why does the gamma power become negative?
#help-10
short lily
obtuse pebbleBOT
why does the gamma power become negative?
timid silo
$\frac{1}{x}=x^{-1}$
warm shaleBOT
Toby (eric tao for honourable)
timid silo
Marcel purchased a television at a price that was less than its list price. The total amount that he paid for the television consisted of the purchase price and a sales tax of $7.20, which was p percent of the purchase price. Which of the following statements individually provide(s) sufficient additional information to determine the value of p ?
Indicate all such statements.
A The total amount that Marcel paid for the television was $127.20.
B The purchase price of the television was $40.00 less than the list price.
C The purchase price of the television was 25 percent less than the list price.
obtuse pebbleBOT
Marcel purchased a television at a price that was less than its list price. The ...
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
rugged acorn
We define A the total amount, T the purchase, t the tax
Let's summarize :
-The total amount is the purchase price + the tax. So we have A = T+t
-The tax is p percent of the purchase price, so t = p/100 × T
And with statements A we know A and t (the tax and the total amount)
Does that help @timid silo ?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
winged aurora
Can i use the quadratic formulae if there are two variables , the eqn is :- x^2 -(5+y)x + 2 +3y =0
obtuse pebbleBOT
Can i use the quadratic formulae if there are two variables , the eqn is :- x^2 ...
brave bramble
Yes. You'll get x = (stuff with y in it)
winged aurora
But quadratic eqn is ax^2 +bx +c , where a is not zero , here the c is not constant but variable is present is that alright?
slim cove
Nope it can be whatever you want
we're assuming here that y is not a function of x
so y is like, independent from x
so for the purposes of solving for x, you can treat y like a constant
obtuse pebbleBOT
@winged aurora Has your question been resolved?
winged aurora
Thanks
hushed gust
obtuse pebbleBOT
hushed gust
Hey guys, could I get some guidance on how to solve this problem?
mint tendon
do you know what determines whether a quadratic will have real solutoins or not?
hushed gust
When the discriminant is less than 0?
mint tendon
yes
true elbow
can someone help me
mint tendon
woah
true elbow
oh
mint tendon
dont raid someone else's help channel m9
hushed gust
I will need to use the discriminant formula which is b^2-4ac right?
mint tendon
yep
hushed gust
Ok I will try it now
I'm not sure what I've done wrong :o
Do I use the quadratic formula to find K since I can't factor it?
Or perhaps?
obtuse pebbleBOT
@hushed gust Has your question been resolved?
obtuse pebbleBOT
@hushed gust Has your question been resolved?
hexed blaze
Or perhaps?
Yes use it
Or
k²-16k+4
=k²-16k+64-60
=(k-8)²-(√60)²
obtuse pebbleBOT
@hushed gust Has your question been resolved?
hushed gust
Yes use it
Or
k²-16k+4
=k²-16k+64-60
=(k-8)²-(√60)²
k=8±2√15
k=15.746
k=0.254033
I'm not very sure of how to answer the question mentioned. Can u help me? This is the question
hexed blaze
Well when a quadratic equation has no real solution?
hushed gust
Would I answer by saying when k = 15.746 and 0.254033, the function has no real solutions?
hushed gust
A quadratic has no real solutions when the discriminant is less than 0
hexed blaze
And what is discriminant
Also this is math so it's always best to write in symbol
ik I'm just guiding him a
tardy epoch
oh i'm an idiot
hexed blaze
Yeah this the problem
You do know discriminants less than 0 but don't know how it is written in math right
It is b²-4ac<0
hushed gust
yeah but it asks me to say for what values of K the function has no real solutions
hexed blaze
k=8±2√15
k=15.746
k=0.254033
you know that when k=8±2√15
the k²-16k+4 will = 0
Draw it in number line
-∞ 8-2√15 8+2√15 +∞
-----------|------------|---------------
You can see there are 3 segments
Which segments make the b²-4ac<0
If you don't know, put a representing value
of each segment
hushed gust
What does the line mean
hexed blaze
It's the number line
to make it easy, pick a representing number of each segment
Any
The left segment, pick a number that is smaller than 8-2√15(~0.25)
hushed gust
"you know that when k=8±2√15
the k²-16k+4 will = 0"
tardy epoch
Draw it in number line
-∞ 8-2√15 8+2√15 +∞
-----------|-----------...
this is some A+ effort
hexed blaze
and substitute (-1) in k²-16k+4
hexed blaze
And it >0 right
hushed gust
yes
hexed blaze
Then the left segment makes the b²-4ac>0
We discard that segment
Pick a number in the middle segment
hushed gust
0.5
warm shaleBOT
hexed blaze
yes
So the middle segment makes b²-4ac < 0
So there, your answer is any number in that middle segment
hushed gust
so that means, when the k is between the two ranges, the solutions are imaginary and there are no real solutions?
hexed blaze
yes
But forget imaginary number now
You need a stable foundation in real world mathematics first
hushed gust
Thank you father!
hexed blaze
so there is your answer
hexed blaze
$k \in(8-2\sqrt{15}, 8+2\sqrt{15})$
warm shaleBOT
Darkness
hushed gust
when dealing when discriminants
hexed blaze
Yes
hushed gust
"When the k value is between 8-2 sqrt15 and 8+ 2 sqrt15, there are no real solutions"
ahhhh I understand now
hexed blaze
idk how you are taught but here in Asia we are made to memorize the trick lol
if a>0 then left and right segment are + and middle is -
If a<0 then vice versa
hushed gust
what is a?
hexed blaze
The coefficient of x²
hushed gust
if a is less than 0, left and right segments are -ve and middle is positive?
This might come in handy. thanks my man @hexed blaze 
This questions asks to find the points of intersection between a vertical line and a circle. The equation of the circle is x^2 + y^2 = 12.5^2. I know that I need to equate the two equations to find the two points of intersection. But I'm unsure of how or what to substitute in this problem.
I think I can't find the equation of the vertical line since I don't know the co-ordinate
Does anyone know how I could approach this problem? Appreciate it help <3
hushed gust
<@&286206848099549185>
frosty spoke
<@&286206848099549185>
bit late in the night for me
so please be patient if I mess this up
hushed gust
That's all good bro, sorry about the ping
frosty spoke
oh I wasn't pinged LOL
but anyway
imagine the top half of the circle for a second
you can write some equation: $y = \sqrt{r^2 - x^2}$
warm shaleBOT
Saccharine
frosty spoke
and the x value for which the cake is 11 centimeters across is simply the x value such that this is equal to y=5.5
hushed gust
i try
I got the x value! thanks
I tried getting the -ve y-point but I got a difference answer that doesn't reflect the 11.225 in the negative plane
Do you know what is wrong with the working or what thinking I got wrong?
frosty spoke
,w solve 5.5 = sqrt(12.5^2 - x^2) for x
warm shaleBOT
hushed gust
cuz the 5.5 becomes -5.5 right?
since we solve for the bottom point
oh wait
im stupid!!!!!
hushed gust
-5.5^2 is positive
warm shaleBOT
frosty spoke
since the equation of the other half of the circle is $y = -\sqrt{r^2-x^2}$
warm shaleBOT
Saccharine
hushed gust
I didn't simplify the expression so after changing sides, the positive should actually be negative
Thank you @frosty spoke I appreciate yo help !!
Why is there a negative here?
ruby path
what was the original input
hushed gust
nah i was just wondering what the negative means. saccharine was helpin' me
frosty spoke
Why is there a negative here?
you asked about the bottom half of the circle
the bottom half's equation is given by y = -sqrt(r^2-x^2)
hushed gust
Why is it not just y = sqrt(r^2-x^2) for both sides?
warm shaleBOT
frosty spoke
,w graph y = -sqrt(9-x^2)
warm shaleBOT
frosty spoke
the basic idea behind it is that the bottom half consists of negative y values, and the sqrt is always positive
hushed gust
the basic idea behind it is that the bottom half consists of negative y values, ...
Understood! Just didn't quite understand it because I wouldn't have caught that detail just by re-arranging x^2+y^2 = r^2 for y
Thanks 
, u're a legend.
obtuse pebbleBOT
@hushed gust Has your question been resolved?
unreal glen
obtuse pebbleBOT
unreal glen
for Question D
would it just be B because you transpose it twice. i.e the transpose cancels out?
tidal ember
yup
obtuse pebbleBOT
@unreal glen Has your question been resolved?
storm rampart
Hello
fierce lagoon
Well
You have the hints above you
What should you do with the 2 for f(3(x+4)) - 2
Okay well
Typo
obtuse pebbleBOT
@storm rampart Has your question been resolved?
storm rampart
What should you do with the 2 for f(3(x+4)) - 2
Move y down by 2
But what do I do for f(3(x-h))
Cuz I know that you change x by -4
obtuse pebbleBOT
@storm rampart Has your question been resolved?
tender prism
obtuse pebbleBOT
tender prism
I can tell you the anawer
proven zephyr
or is there any additional information
timid silo
sin^2(a)-sin^2(b) = sin(a+b)*sin(a-b)
ruby path
Has that always been a thing
timid silo
yeah
tender prism
Can someone show me the full process?
proven zephyr
didnt know you could do that too
tender prism
How to reach the answer
timid silo
proof:
tender prism
Not this
ruby path
Ah
tender prism
I am asking about my problem
pine sail
I thought that only worked for cosine
It works for sine lol.
proven zephyr
oh i see
tender prism
This
proven zephyr
sin^2(a)-sin^2(b) = sin(a+b)*sin(a-b)
you do this @tender prism
tender prism
Then what
timid silo
are you sure (A+B) = 90 - (A+B)?
proven zephyr
and what is sin2, sin^2 or sin (2(a+b))
tender prism
are you sure (A+B) = 90 - (A+B)?
Yes
proven zephyr
I mean sin^2-sin^b= 1/2(sin2(a+b))
are you sure it's 1/2(sin2(a+b)) and not sqrt2/2(sin(a-b))?
timid silo
hmm then the answer should be $\frac{\sqrt{2}}{2} sin(A-B)$
tender prism
are you sure it's 1/2(sin2(a+b)) and not sqrt2/2(sin(a-b))?
Yes
warm shaleBOT
Jester
timid silo
where the hell is latex?
tender prism
This is the answer
But I have to prove this one
timid silo
proccess: $sin^{2}A - sin^{2} B = sin (A+B) sin (A-B) = sin (45) sin (A-B) = \frac{\sqrt{2}}{2} sin(A-B)$
warm shaleBOT
Jester
obtuse pebbleBOT
@tender prism Has your question been resolved?
tender prism
No
tender prism
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
humble wind
obtuse pebbleBOT
humble wind
part d
obtuse pebbleBOT
@humble wind Has your question been resolved?
humble wind
<@&286206848099549185>
obtuse pebbleBOT
@humble wind Has your question been resolved?
frosty spoke
I guess you might find a p-value from the correlation coefficient & standard error?
timid silo
obtuse pebbleBOT
timid silo
So I know that to find the inverse you change the x and y values
So the inverse would be x = 1/3y^2 - 3y + 5
And from there we'll just solve for y
So, for my answer, I got
y = 9 + /root 21 + 12x / 2
and
y = 9 - /root 21 + 12x / 2
Is that correct?
Here is what I've done so far
timid silo
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
golden onyx
<@&286206848099549185>
This is what WolframAlpha says
I recommend using tools like these to check your answer
But it seems like you are indeed right
warm ether
how do I get rid of the exponent in $-3x^2 = -2x + 1$
obtuse pebbleBOT
how do I get rid of the exponent in $-3x^2 = -2x + 1$
warm shaleBOT
LGap
warm ether
I forgot how to
haughty coyote
This is a quadratic equation so you can just use the quadratic formula
stray elk
how do i integrate 7 over x
obtuse pebbleBOT
how do i integrate 7 over x
nocturne minnow
how do i integrate 7 over x
You mean $\int \frac{7}{x}$?
warm shaleBOT
dldh06
nocturne minnow
Do you recognize that $\frac{7}{x} = 7 \cdot \frac{1}{x}$?
warm shaleBOT
dldh06
nocturne minnow
So 7 is a constant that you can pull out
stray elk
yes
nocturne minnow
So then you have $7 \int \frac{1}{x}$
warm shaleBOT
dldh06
stray elk
yes
nocturne minnow
Can you handle the rest now?
stray elk
i think the answer is something like 7 / ln(x)
(dont know how to make the integral symbol)
nocturne minnow
What's the integral of 1/x?
nocturne minnow
and the stem function of that is ln(x)
Yes
stray elk
so the answer is 7 / ln(x)
versed cave
7 · ∫ (1/x) dx
stray elk
thanks
versed cave
I mean, you said what the antiderivative of 1/x is, so just substitute that instead of that whole integral
There's a small mistake in your answer
stray elk
alright, thank you very much
versed cave
Wait did you understand what was the mistake?
solar trellis
Is "/" supposed to be an integral sign or division
solar trellis
Lol
versed cave
oh
stray elk
its supposed to be an integral sign
versed cave
Ok, next time use another symbol ahah, / is already used for fractions
stray elk
how do i make those signs?
versed cave
I copy them from the internet
For this time if you want you can copy the symbol I pasted in the previous message
solar trellis
So then you have $7 \int \frac{1}{x}$
Follow by example
versed cave
so the answer is 7 / ln(x)
∫ 1/x dx = ln(x), as you said
∫ 1/x dx is not ∫ ln(x), which is what you wrote in your expression here
Basically you left the integral sign, but it wasn't supposed to be there
stray elk
right, so the proper answer would be ∫7 dx=ln(x)+k
versed cave
Not quite
7 · ∫ (1/x) dx
Find what ∫ (1/x) dx is, which we have already done, and then multiply that by 7
versed cave
right, so the proper answer would be ∫7 dx=ln(x)+k
( ∫7dx = 7x + k, not ln(x) )
stray elk
right, sorry all these letters are confusing
versed cave
It's ok, the important thing is that you understand what's going on
So did you get the answer?
stray elk
7 ln(x)?
versed cave
This probably doesn't matter, but check your notes, the integral of 1/x should be ln|x| with the absolute values too
If it isnt in your notes you can probably ignore it
versed cave
I think it's more commonly denoted as c
Yeah, they used +k so I used that too
stray elk
yeah that how its written in denmark
nocturne minnow
I mean same concept of it being an unknown, but in calc, they mainly use c
stray elk
but thank you very much both of you, its much appreciated
obtuse pebbleBOT
@stray elk Has your question been resolved?
rapid marsh
https://cdn.discordapp.com/attachments/538865295167586304/1011019921326620863/unknown.png I need help with this
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/538865295167586304/1011019921326620863/un...
rapid marsh
these linear equation word problems make 0 sense to me
versed cave
Basically what you need to do is to get an equation which describes the given info in the problem, so, for example, you can find Nour's altitude after 4, 5, 7 hours, or how much you like
We have to express the altitude (y) in terms of x hours, so the number of hours will be the x axis (and x value of course)
At 0 hours, The altitude is -400 (because it's below the sea level)
At 2 hours, The altitude is 1000
Edit: little mistake in the altitude at 0 hours, now fixed
What's left to do is to find an equation of a line with those properties, so
x | y
0 | -400
2 | 1000
slow fulcrum
below sea level
versed cave
below sea level
Oh good catch! I didn't pay much attention while reading, thanks!
versed cave
What's left to do is to find an equation of a line with those properties, so
__x...
So now you have to find an equation of a line which passes through those two points, if you prefer to word the problem like this
rapid marsh
So now you have to find an equation of a line which passes through those two poi...
could you finish the rest of the problem cause I genuinely have no clue what to do
versed cave
could you finish the rest of the problem cause I genuinely have no clue what to ...
I'm not here to finish the problem, but if you want I can help you to!
y = mx + b, that's the equation of a line, do you agree?
rapid marsh
yes
versed cave
+b in some countries is called in other ways, let me know if you use another name for that
Which parameters are we missing?
rapid marsh
m and b?
rapid marsh
no clue
versed cave
Mh ok, for the m there's a formula
let me type it
$m = \frac{y_a - y_b}{x_a - x_b}$
warm shaleBOT
Nonna
versed cave
A and B are two points
We have the points (0, -400) and (2, 1000)
It doesn't matter which one you call A and which B
versed cave
**Nonna**
The important thing is that you substitute it properly here
Let me know what you get
versed cave
Yes!
So now to find b
b has a very nice property, it's the y value when x = 0 (so it's the y-intercept, this may sound familiar)
We know that
y = 700x + b
and we have the point (0, -400), which has x = 0, that's exactly what we need!
Substitute the x and y of that point into that equation and then "solve" for b
solve is in "" because everything should cancel out leaving the value of b only
So what do you get?
rapid marsh
so y would be 0 and x would be 400?
versed cave
-400
rapid marsh
-400 = 700(0) + b
versed cave
Yeah
So we found all we needed
y = mx + b
m = 700
b = -400
So what's the final equation?
rapid marsh
-400 = 700(0) + -400
rapid marsh
wait hold up
versed cave
We are finding an equation of a line
So we have to leave x and y, otherwise that will be just what's called an "identity", so something that is equal to something else
Other examples of identities: 4 = 4, -5 = -5, and so on
Remember that the parameters are only m and b, x and y need to stay as variables
rapid marsh
im lost right now I'm not gonna lie
versed cave
Let's remember what we are trying to do
We need to express the altitude (→y) in terms of hours (→x)
But that has to be general
Not for a point only, like we did in our case
We are trying to find a relation between x and y
Basically I give the equation the x, and it gives me back the y
We have all the parameters we need, we have m and b
and we know that a line has equation y = mx + b
So what's left is just to substitute in this line equation the values we found for m and b
rapid marsh
im really trying here nothing is clicking though 
versed cave
That's ok, let me explain it in another way
rapid marsh
versed cave
I think that this may help you here:
[Altitude] = m · [Hours] + b
We are calling the altitude y, and the hours x
versed cave
[Altitude] = m · [Hours] + b
Leave [Altitude] and [Hours] as they are, don't change them
Substitute m and b only
versed cave
700(x)+-400
YES! Exactly
y = 700x - 400
So now we can do some cool stuff with this, which is the reason we found it in the first place
Now if we want to find the altitude when, for example, 3 hours passed we can just say that x = 3, and we get
y = 700 · (x) - 400
y = 700 · 3 - 400
y = 2400
So 2400 is the altitude after 3 hours
rapid marsh
makes sense
versed cave
It's just fancy ways to write formulas
rapid marsh
so I can just replace the x with 2 and solve and theres my answer?
versed cave
If you do that you will find the altitude when 2 hours passed
We already found the equation of the line, it's
y = 700x - 400
versed cave
That's just a point of the line
versed cave
https://cdn.discordapp.com/attachments/538865295167586304/1011019921326620863/un...
The problem is asking for the relationship between altitude and number of hours,
in other words the problem wants a formula to find the altitude in terms of hours
which is what we found,
y = 700x - 400
rapid marsh
ohhh
versed cave
I don't understand what you are having difficulties with
Are you struggling with understanding why we did what we did (How we found that equation) or is the hard part understanding how lines work in general?
versed cave
Yes by practicing this becomes much easier
I recommend revising a little bit on how lines work in general, without solving problems yet
Just exercises like finding the line passing through two points, or smaller problems like that
This was a pretty hard problem if you are not super familiar with working with lines
rapid marsh
do you have a good video on learning about lines?
versed cave
These two videos look pretty good
https://www.youtube.com/watch?v=ys0Dxj-jKTk
https://www.youtube.com/watch?v=Wmi1EysOHUQ
Check out khanaccademy too, it has some nice explanations
https://www.khanacademy.org/math/algebra-basics/alg-basics-graphing-lines-and-slope
rapid marsh
ok I'll check them out
anyways thanks a lot for the explanation
even though I dont fully understand it
I still understand it 1000 times more than before
versed cave
These two videos look pretty good
https://www.youtube.com/watch?v=ys0Dxj-jKTk
ht...
Hey just noticed the second video talks about other forms of lines too, at the beginning stick with y = mx + b only
obtuse pebbleBOT
@rapid marsh Has your question been resolved?
eager hill
I need help remembering values for sin cos tan, csc sec cot and I only have 15 seconds for each question how do I memorize them quick the test is tmr
obtuse pebbleBOT
I need help remembering values for sin cos tan, csc sec cot and I only have 15 s...
fast tiger
I need help remembering values for sin cos tan, csc sec cot and I only have 15 s...
repeat it over and over again to yourself
eager hill
repeat it over and over again to yourself
Tried but it just doesn’t stick in my head and it takes too long for me to remember
fast tiger
sin= opp/hyp
cos= adjc/hyp
tan= opp/adjc
eager hill
Yea I know that
fast tiger
Yea I know that
tan is basiclly sin/cos divided together
the similar ones get crossed whihc is hyp
do u are left with opp adjc
timid silo
with values do you mean like sin(π/2)=0 and so on?
eager hill
But like on the test it says cos(7pi/6) and I need to know that it’s like root3/2
eager hill
with values do you mean like sin(π/2)=0 and so on?
Yes
fast tiger
But like on the test it says cos(7pi/6) and I need to know that it’s like root3/...
eh ion know how to explain it to you man
imma go sleep gn
timid silo
hmm, do you at least know the multiples of π/2? so π/2, π, 3/2π, 2π,...
eager hill
Yes
timid silo
and they really want you to memorize multiples of π/4 and π/6 and so on?? sorry I think i cant help you with that
obtuse pebbleBOT
@eager hill Has your question been resolved?
obtuse pebbleBOT
eager hill
.reopen
obtuse pebbleBOT
✅
eager hill
and they really want you to memorize multiples of π/4 and π/6 and so on?? sorry ...
They want me to memorize all the values for everything
slow fulcrum
thats the unit circle i think...
theres a pretty easy way to memorize it
just memorize one quarter of the circle, the rest is just the same numbers but negative
obtuse pebbleBOT
@eager hill Has your question been resolved?
timid silo
how did they arrive at that underlined part?
can anyone explain to me..
obtuse pebbleBOT
how did they arrive at that underlined part?
can anyone explain to me..
charred plume
So, I think it should be minus 2ab cos theta, not plus...
If a+b=c (as vectors) then a, b and c form the sides of a triangle. Take theta to be the angle between sides a and b (draw this out for yourself). The underlined equation (with a minus where I said) is a famous fact about a triangle like that... I think it's called the law of cosines?
Ah, sorry plus is correct. My bad.
timid silo
so it is just a eq that have already derived right ??
charred plume
But another way of saying it is: the length of the vector a+b is sqrt(a^2 + b^2 + 2ab cos theta). So squaring both sides of the previous line gives the one you asked about
charred plume
so it is just a eq that have already derived right ??
Yeah, I think so.
For example if you know the relationship between length and dot product, then you can say $|\vec a+\vec b|^2 = (\vec a+\vec b)\cdot(\vec a+\vec b) = \vec a\cdot\vec a + \vec b\cdot\vec b + 2\vec a\cdot\vec b = a^2 + b^2 + 2 ab \cos \theta$.
warm shaleBOT
daveamayombo
timid silo
one more... how did they get blue from red??
charred plume
That one's easier... Replaced the a^2 + b^2 on the left of the line above with c^2.
timid silo
k
charred plume
a^2 + b^2 + blah becomes c^2 + blah.
timid silo
I understand why H is less than zero, but why is A less than zero?
obtuse pebbleBOT
I understand why H is less than zero, but why is A less than zero?
fickle turret
Because of 0 < b < 1
nocturne minnow
Do you know what $log_{b}(x)$ looks like between $0 < b < 1$?
warm shaleBOT
dldh06
timid silo
Because of 0 < b < 1
but how does that dictate a?
nocturne minnow
Plot $log_{b}(x)$ with a value between $0 < b < 1$
warm shaleBOT
dldh06
nocturne minnow
And you can see the shape of the graph
fickle turret
Maybe use the law of changing the base in log
If you want to further unserstand it
obtuse pebbleBOT
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proper forum
obtuse pebbleBOT
proper forum
How did we reach this conclusion?
pine sail
See
It's infinite gp.
And the sum is finite.
So |r| < 1
Otherwise the sum just can't be finite.
While |r| < 1, it still isn't a good enough reason for r to be 0. I mean, that causes a lot of problems, wouldn't you agree?
proper forum
Otherwise the sum just can't be finite.
Thank you for the explanation, that makes sense.
Last line yes, it would all be zero..
pine sail
That too, and the first term isn't defined.
proper forum
or tend to infinity in the case of a/r
pine sail
Yes.
proper forum
Thank you for your time and assistance, I hope you eventually figure out what you are doing here.
.close
obtuse pebbleBOT
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dry zenith
Someone help
obtuse pebbleBOT
Someone help
dry zenith
ik I’m stupid (I’m disabled)
warped flame
(2yd * 8yd) + (2yd * 3yd)
dry zenith
Just add those?
warped flame
Yup
warped flame
You can think of it as one rectangle on top of the other
warped flame
It's the sum of two products
I think this technically goes against the rules laid out in #❓how-to-get-help
dry zenith
I think this technically goes against the rules laid out in <#488120190538743810...
oh
sorry
warped flame
Not allowed to help you with tests or exams :/
People take this stuff very very seriously
obtuse pebbleBOT
warped flame
Dw I'm not a mod or anything, but you might get a warning later on or something
warped flame
Oh shit
dry zenith
bye
warped flame
Hey good luck
obtuse pebbleBOT
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still roost
Anyone know how to prove this?
obtuse pebbleBOT
Anyone know how to prove this?
compact shadow
Just prove this hint
Suppose that there exists a color , call it c, that doesn’t satisfy the condition in the hint, then any x with color c, there exists a color c(x) such that c(x) doesn’t equal c and c(x) isn’t color of any vertices adjacent to x. Then for each x we replace color c with c(x), this way we can coloring this graph with <χ(G) many colors, contradiction
The rest is clear, each color has at least one vertex having the property stated in the hint, so those at least χ(G) many points are of degree at least χ(G)-1
obtuse pebbleBOT
@still roost Has your question been resolved?
still roost
okay think i get it, thanks
red snow
obtuse pebbleBOT
red snow
why is the least possible integral of k=6?
wild vigil
obtuse pebbleBOT
wild vigil
How does this wwork?
kindred oasis
Try to set up a system of equations
Use J for John's age and use M for Mary's age, you have the sum of their ages and the ratio of their ages 4 years ago, so that should be enough to solve the problem
wild vigil
Is it x-4 + x-4*2?
kindred oasis
You can't use the same variable for two different things
J-4=2(M-4) would be one or the equations, since 4 years ago John's age was equal to two times Mary's age
obtuse pebbleBOT
@wild vigil Has your question been resolved?
obtuse pebbleBOT
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wispy flare
does anyone know how to solve this?
obtuse pebbleBOT
does anyone know how to solve this?
tardy stratus
This is a tricky question. Here are a few initial observations.
Set x = 0, so that we conclude f(0)u(0) = 0.
Set y = 0 too, so that we conclude f(x) = f(x)u(x) + f(0). Perhaps you can work out what this means in the context of the above.
There may be some casework involved.
Do you want to give this a shot given these hints? I have by no means solved the question, but I think these may be handy.
(Apologies, I made a typo above)
obtuse pebbleBOT
@wispy flare Has your question been resolved?
obtuse pebbleBOT
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cerulean bison
what's happening here?
obtuse pebbleBOT
what's happening here?
tardy stratus
What is (-1)^n - 1^n, when n is even? And what if it's odd?
cerulean bison
ohhh yeah she made a distinction between odd and even
we usually change the letter by k for example when we do this
but thank you!
tardy stratus
no worries
cerulean bison
.close
ruby path
$4\cos \theta - 3\sec \theta = \tan \theta$
obtuse pebbleBOT
$4\cos \theta - 3\sec \theta = \tan \theta$
warm shaleBOT
NEONPerseus
ruby path
Need to find a general solution to this
I got it down to
$\cos^2 \theta - 3\sin^2 \theta - \sin \theta \cos \theta = 0$
warm shaleBOT
NEONPerseus
haughty coyote
If you just multiply by cos theta at the start it becomes a quadratic equation in sin actually. Using cos^2 = 1 - sin^2
obtuse pebbleBOT
@ruby path Has your question been resolved?
obtuse pebbleBOT
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ashen bone
obtuse pebbleBOT
@ashen bone Has your question been resolved?
lethal bone
The limit from the left must equal the limit from the right which must equal the function value at x=3 and 2
fathom thistle
this looks kinda ugly and sloppy. yes or no?
obtuse pebbleBOT
this looks kinda ugly and sloppy. yes or no?
fathom thistle
can I add a comma before the \forall
hushed abyss
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neon hearth
((x+3)/(x+6)) <= 5
((-4x-27)/(x+6)) <= 0
obtuse pebbleBOT
((x+3)/(x+6)) <= 5
((-4x-27)/(x+6)) <= 0
neon hearth
how does x <= -27/4?
gilded needle
well if a/b <= 0, then a and b must have opposite signs (or a is zero)
so consider the possibilities
a < 0 and b > 0
or
a > 0 and b < 0
or
a = 0
neon hearth
sorry I don't know how to proceed from there
neon hearth
-4x = -27 best I can do so far
gilded needle
a = -4x-27, b = x+6
neon hearth
a = -4x-27, b = x+6
-4x -27 < 0?
x + 6 < 0
-4x - 27 = 0
-4x = 27
x = -27/4
lol wtf
gilded needle
how did you go from inequalities to equalities
neon hearth
why was that hard
neon hearth
how did you go from inequalities to equalities
it was a separate one
because you said a = 0
gilded needle
oh
neon hearth
etc.
gilded needle
yeah that's one solution, x = -27/4
neon hearth
damn I must be tired to not be able to isolate x
for some reason I didn't think it is a thing...
gilded needle
but any number less than -27/4 also works
gilded needle
what can I say, tiredness is badd
math while tired is hard for sure
neon hearth
that's my root eh?
neon hearth
math while tired is hard for sure
bad thing is I work 7 days a week, I'll be doing tests when I shuld be asleep.
hopefully it works out
gilded needle
ah well try to catch a nap somewhere in there
neon hearth
x = -27/4 and x = - 6 are called the roots AFAIK
neon hearth
ah well try to catch a nap somewhere in there
yeah that's hard when it's the day time
gilded needle
careful, x = -6 is a root of the denominator, it's not actually allowed
neon hearth
I get off of work at 7 am and I drive until 8 am when I get home
gilded needle
(can't divide by zero)
neon hearth
no class until 10:30 am but that's not enough.
gilded needle
the root of the overall fraction is x = -27/4
neon hearth
yeah I figured that the root is not the answer though, like it's not included
hmm
so like x > -6
gilded needle
that's why i was saying to check the two cases separately:
-4x - 27 < 0 and x > -6
OR
-4x - 27 > 0 and x < -6
there are actually two disjoint intervals of x that work
neon hearth
well I think it's safe to say that (-inf, -27/4] for the first part just because I tried -27/4 and it's valid, and -7 (-0.25 less) is also valid)
gilded needle
notice that (x+3)/(x+6) <= 5 is true for both large positive x and for large negative x
because the fraction is approximately 1 in both cases
neon hearth
hopefully that's good enough for solving these things. I've never graphed it like I think I'm supposed to. I use a number line though, which I think is how you do this anyways.
gilded needle
yeah (-inf, -27/4] is one half
there's another interval that works too
it comes from this case: -4x - 27 < 0 and x > -6
neon hearth
(-inf,-27/4] U (-6,inf) I just tried -5 and it is valid so
I hope that's what u mean by another interval
gilded needle
yep that's what i meant
gilded needle
cheers, get sleep!
ashen bone
obtuse pebbleBOT
ashen bone
how do i do the bottom part
ashen bone
obtuse pebbleBOT
royal shard
you want to use the general motion formulas
let a (acceleration) be constant
then:
v(t)=v0+a * t
s(t)=s0+v0 * t+0.5 * a * t^2
but first i would divide the graph into segments
royal shard
so for the blue segment you get:
v(t)=0+2t
0 because the starting velocity v0 is 0
v(t)=2t
this means that a=2
this is because we get a(t) by differentiating v(t)
the whole point of this is to get v0 and a
here we have v0=0 and a=2
put that into s(t)
remember:
s(t)=s0+v0 * t+0.5 * a * t^2
so we get s(t)=0+0+0.5 * 2 * t^2
now recall that our segment goes from 0 to 2
so we put in 2
we get
s(2)=4
now we focus on the next segment, the green one
notice that here s0 is not 0
royal shard
kk
so we just calculated s(2)=4
which we will use as the starting position of the green segment
the green segment goes from 2 to 5
v is constant here
we can see that v=4
because v is constant, a is 0
so we put all of that into s(t)=s0+v0 t+0.5 a t^2
we get
s(t)=4+4t
put in t=5
we get s(5)=25
this is the way we continue for the following segments
so for the red segment we would start with
s0=25
then calculate the slope
a=15/5=3
we can see v0
v0=v(5)
v0=4
put that into s(t)
we get
s(t)=25+4 t+0.5*3 t^2
s(t)=25+4t+1.5t^2
the red segment goes from 5 to 10
so we want s(10)
s(10)=25+40+150=215
now continue this for the last segment
alternative
we get a(t) by differentiating v(t), which we get by differentiating s(t)
we can think this the other way around
"anti differentiating"
while the diffentiate of a function gives the slope of the function, the "anti differentiate" gives the area underneath the function
we get v(t) by differentiating s(t)
this means we get s(t) by anti differentiating v(t)
which means that s(t) is the area under v(t)
this is way easier, because we can divide the area under v(t) into geometric shapes
example:
for the blue segment, we have a triangle
A=base * height / 2
A=2*4/2=4
you can use either way
i dont know what you are doing in class right now
if you havent covered anti differentiating, i would advise you use the other way
royal shard
either you carry on with the way i discribed, or you just calculate the area under the function
but you should only do the area trick if you have covered that in class
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
How would I solve this question?
timid silo
How would I solve this question?
do u see the triangle with 33° and 46°?
Yup
u know how much degrees a triangle has?
180
exactly
how do u get the degrees of the 3rd corner?
Would I do 46+36+x = 180
good
whats x?
X=101
yep
That’s the wrong answer
yes
lemme draw u sth
Gotcha
how much degrees is the purple angle
if its even an angle idk like the line
180
It’s supplementary
This question is confusing lmao
so u got the angle next to x right
and the entire thing is 180
Yes
so how much is x
I don’t know
look
Oh wait
Is it 180-101
yesss
Wait
How would I know that
so u know alpha
and 180-alpha = x
its makes sense doesnt it
Yes it kinda does
yay
civic ridge
Np.
obtuse pebbleBOT
@timid silo Has your question been resolved?
ashen bone
fringe hawk
I know that he travelled 2/3d by car and 1/3d by boat but I'm confused where to go from there
obtuse pebbleBOT
I know that he travelled 2/3d by car and 1/3d by boat but I'm confused where to ...
sharp crow
let velocity ot car be 3v and boat be v
so time taken by car is 2/3d / 3v = 2/9 d/v
time taken by boat is 1/3d / v = 1/3 d/v
so
3t = (2/9 + 1/3) d/v
d/v = 3t * 9/5 = 27/5 t
sharp crow
time taken by boat is 1/3d / v = 1/3 d/v
so put value of d/v here
obtuse pebbleBOT
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timid silo
can you show me a triangle on which i can apply a sine rule and how would it look like
obtuse pebbleBOT
can you show me a triangle on which i can apply a sine rule and how would it loo...
obtuse pebbleBOT
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timid silo
What is the units digit of 7^42?
obtuse pebbleBOT
What is the units digit of 7^42?
tardy epoch
,calc 7^42
warm shaleBOT
Result:
3.1197348228454e+35
,calc 7^42 % 10
warm shaleBOT
Result:
0
civic zealot
calculate a few powers of 7 and look at the units digit. what do you see?
sharp crow
umm the unit digit of 7^n has cyclicity of 4 like 7 , 9 , 3 , 1 , 7 and so on
timid silo
calculate a few powers of 7 and look at the units digit. what do you see?
7, 9, 3, 1
40 is 4 * 10
so the final digit is 1
so then whats 7^42?
9?
sharp crow
yes
tardy epoch
is that just an arithmetic sequence
sharp crow
d = -6
nocturne minnow
d = -6
Why are you giving them this instead of seeing if they can find it themselves?
sharp crow
Why are you giving them this instead of seeing if they can find it themselves?
umm oh ok
timid silo
a(100) = 77 + (n-1)d
sharp crow
um difference of two consecutive terms
timid silo
.close
crimson orbit
help
proven zephyr
,rccw
warm shaleBOT
crimson orbit
how do should i approach it?
hasty flint
which question
crimson orbit
question d
pine sail
Induction?
crimson orbit
Wym
pine sail
Mathematical induction is the way to go.
royal basin
oh god
rigid pine
There's a trick I'm trying to remember.
crimson orbit
oh okay
pine sail
Oh yeah, now that I think about it. That's how I was taught too initially.
crimson orbit
And then what whats next
pine sail
Consider, a^3 - (a-1)^3
Factor this.
If curious, this was the end goal
$n^3 - n = 3\sum_{k=1}^n{(k^2 - k)}$
warm shaleBOT
What the hell am I doing here?
obtuse pebbleBOT
@crimson orbit Has your question been resolved?
rigid pine
This was the thing I had a memory of. It would need slightly adjusting though. It turns into a telescoping series in this image.
obtuse pebbleBOT
rigid pine
Then you just need to simplify n(n + 1)(n + 2)/3 - n(n + 1)/2 to give the desired result. Obviously the appeal to make a telescoping series doesn't always come naturally.
obtuse pebbleBOT
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kind chasm
is the answer to x² + 7x + 12 = 0 is x=−3 or x=−4?
obtuse pebbleBOT
is the answer to `x² + 7x + 12 = 0` is `x=−3 or x=−4`?
kind chasm
is the answer to `x² + 7x + 12 = 0` is `x=−3 or x=−4`?
quadratic
rigid pine
Substitute x = -3 and x = -4 into x^2 + 7x + 12 and see.
kind chasm
ok
rigid pine
You will find that they are indeed solutions to the quadratic.
obtuse pebbleBOT
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crisp dune
