
#

Hi. could someone help with this? I tried several methods of splitting this up and none worked

midnight plankBOT
#

@neon dune Has your question been resolved?

sharp coral
#

what are you trying to find?

neon dune
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in terms of n

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im still stuck lol

sharp coral
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,w sum from r=1 to n of (2r+3)/(3^r*(r+1))

neon dune
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doing here

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how did they get there

sharp coral
neon dune
sharp coral
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i don't think you can reasonably be expected to find such a formula yourself

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inner onyx
#

can someone explain local maximum and local minimum in a way I would understand?

polar mortar
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what about them? the definition?

inner onyx
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well i'm given this:

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and i need to figure out where local minimum and maximum is

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i'm guessing it's where it's low and begins going up

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and where it's high and begins going down?

jovial crest
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Yeah

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Those are the local maxima and minima

polar mortar
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local maximum means the graph has a peak, or highest point, in some region.
local minimum means it has a valley, or lowest point, in some region

inner onyx
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so in this case, the local minima would be (-2,1)

jovial crest
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So if you see a " downwards peak " it is a local minimum and an " upwards peak " is a local maximum

inner onyx
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cause that's the lowest point i'm given

inner onyx
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alright, thanks

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i dont understand none of this

jovial crest
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Well did you understand how to find the minima and maxima graphically?

inner onyx
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any of you happen to know what monotonicity is?

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yeah! thanks!

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i had this in school but was sick ://

jovial crest
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If a function is strictly increasing or decreasing all across its domain it's monotonic

inner onyx
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so this case is not strictly increasing or decreasing

jovial crest
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Yeah

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So it's not monotonic

inner onyx
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okay, perfect, thanks

jovial crest
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An example of a monotonic function is a linear function

inner onyx
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very tough to remember haha

jovial crest
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Or e^x

inner onyx
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yeah I was about to ask about that

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but like uh

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the graph for sinus?

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that goes like up and down

jovial crest
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Sine isn't monotonic

inner onyx
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yeah okay

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perfect

jovial crest
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Cause the slope isn't strictly increasing or decreasing in the domain

inner onyx
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yeah it goes like woosh woosh

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up n down

jovial crest
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Yeee

inner onyx
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i've got one last question tho

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what is definitionamount?

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wait let me figure out the proper english word

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domain and range i think?

jovial crest
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Domain is basically all the values that you can define a function for

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Example, √x

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Here the domain is x≥0

inner onyx
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wait huuuh

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what is √x

jovial crest
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Square root of x

inner onyx
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oh

jovial crest
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So, negative square roots aren't defined in the real numbers

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So √x you can only input values greater than or equal to 0

inner onyx
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uhhhh

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like in x's place?

jovial crest
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Yup

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So think of x as a computer

inner onyx
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why not negative numbers tho?

jovial crest
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The domain is all the values the computer can accept

jovial crest
inner onyx
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oh yeah

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thats

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correct

jovial crest
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And the range is all the values the computer gives to you

inner onyx
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ohhhh so it's like

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if you're given

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y=ax+b

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or y=mx+b

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your range would be y

jovial crest
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Noo

inner onyx
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and your domain would be x?

jovial crest
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Your range will be all the possible values of y

inner onyx
#

ohhhhhhhhh

jovial crest
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And your domain will be all the possible values of x

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For all linear functions, both domain and range are all real numbers

inner onyx
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so if I go back to this:

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it would be every value?

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cause wouldn't it just continue?

jovial crest
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This looks like a cubic to me so assuming it is, yes

inner onyx
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hmmm

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i wasn't fiven much information about this lol

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but if i have

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the sine thingy

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then there would only be some range

jovial crest
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Yeah

inner onyx
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cause it's not infinitely tall

jovial crest
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But the domain is all reals

inner onyx
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but there would be infinite domains

jovial crest
inner onyx
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yeah okay

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and for tangent it would be opposite?

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if i remember them correct

jovial crest
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Well the tangent function doesn't have a domain of all reals

inner onyx
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it doesnt?

jovial crest
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It's undefined for integer multiples of π/2

inner onyx
#

uhhh in english please? 😂

jovial crest
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What's the tangent of π/2

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Or tangent of 90°

inner onyx
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uhhhhh 1?

jovial crest
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I mistyped

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What's the tangent of π/2

inner onyx
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i'm supposed to know that by heart?

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cause i'll be honset, I have no clue

jovial crest
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Well

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Yes

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You should know it only for 5 angles tho

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Just memorise the sin values of
0, π/6,π/4,π/3,π/2

inner onyx
#

uhm... how...

jovial crest
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Well you can find " tricks " online

inner onyx
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well for 0 it would just be 0, no?

jovial crest
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Yeah!

inner onyx
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hmmm

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i'm still a bit confused

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when in math do you use this? Like under which subject?

jovial crest
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Trigonometry

inner onyx
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HUUHHHHHH

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i never heard of it

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like doing it by head

jovial crest
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Maybe it's called something diff in ur country?

inner onyx
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wait

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isn't it for balls?

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pi/6

jovial crest
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Well it's more so for triangles

inner onyx
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oh...

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we just... finished trigonometry lmao

jovial crest
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Oh

inner onyx
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we had about sine, cosine and tangent awhile ago aswell

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but we had like how to utilize it etc

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using cas

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anyway it's unimportant

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i still don't get why tan(x) wouldn't have infinite domains?

jovial crest
river scarab
#

mb

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wrong chat

inner onyx
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all good 😄

jovial crest
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Its range is all reals tho

inner onyx
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wait

river scarab
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sorry about that

inner onyx
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OH SHI

inner onyx
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wait

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wait

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domain = all possible x's?

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range = all possible y's?

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then yeah the range is all possible values, my bad

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cause i drew it

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and these are all possible y's

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not x's

jovial crest
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Ye

inner onyx
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yeah my bad

jovial crest
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But u see how it's asymptote when x=π/2 or its multiple

inner onyx
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asymptote???

jovial crest
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That it tends to infinity

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Meaning it's undefined

inner onyx
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yeah the y?

jovial crest
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Ye

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Or wair I can explain it better

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U know what's cos π/2?

inner onyx
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yeah it seems like it continues for infinity

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uhhhhh

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negative?

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i'd guess like

jovial crest
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No

inner onyx
#

1.6?

jovial crest
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It's 0

inner onyx
#

oop

jovial crest
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And sin π/2 is 1

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Tan π/2 is sinπ/2/cosπ/2

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Which is 1/0

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Which is undedined

inner onyx
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OHHHHHHHHHHHHHHHHHHHHHHHHH

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cause Tan(v)=opposite/cos

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idk how to explain it

jovial crest
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Ye

inner onyx
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but yes i figure you understand what I meant lmao

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so it's undefined because it doesn't have an answer?

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but wouldn't 1/0 = 0?

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wait am i failing elementary school math holdups

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nevermind

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shush

jovial crest
inner onyx
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dont mention anything

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you can't say 1/0

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1/0 = undefined

jovial crest
#

Ye

inner onyx
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so Tan(pi/2) is also undefined

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and Tan(v)=sin(pi/2) / cos(pi/2 is also undefined

jovial crest
#

Yw

inner onyx
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well i got that much smarter today, thank you!

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i hope i can catch up on this haha

jovial crest
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Dw u can, i was confused same time last year while learning trigo

inner onyx
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haha thanks

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we have about functions now

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i missed one day in half a year and i felt so confused when my teacher said all this was homework

jovial crest
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What grade are u in if I may ask?

inner onyx
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well here it would be inbetween highschool and college

jovial crest
inner onyx
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HUH

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here the bare minimum is like the same, but in math i have like 98% lmao

jovial crest
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We don't have it class wise

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We have it overall

inner onyx
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ah yeah us aswell

jovial crest
#

Cause everyday we have all the subjects

inner onyx
#

ohhhhhhh

jovial crest
#

Where are u from?

inner onyx
#

denmark!

#

you?

jovial crest
#

Oh I'm indian

inner onyx
#

dang that's far away

jovial crest
#

Ye

inner onyx
#

i'm thinking of studying abroad

jovial crest
#

Same!

#

I probably will do a bachelor's here though

inner onyx
#

oh you're at your bachelors?

jovial crest
#

No

#

I'm in grade 11

inner onyx
#

i'll start my bachelors in a little over 2 years

#

wait so you're

#

17?

jovial crest
#

Grade 11 is for 16 year olds

#

No, I'm 15 going on 16

inner onyx
#

holy

#

you're hella good at math for your age lmao

jovial crest
#

We have a different curriculum, our grade 10 ( for kids who are 15 ) has basic trigo

inner onyx
#

ahhhhh

jovial crest
#

We domt have functions tho

inner onyx
#

lucky you

jovial crest
#

We have functions next year

inner onyx
#

it's painful

#

we have basic trigonometry last year aswell

#

but i went to the 7th worst school in denmark

#

so yeah i didnt learn shi lmao

jovial crest
#

Lmfao yeah my school isnt the best eitherz but I'm changing schools this year

#

For coaching

inner onyx
#

ohhhhh

jovial crest
#

Coaching is basically preparation for an exam which grants you entrance into most engineering degrees in the country in case u don't know

#

As well as some other bachelors

inner onyx
#

ohhhh

#

you're gonna be able to take your bachelors early then?

jovial crest
#

No

#

Everyone starts their bachelor's ar 18-19

inner onyx
#

ah okay

jovial crest
#

And at 17-18 if you wanna pursue engineering you give an exam, which is what I'm gonna be coached for

#

It's a retrace honestly

inner onyx
#

ahhhh

#

that makes sense

#

it's kinda boring for me tho

#

we have one of the most prestigious schools for engineering in europe like

#

5 minutes away from me

jovial crest
#

Oh wow

inner onyx
#

but i wanna study abroad so ´bad lmao

jovial crest
#

I wanna study abroad mainly because I wanna leave the country someday

inner onyx
#

oh?

jovial crest
inner onyx
jovial crest
# inner onyx oh?

Yeah India's slowly becoming shitty cause of our islamophobic and xenophobic govt

inner onyx
#

ahhh i see

#

ours is very much the opposite haha

jovial crest
#

Yeah that's expected of Europe haha

inner onyx
#

yeah but people here are so spoiled

#

and entitled

#

and very racist

#

i grew up in a ghetto here

#

meaning most of my friends were of other ethnic backgrounds

#

and while going out with them they would always get racist comments

jovial crest
inner onyx
#

but here it's only the older people

#

or as they call it "cozy racism"

jovial crest
#

Yeah I'd assume the young people are more tolerant

inner onyx
#

idk how that correlates but wtv

jovial crest
inner onyx
#

but the people here were too rich for too long

#

so the second something bad happens, they put the blame on immigrants

jovial crest
#

First world problems 😭

inner onyx
#

bro it is fr 😭

jovial crest
#

Europeans blaming immigrants for every issue under the sun

inner onyx
#

like even my family does

#

i went to my grandparents

#

who I love very much

#

and they're discussing like crime rates in denmark

#

and like atleast they're not that eyed towards one direction, but I see where they wanted to put the blame

jovial crest
#

Thats basically backhanded racism

inner onyx
#

yeah

#

it's whatever tbh

#

people here just love it involve themselves

jovial crest
#

Here, people are discriminatory too but more about religion than race

inner onyx
#

ahhhh

#

i see

jovial crest
#

Like the Country has 80%+ Hinduism followers who hate all the Muslim ppls and blame them for the shortcomings of the country

inner onyx
#

of course

#

it's kinda the other way around here

#

like i'm an atheist

#

and so many people, especially islamics, have commented on why I am

#

even blamed me for not being muslim

#

and most of denmark is atheistic

#

or like they're christians, but it's more for the culture

jovial crest
jovial crest
inner onyx
#

it's kinda overboard but whatever

jovial crest
# inner onyx or like they're christians, but it's more for the culture

Sort of similar situation here
Here we have to declare our religion in all government papers along with our birth certificates, in all of those I'm a Hindu but practically I'm an atheist, a large portion of the population is like this where they're atheist but on paper they follow xyz religion

inner onyx
#

yeah exactly the same here

#

except we dont put it on papers

#

but they're christians who dont believe in christ

jovial crest
#

We have to declare it on paper cause skme religions get benefits by virtue of being a minority

inner onyx
#

oh wow

#

that sounds

#

odd?

jovial crest
#

It is

inner onyx
#

tbh all these countries are whatever

jovial crest
#

We have a lot of reservation in government institutes for minoritirs

#

And people who are in marginalised groups

#

Maybe 27% I think in government jobs and colleges

inner onyx
#

that's kinda weird, no?

#

also i found out how stupid the danish politicians were today

#

someone said that nigerian people go to denmark to fix their phones

#

and they said that there were no nuclear reactors in europe?

jovial crest
jovial crest
inner onyx
inner onyx
jovial crest
#

Ye, sometimes here rich kids will get admissions into prestigious colleges that they don't deserve

#

Cause their great grandfather was part of a marginalized community

inner onyx
#

that's odd

#

here it's far more fair in that sense haha

jovial crest
jovial crest
#

To gain support from that community

jovial crest
inner onyx
jovial crest
#

I can give u an example

inner onyx
inner onyx
#

but you have to have a certain grade in order to apply for the schools

#

for example I'll need an average of 7, which is just above average for my university

#

and they have systems like that for all universities, aswell as highschools

jovial crest
#

Sometimes they ask u for extra money

#

If ur kid isn't that good at acadmeixs

inner onyx
#

ahhhh

#

yeah it's free here

jovial crest
#

In grade 12z the last year before graduation

#

We have a nation wide standardized exam

#

Most schools require that you get around 75% in that which isn't that good

#

And if u do get 75% you'll have to attempt another standardized exam depending on what u wanna pursue

#

And some schools require that u write their entry exam

inner onyx
#

ah kinda the same here, if your average isn't high enough

jovial crest
# inner onyx here anyone can get into any public school, highschool or university (we have 3 ...

The example I was talking about, here we have an exam called JEE which has 2 stages - mains and advanced. Mains is common for most engineering courses in the country but advanced is for the IIT's which are basically the best in the whole country ( acceptance rate of 0.5% ). You need a certain percentile in the mains exam to even qualify for advanced. For most of us ( general category ) it's 90 percentile meaning u need to score more than 90% of testtakers but for certain groups it's only 50 percentile meaning they only need to score more than 50% of testtakers

inner onyx
#

that's kinda weird

#

ANYWAY

#

i've got a mad mad woman screaming at me

#

(my mother)

#

since it's a little late here in denmark lmao

#

and i've gotta be up again in less than 5 hours 💀

jovial crest
#

Same

#

I have an orientation todsy

inner onyx
#

dang go to bed bro

jovial crest
#

For my new school

inner onyx
#

ohhhh

#

then get ur ass to bed

jovial crest
#

I'm in bed but I just can't fall asleep 😭

inner onyx
#

close ur eyes and make it work

#

anyway, gn

#

and thanks 😮

#

.close

midnight plankBOT
#
Channel closed

Closed by @inner onyx

Use .reopen if this was a mistake.

midnight plankBOT
#
Available help channel!

Send your question here to claim the channel.

Remember:
Ask your math question in a clear, concise manner.
Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

earnest ermine
#

(Op A PAU junio 2014) It is known that the graph of $f(x) = ax^2 + b$ has a horizontal tangent line at the point $(2, 4)$. Determine the values of $a$ and $b$.

grand pondBOT
#

MortterGx

earnest ermine
#

please

dull yoke
#

what have u tried

earnest ermine
#

f'(x) = m = 0

dull yoke
#

f'(x) = 0 at what value of x?

earnest ermine
#

2

#

right?

dull yoke
#

good

#

so how can we use that information

#

if we know the slope is 0 at x = 2

earnest ermine
#

$f'(x) = \frac{ax^2-b}{x^2}$

grand pondBOT
#

MortterGx

dull yoke
#

howd u get that?

earnest ermine
#

in the function I have to substitute x,y in the values to clear point a or b

earnest ermine
#

before substitute

dull yoke
#

no that is wrong

#

try taking derivative of ax^2 + b again

earnest ermine
#

this one

dull yoke
#

what is that

#

where is that coming from

earnest ermine
dull yoke
#

oh

earnest ermine
dull yoke
#

ok

earnest ermine
#

$f(x) = \left(\frac{ax^2+b}{x}\right)$

grand pondBOT
#

MortterGx

dull yoke
earnest ermine
#

a

earnest ermine
dull yoke
#

numerator

#

do u remember quotient rule

earnest ermine
#

$\frac{2axx-1\cdot \left(ax^2+b\right)}{x^2}$

earnest ermine
grand pondBOT
#

MortterGx

dull yoke
#

oh wait

earnest ermine
#

no?

dull yoke
#

a

#

sip

#

lo siento

earnest ermine
#

no pasa nada

dull yoke
#

ok, now we have

#

f'(2) = 0

earnest ermine
#

$\frac{4a+b}{2}$

dull yoke
grand pondBOT
#

MortterGx

earnest ermine
#

=0

#

a= -b/4

dull yoke
dull yoke
earnest ermine
#

yes

#

its the rigth

dull yoke
#

$f'(2) = \frac {a(2^2) - b}{2^2}$

grand pondBOT
#

Stephen

earnest ermine
#

$f(x) = \left(\frac{ax^2+b}{x}\right) ; \frac{a2^2+b}{2}=0; a2^2+b=0$

grand pondBOT
#

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

earnest ermine
#

oh

#

i see

dull yoke
#

no, we dont set f(2) = 0

#

f(2) = 4

#

not 0

#

f'(2) = 0

#

entiendes?

earnest ermine
#

$f'(x) = \frac{ax^2-b}{x^2}$

grand pondBOT
#

MortterGx

earnest ermine
#

wait

#

$4=:\frac{a2^2-b}{2^2}$

grand pondBOT
#

MortterGx

earnest ermine
#

$16=:4a-b$

grand pondBOT
#

MortterGx

earnest ermine
#

$a=:4-b$

grand pondBOT
#

MortterGx

dull yoke
#

f'(2) is not equal to 4

earnest ermine
#

+b

#

mmm

dull yoke
#

f'(2) = 0

#

$f'(2) = \frac {a(2^2) - b}{2^2} = 0$

grand pondBOT
#

Stephen

earnest ermine
#

I do not have to replace the y?

#

mb

#

f'=0

dull yoke
#

f'(2) = 0

dull yoke
earnest ermine
#

$4a-b:=0$

grand pondBOT
#

MortterGx

dull yoke
#

sip

earnest ermine
#

$4a:=b$

grand pondBOT
#

MortterGx

earnest ermine
#

xd

#

then

dull yoke
#

asi ahora tenemos la primera equacion

earnest ermine
#

eres español?

dull yoke
#

necesitamos la segunda

#

no

earnest ermine
#

ok

dull yoke
#

sabes? como lo podemos hacer?

earnest ermine
#

the second is by substituting in the initial function?

dull yoke
#

yes

earnest ermine
#

2-a=b

dull yoke
#

howd u get that?

earnest ermine
#

I did it before

#

its wrong btw

dull yoke
#

we know that f(2) = 4

#

plug in 2 into original function

earnest ermine
#

$\left(\frac{4a+b}{2}\right)$

grand pondBOT
#

MortterGx

earnest ermine
#

=4

dull yoke
#

si

#

keep going

earnest ermine
#

8/4 -b

#

=a

dull yoke
#

no

#

$\frac {4a + b}{2} = 4$

grand pondBOT
#

Stephen

dull yoke
#

$4a + b = 8$

earnest ermine
#

$a=\frac{8-b}{4}$

grand pondBOT
#

Stephen

#

MortterGx

dull yoke
#

yes

#

and we know 4a = b

#

$4a + b = 8 \newline 4a = b$

grand pondBOT
#

Stephen

earnest ermine
#

2b=8

#

b=4

dull yoke
#

yes

earnest ermine
#

a=1

dull yoke
#

yea

earnest ermine
#

let's summarize the steps xd

#

today I am not working well

dull yoke
#

we had the point (2,4)

#

therefore we know f(2) = 4

earnest ermine
#

initial function, I substitute both x and y to clear one variable

dull yoke
#

we also know f'(2) = 0 because theres a horizontal tangent at x = 2

dull yoke
earnest ermine
#

then I do the derivative of the function to substitute only x and take out the variable again.

#

I solve the system and that's it

dull yoke
#

yea

earnest ermine
#

then the tangent line q is the formula

#

y - 4= 0 (x - 2)

#

y=4

#

rigth?

dull yoke
#

that just simplifies to y = 4

#

thats the tangent line at x = 2 yes

#

but why do u need that?

earnest ermine
#

just to remind myself

#

I have a global in little and tangent line exercises there are many types I think.

#

and I get quite confused

earnest ermine
dull yoke
#

ok

earnest ermine
#
  1. (Op B EBAU sep 2020)
    Find the values of a and b so that the line of equation y = 6x + a is tangent to the curve ... at the point of abscissa x = 0. Write the functions obtained.
dull yoke
#

ok have u tried anything?

earnest ermine
#

starting

#

$\frac{b\left(bx+1\right)-b\left(bx-1\right)}{\left(bx+1\right)^2}$

grand pondBOT
#

MortterGx

earnest ermine
#

derivating

dull yoke
#

we already know the slope at x = 0

earnest ermine
#

$\frac{2b}{\left(bx+1\right)^2}$

grand pondBOT
#

MortterGx

dull yoke
#

ok

earnest ermine
dull yoke
#

y = 6x + a is tangent to f(x) at x = 0, so f'(0) = 6

earnest ermine
#

i see

dull yoke
#

just do

#

1 sec

dull yoke
#

set this equal to 6

#

and then plug in x = 0

earnest ermine
#

$\frac{2b}{\left(bx+1\right)^2}=6$

grand pondBOT
#

MortterGx

dull yoke
#

yes,

#

plug in x = 0

earnest ermine
#

b=3

#

then

#

$fy=:\frac{b0-1}{b0+1}$

dull yoke
#

we know that f(0) = y at x = 0

#

so find f(0)

grand pondBOT
#

MortterGx

dull yoke
#

so what is f(0)

earnest ermine
#

-1

dull yoke
#

yes

#

y = 6x + a

#

x = 0, y = -1

earnest ermine
#

y= a

#

a = -1

dull yoke
#

yes

earnest ermine
#

b= 3

#

this one seemed easier

#
  1. (Op A PAU June 2015)
    Consider the function f(x) = ln(x 1) defined on the interval [2, e + 1]. Determine the equation of the line tangent to the curve y = ln(x-1)
    parallel to the line passing through the points P(2, 0) and Q(e + 1, 1).
dull yoke
#

i gotta get going now

earnest ermine
#

oh ok

dull yoke
#

cya

earnest ermine
#

cya

#

.close

midnight plankBOT
#
Channel closed

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midnight plankBOT
#
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Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
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rain wasp
midnight plankBOT
rain wasp
#

asking again cuz i still dont get it

#

and i was afk

pearl kindle
#

see it from this angle

#

i hope its clear in the picture

#

thats like its projection from that angle

rain wasp
#

since A is not fixed

pearl kindle
#

thats not AC that we want at the moment

pearl kindle
rain wasp
#

yeah

#

triangle ADC is a right triangle too

pearl kindle
#

alright, so 4r^2 = AB^2 + AC^2, so here is AB, we still need to get BC^2 into the eq.

#

can u find a relation between BC and AC?

pearl kindle
rain wasp
#

i think i can actually find the diameter

#

since we are given sphere equation and the plane equation

pearl kindle
#

try to find a plane that has both AC and BC together

rain wasp
pearl kindle
old iron
#

Damn

rain wasp
#

so we sub this into the first equation?

#

we would get BC = 2r

pearl kindle
#

?

pearl kindle
#

wait

#

no

pearl kindle
pearl kindle
rain wasp
#

AD^2+AC^2=4r^2
AB^2+AC^2=BC^2

#

so therefore BC^2=4r^2 no?

pearl kindle
rain wasp
#

oh right yeah

#

so we would get AD^2+BC^2-AB^2=4r^2

pearl kindle
#

yepp

#

solve for AD^2 + BC^2

rain wasp
#

ahh i see now

#

ok brb imma do some calculations

#

64

#

seems correct too

#

@pearl kindle thanks!

midnight plankBOT
#

@rain wasp Has your question been resolved?

midnight plankBOT
#
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#
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Ask your math question in a clear, concise manner.
Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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steady lotus
#

Hi, I'm hoping to get some help with solving this equation:
I always do some kind of algebra which is like "illegal" so I usually end up getting the wrong answer. Can anyone offer some useful advice/tips when it comes to solving the bottom line for V_c1? When I look online it says to use the common denominator etc. but I actually don't know how to quickly work it out.

hearty rune
#

it would be easiest to just split the fractions then factor the Vc1 terms

#

then you dont actually have to find the common denominator

steady lotus
#

I think that's the process I typically do, and that's where I always end up doing something that I don't realise I'm not allowed to do, and I end up getting it wrong lol

hearty rune
#

hm, how would you do it here?

steady lotus
#

Just writing it out

#

Alright well I've worked it out and it's correct lol, but I got it wrong originally because I pressed something wrong in my calculator

#

Maybe I just have to be mindful that I'm putting it correctly into my calculator for exams

#

this was my working out for reference

hearty rune
#

always helps to double check what you type

#

or even just type it again with fresh eyes

steady lotus
#

yeah probably hey

#

but yeah that method will probs be the best one to do, I think I remember a tutor telling me last year in a different course to use that method as well

midnight plankBOT
#

@steady lotus Has your question been resolved?

midnight plankBOT
#
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After 15 minutes, feel free to ping <@&286206848099549185>.
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half crest
#

I'm not sure why this wouldn't be the answer, I also tried make j as 1

sharp coral
#

are all vectors in V parallel to the y-axis?

half crest
#

I thought so?

#

because if x is whatever x is and y is 0 then its just pointing straight up i thought

sharp coral
#

are they pointing straight up?

half crest
#

or straight down

#

but i feel like maybe its not then 😭

#

but i dont understand why not

sharp coral
#

what is the unit vector that points straight up?

half crest
#

im not sure flonshed

#

sorry let me check the notes

#

could it be just <1,0>?

#

OR NO

#

THATS SIDEWAYS

#

<0,1> or <0,y>

#

idk why i was thinking like that my bad

#

could you help me with this one too?
originally i said C A B (dumb idk why i did that), but does this make sense for my answers?

sharp coral
#

the gradient field always points in the direction of greatest change

#

the countour plots always go along the direction of no change

#

so, the gradient field is always perpendicular to the contours

half crest
#

ohhh?

#

i struggled with countor plots so its causing me problems again lol

#

let me think real quick

#

so far im sure that 3 is A

#

I'm thinking C B A

sharp coral
#

try to imagine the two images on top of each other. for which combinations is the vector field always perpendicular to the curves?

half crest
#

mmm okok

#

B C A

#

i felt confident so I submitted it and it was right catgiggle

#

thank you for your help! it was my last problem so i can sleep early tonight as a result!

#

.close

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#
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

harsh mauve
#

If I am asked to find the roots of the quadratic equation: y=-2(x-1)^2-3, you can get two values of x that incorporate the imaginary number i, but would those still count as roots as the quadratic?

zealous schooner
#

Yes they would

#

They’re just not real roots, they’re still roots

harsh mauve
#

Because if you graph the quadratic out there are no points that intercept with the x-axis

#

So I should still write them as the roots right, I wouldn’t just put “no roots” as the answer?

zealous schooner
#

Well depends on what type of exercise it is?

#

Did they ask you specifically for real roots?

harsh mauve
#

it only says roots:, but its only 9th grade math so im assuming my teacher wouldn’t be asking for something that complex

zealous schooner
#

If you haven’t been taught complex numbers then I guess you don’t need to write those roots

harsh mauve
#

Alright well thanks for clarifying, I just wanted to make sure the roots are still considered an answer although the graph doesn’t have any

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🙏🙏

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hardy mica
#

Where error

midnight plankBOT
hardy mica
#

,rotate

grand pondBOT
shrewd sapphire
#

I'm pretty sure

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u can't take out square from sin^2

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u can use identity tho

hardy mica
#

Why not

shrewd sapphire
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cuz

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sin is kinda like a function probably

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so like imagine sin function called f(x)

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if it's sin^2

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it's f^2(x)

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not ( f(x))^2

#

try using

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sin^2(x) = 1-cos2x/2 identy to finish

hardy mica
#

Is trig identity the same as rules for trigonometry

shrewd sapphire
#

likely correct

hardy mica
#

Ok
.

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tidal token
sleek dagger
tidal token
#

$ \sin^{2}(x) = [\sin (x)]^2 $

sleek dagger
#

0<sin^-1(x)<1

#

i think thats the problem

#

you insert pie which is larger then 1 therefore it cant be

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junior horizon
#

Question: A is a set of straight lines. Write a statement that says that there is no pair of two lines in A that are parallel

junior horizon
#

Is this statement true?

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junior horizon
#

<@&286206848099549185>

small ferry
#

Hello

#

State your question.

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///

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//

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/

#

Cancelled

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latent plover
midnight plankBOT
latent plover
#

in this differential equation would the particular integral be:

Ax^2*e^-2x + Bx + C?

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#

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latent plover
#

<@&286206848099549185>

latent plover
#

like compare coefficients and stuff it's soo messy so I think im going wrong

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umbral rampart
midnight plankBOT
umbral rampart
#

Am fine with question B, need help with A

hearty rune
#

all interior sum to 360
opposite pairs sum to 180

umbral rampart
#

i mean

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i don't understand how for example x+2y=160 came about

hearty rune
#

opposite pairs sum to 180

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DAB and BCD

umbral rampart
#

oh shit jus saw that

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thought it's 8 not 18

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last slate
midnight plankBOT
last slate
#

Why is it safe to conclude the vertical U = 0 ?

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It only says horizontal u = 21 but never mentions vertical u so why can we infer it is 0

dull yoke
#

pebble is thrown horizontally

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means vertical component of velo is 0

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@last slate

last slate
#

Thanks

last slate
dull yoke
#

wdym

last slate
#

It has vertical values for acceleration

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so why cant it have vertical values for initial velocity?

dull yoke
#

yea, its just saying initially, vertical velo is 0

last slate
dull yoke
#

pebble is thrown horizontally

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means initial vertical velo is 0

last slate
#

Ah okay thanks ill make a note of that

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.close

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last slate
#

.reopen

midnight plankBOT
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last slate
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Just want to make sure i understand it fully

dull yoke
#

well when it hits the ground, ofc vertical velocity is 0

last slate
#

no i mean just before

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just before it hits the ground becuase it isnt written so i dont know

dull yoke
#

just before it hits the ground, it has nonzero vertical velocity