.close
#help-10
steady void
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
pulsar glacier
Need help
pulsar glacier
Hello
trim portal
Do you also have the image of the partial construction?
pulsar glacier
Yes
rigid skiff
show
trim portal
So this asks us to draw a line segment on line RS, which is of the same length as PQ
pulsar glacier
Okay
trim portal
Do you guys just want my ixl account and do it
no, we want to help you to do it yourself
pulsar glacier
Okay sorry
trim portal
circle of radius |PQ| centered at R is the set of points which are distance |PQ| away from R
pulsar glacier
So I circle the middle right?
trim portal
So I circle the middle right?
what do you mean by "the middle"
rigid skiff
connecting the centrre\
pulsar glacier
R
rigid skiff
to any point on the circumference
pulsar glacier
what do you mean by "the middle"
R ?
rigid skiff
so if u were to draw a line from r
to any point on the circuference
it would be the radius ?
u understand that ?
pulsar glacier
8th
rigid skiff
do u know how a circle works ?
.
pulsar glacier
My old school was a failure
rigid skiff
so ??
trim portal
The key fact is that every point on the circle is distance |PQ| from R. And we need to draw a line segment starting at R, whose length is |PQ| and which lies on RS.
rigid skiff
The key fact is that every point on the circle is distance |PQ| from R. And we n...
this just gonna be more confusing
trim portal
this just gonna be more confusing
Hm, why should it be?
pulsar glacier
Don’t worry im dumbing it down on chat gpt
rigid skiff
Hm, why should it be?
he dont understand what a radius is
pulsar glacier
So basically all im doing is a straight line from R in the direction of S?
rigid skiff
until it meets the circle
trim portal
and the length must be |PQ|
rigid skiff
and then u stop
pulsar glacier
How would I move S
trim portal
S is a fixed point already
pulsar glacier
Isn’t possible
pulsar glacier
Sorry if im stressing you how would I do that
trim portal
Looking at this, I think you can choose the "point" thing, and then place the point
and then make a segment which connects R and the new point
pulsar glacier
I can’t place anything only sets of lines
trim portal
okay, can you make a segment that starts at R ends where T is?
pulsar glacier
trim portal
Yes, this looks fine
pulsar glacier
I have 14 more
rigid skiff
I’m learning more stuff in here than in class
well we aint paid like peasent
trim portal
Just a moment, do you understand why RT is of the same length as PQ?
rigid skiff
we care what we study abt
pulsar glacier
Just a moment, do you understand why RT is of the same length as PQ?
Hold on lemme see
If R S were to line up it wouldn’t be congruent
Meaning wrong ?
rigid skiff
If R S were to line up it wouldn’t be congruent
wdym
trim portal
If R S were to line up it wouldn’t be congruent
"congruent" for line segments means they have the same length
every line segments of same lengths are congruent
more generally, if 2 shapes are congruent, then you can move on and place it on top of the other, such that they perfectly match and overlap
rigid skiff
like ur hands
if u join them
and see them from the top
u can only see one
because they perfectly overlap
pulsar glacier
Oh okay
rigid skiff
its the same ?
pulsar glacier
I’m gonna assume I have to put a point
That’s why I put a point
Can you fact check ?
next granite
1+1=3
pulsar glacier
So another point ?
rigid skiff
yeh
pulsar glacier
It said it needed to be a segment
rigid skiff
just do it like the prevs
pulsar glacier
rigid skiff
what all can u make
pulsar glacier
Point, Segment, Ray, Line, and circle
rigid skiff
with the centre as A , yes
pulsar glacier
What type of line do I use for A
rigid skiff
segment
pulsar glacier
A or Z ?
rigid skiff
Z
pulsar glacier
And then
rigid skiff
bring the circle down
if u can
while it still aligns with Z
and then the line segment that starts from z
and ends at the cnetre of the circle
limber sand
Can you help me with this?
Jack stands due south of a building 40m high to take a photograph of it. The angle of elevation to the top of the building is 23 degrees. What is the angle of elevation, correct to two decimal places, after he walks 80m due east to take another photo?
I got the answer ||17.93 degrees|| but my friends are disagreeing with me? Is it wrong and how do I do it if so?
(I'm having trouble visualizing 3D Trigonometry)
obtuse pebbleBOT
Can you help me with this?
Jack stands due south of a building 40m high to take...
limber sand
<@&286206848099549185>
opaque dome
So for the first photo, the distance d = 40/tan(23) and for the second photo, his distance d' is (d')^2 = d^2 + 80^2
The angle elevation will be arctan(40/d')
Im pretty sure its a rounding error, youre close to the answer
obtuse pebbleBOT
@limber sand Has your question been resolved?
limber sand
So for the first photo, the distance d = 40/tan(23) and for the second photo, hi...
d' is different from d right?
opaque dome
Ye
limber sand
so you will use tan, then pythag then arctan right?
opaque dome
Its the distance at the second photo
limber sand
Its the distance at the second photo
ohh ok
I will do it again in the same way to see if there is a rounding error
opaque dome
(Correct answer should be 17.36°)
limber sand
i got d' is equal to 123.6125584 using exact values
and using that with arctan(40/d') is giving me 17.93 degrees still
graceful marten
obtuse pebbleBOT
graceful marten
A B C are types of faults the 214 are non faulty things
Q. Given has A FAULT, find Prob it has TWO FAULTS
.
notation form
P(Two Faults | A Fault)
two faults is 5+8+7 | a fault is sum of ABC so 36
20/36 = 5/9
My question is If it was phrased given it has 1 fault, find the probability it has 2 faults
Would it be 20/ 14
.close
obtuse pebbleBOT
obtuse pebbleBOT
✅
graceful marten
FROM HERE
A, B & C are faulty, 214 isnt
The answer is 20/36
nvm
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
floral siren
hi
junior granite
what method should i use to calculate this?
have you tried any?
brazen gorge
DI/tabular method, or spam integration by parts
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
urban parrot
obtuse pebbleBOT
urban parrot
i am stuck idk what to do
trim portal
alternatively, just do long division
that will also help you find the full factorization
obtuse pebbleBOT
@urban parrot Has your question been resolved?
hidden compass
i am stuck idk what to do
Use remainder theorem
Ups sorry they've already helped you
robust charm
Hey guys. So i actually solved this problem and was able to get the correct answer but i have got a simple question. Isn’t 289 the greatest value of n here?
obtuse pebbleBOT
Hey guys. So i actually solved this problem and was able to get the correct answ...
robust charm
the reason why i say this is because
c > n
c > 289
so 289 is the greatest value n can be. because n could be 2 as well -example-.
am i right here or if im wrong could someone explain why?
wooden cipher
c>289, c does not have to be an integer
e.g. c=289.000002 would not give any real solutions
wooden cipher
you are looking for the value of n which provides a lower bound for values of c which do not give real solutions
robust charm
n is something independent from the equation
wooden cipher
the problem is asking you for what value of n is the smallest n you can choose such that any value of c greater than it when plugged into the equation gives imaginary solutions only
if you picked n=2 like you said, then me picking c=3 still yields real solutions
robust charm
as i said n doesn't have to do with the equation as i understand
c is
and c > n and c > 289 n can be 289 for sure but how can this be the least solution when n can be anything lower than or equal to 289?
oh wait
okay
i think i got it
robust charm
n can't be 2 because c needs to be greater than 289 not greater than 2 is this why
wooden cipher
yes
robust charm
bc if
c > 289
and
c > n
n can not be equal to 2 since
c > 2 includes c being 20 but c needs to be greater than 289
oh got it
thanks
wooden cipher
youre welcome
robust charm
.close
glossy warren
How to do c
obtuse pebbleBOT
How to do c
glossy warren
what does c-part say?
Use the s71 and s50 to find the differences
junior granite
you should just apply the summation and calculate it
round stone
Hello
abstract gale
steady silo
i think you should rewrite $5^{2a}$ as $e^{2a\ln(5)}$, and do the same for the other factors
warm shaleBOT
pixel
rough stream
Try to put together 5^a and 3^a (3^a 5^a) = (3x5)^a = 15^a
hoary kraken
$3^{a+1} = \frac{15^a}{5^{2a}}$
\par \par
$(a+1)ln(3) = aln(\frac{15}{25})$
warm shaleBOT
thijs2725
hoary kraken
Would this help?
Right side can be further rewritten to split the natural log
Then just solve for a and possibly use the necessary algebra to get the lnx/lny form?
Just a guess
obtuse pebbleBOT
@round stone Has your question been resolved?
mossy crown
If the light intensity of a lamp (X) is inversly proportonal to the square of the distance (Y) between the lamp and a student who is studying bellow the lamp by 8 meters. If the intensity was X at this place. Then at what distance should the lamp be to achieve an intensity of 4X?
obtuse pebbleBOT
If the light intensity of a lamp (X) is inversly proportonal to the square of th...
normal cairn
well the inverse square law tells us that the intensity is (output)/r^2, where r is the distance
the output wont be changing ofcourse, so if we want a different intensity then we want a different distance
the first scenario tells us that X=(output)/(8^2), or X=(output)/64
so 4X would be (output)/16, if we multiply both sides by 4
so do you see what that tells us
mossy crown
so 4X would be (output)/16, if we multiply both sides by 4
oh so the distance is 4?
normal cairn
yeah basically, since 4x=(output)/16 but 16=4^2
if you want to write that down though id use the actual formula for intensity if you were taught it already, its been a couple years since i did it i dont remember it exactly
mossy crown
its 4 right?
I donno :\\
jovial flame
ok listen
x prop 1/y^2
right?
when y is 8
x is x
lets say x= k(1/Y^2)
k is proportianality constant
if u want i can explain it well in vc
kinda like this
jovial flame
the first scenario tells us that X=(output)/(8^2), or X=(output)/64
just divide them
after you get two equations
@mossy crown did u understand this?
mossy crown
<@1229514189198987418> did u understand this?
yeah, I think I understand it now
thanks guys! <33
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Anyone know how to do c and d?
obtuse pebbleBOT
Anyone know how to do c and d?
viral blade
Probably solve the problem symbolically (in terms of v0) and see what happens
fossil crag
Anyone know how to do c and d?
Intuitively for c, ||if the first ball is thrown too fast up, then it's not even gonna be able to start going downwards by the time the second ball is dropped...||
And for d, ||if the first ball is thrown too softly, then it will go under the roof height and go faster than the second ball before it's even dropped||
for the concrete values of vmax and vmin, as said, solve for h and see when the expression of h is impossible
fossil crag
yes, what does that value represent?
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
yes, what does that value represent?
if the basll is thrown too fast
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gaunt flower
how to do b
obtuse pebbleBOT
how to do b
worn yoke
if it was more than 5 cm, the frame would overlap itself
gloomy vector
bc the equation of the picture inside is (20-2x)(10-2x)
yes
obviously, the lower bound would be 0
since it cant be negative
gloomy vector
bc the equation of the picture inside is (20-2x)(10-2x)
then, if you see both of these, 20-2x would mean that x<=10
10-2x would mean that x<=5
so you got your lower bound (minimum) and upper bound (maximum) for x
gaunt flower
ohh ok
obtuse pebbleBOT
@gaunt flower Has your question been resolved?
lucid sonnet
I need help with question 24 please
obtuse pebbleBOT
I need help with question 24 please
lucid sonnet
I don’t even know where to start
Only thing I can think of is doing (4x2)-(2x1)
For a1
cedar dune
which one are you trying to solve?
lucid sonnet
24
rough stream
for a1 i dont think it works , just my thought process maybe a reasoning like the shaded area = big rectangle area - unshaded area
lucid sonnet
Yea that’s what I did
rough stream
Only thing I can think of is doing (4x2)-(2x1)
with that you calculated the green area
lucid sonnet
with that you calculated the green area
Yea
Can’t figure out orange it’s probably something obvious I’m missing tho
lucid sonnet
Yea
rough stream
so each smaller rectangle as half of lengh of the sides of the previous one
lucid sonnet
so each smaller rectangle as half of lengh of the sides of the previous one
Oh in that case it’s easy
rough stream
my english is not the best i am sorry if i say something wrong
obtuse pebbleBOT
narrow gate
meow
obtuse pebbleBOT
Available help channel!
mystic cypress
The theoretical question is as follows: Define the derivative of the function f(x) in point a and explain the geometrical meaning of this derivative. (sketch!)
Could somebody help me with the second part of this question? I don’t know if the answer to the question is the first graph, the second graph, both of them, or none of them and actually something entirely else. My friend said that the answer is the tangent to the graph but I don’t know if it really is.
Also, this question is a translation from Slovenian to English so the translation may not be perfect.
obtuse pebbleBOT
The theoretical question is as follows: Define the derivative of the function f(...
@mystic cypress Has your question been resolved?
mystic cypress
The theoretical question is as follows: Define the derivative of the function f(...
<@&286206848099549185>
hoary kraken
The derivative indeed represents a tangent line to the graph at a point which thus represents the slope of the graph at that location
mystic cypress
The derivative indeed represents a tangent line to the graph at a point which th...
so then none of the 2 screenshots would be my answer?
Would this be enough of an answer to the second part of the question: (sketch of the graph in the screenshot) translated text: The limited line, which includes the point A(x0, f(x0)) and has the slope f'(x0), we call tangent of the function f(x) in the point A.
obtuse pebbleBOT
@mystic cypress Has your question been resolved?
mystic cypress
Would this be enough of an answer to the second part of the question: (sketch of...
<@&286206848099549185>
rough stream
derivative in some point is a tangent line to the graph in that point
sick patrol
obtuse pebbleBOT
mystic cypress
What do you need help with here?
I could give you the answers but I would rather help you understand the process of getting them
mystic cypress
so the amount of chage at 1.) and 4.) is?
sick patrol
What do you need help with here?
the whole topic actually, decrease and increase of percentage
sick patrol
so the amount of chage at 1.) and 4.) is?
wait so i have to like 150 minus 117?
mystic cypress
the whole topic actually, decrease and increase of percentage
I dont have that much time sorry, I can only help you with this then close this and open another thread with this question
mystic cypress
wait so i have to like 150 minus 117?
yes
sick patrol
33
mystic cypress
It may be a negative number, I'm its either 33 or -33
sick patrol
33?
mystic cypress
if were looking at the change then it changed by 33 units
now how would you go about calculating the change in %?
tell me your thinking process and I'll correct you if something's off
sick patrol
now how would you go about calculating the change in %?
multiply 100?
mystic cypress
multiply 100?
what number?
sick patrol
33
mystic cypress
no, thats not the number we multiply by 100
do you remember anything else in the process of getting the procentage of change?
sick patrol
unfortunately no
mystic cypress
so this is the process. You first do c = | o - n | where o is represents the original value aka. initial value and n represents the new value. You calculate the difference between these 2 and get the absolute value of the change. Do you know what the absolute value of -10 is?
sick patrol
okay so i calculate initial value and the new value but how do i calculate the differences?
mystic cypress
so this is the process. You first do c = | o - n | where o is represents the ori...
like this
you just do one minus the other
and if you get a - value just take out the minus sign
so in the case of the initial value being 80 and the new value being 90 you would get 80 - 90 = -10, you take out the - sign and get that the difference is 10
and if the original value were 90 and the new value 80 you would get 10
in mathematics we call this the absolute value of a number where | 80 - 90 | = | 90 - 80 | = 10
that's your difference, now that you have it, you divide it by the initial value so 10/80 = 0.125
then the number that you got after the division, you multiply it by 100 and get 12.5 which is how much % of the initial value the change is
now I'm not sure what way we are looking at this task, if we're looking at change from the initial value that precent of change would be 112.5%, if we're only looking by the amount of change than it would be 12.5%.
mystic cypress
now I'm not sure what way we are looking at this task, if we're looking at chang...
In the first case the answers would be 2.) 78%, 3.) 112.5% and 5.) 92% and in the second case it would be 2.) 22%, 3.) 12.5% and 5.) 8%
mystic cypress
In the first case the answers would be 2.) 78%, 3.) 112.5% and 5.) 92% and in th...
you should ask your teacher this
urban parrot
basically units cannot be negetive in this case so 150-117= 33(1), percent of change will be 33/150*100
.calc 33/150*100
ahh imma use a calc
mystic cypress
22%
urban parrot
so 2 should be uhhh 22 percent
generally in my school we had to write percent increase or percent decrease
urban parrot
generally in my school we had to write percent increase or percent decrease
check with your teacher
if they say it to write it in terms of decrease
then if the new value is more then inital value , the answer will exceed 100%
for number 5 it will be 50-46/50*100
so number 5 will be 8
it will be 8 % increase
sick patrol
ohh okay, i get it
so the formula is that i have to calculate the differences and get the absolute value of the change by one minus the other, and then if like the number has the negative sign i take it out so the difference will be (n)?
and after i get the difference, i have to divide it and multiply by 100?
urban parrot
ohh okay, i get it
so the formula is that i have to calculate the differences an...
so new value/inital value*100
urban parrot
ohh okay, i get it
so the formula is that i have to calculate the differences an...
for e.g. u have 25 tennis balls, u sell 5 of em so u have 20, so u sold 20% of ur tennis balls
but if u buy 5 more of them u will now have 30 (new value)
so u have a 20 % more stock of balls
if u require any other help ping me
@sick patrol
sick patrol
thank youu!! i js took down notes and i understood it more than my teacher omg
thank u both!! <33
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
native gale
How do i disprove this function is uniformly continious in [0, +inf)?
obtuse pebbleBOT
How do i disprove this function is uniformly continious in [0, +inf)?
solemn basin
How do i disprove this function is uniformly continious in [0, +inf)?
Find a point of discontinuity
native gale
that's not it
solemn basin
that's not it
Take limit at infinity
There will be discontinuity there
Oscillating type
native gale
generally you need two serieses Xn, Yn where Lim|Xn-Yn| = 0 but Lim|f(Xn)-f(Yn)|>0
native gale
<:what:561568026210730004>
who are you asking?
zenith raft
not you
solemn basin
do you know what uniformly continuous means
In layman terms - a function which we can draw without lifting our pen
And the rigorous def - when lhl = rhl = finite and limit at a point equals the value of function at that particular point when this is valid for all points between 0 to infinity the function is uniformly conti.
solemn basin
In layman terms - a function which we can draw without lifting our pen
And the ...
For our case it's 0 to inf
zenith raft
In layman terms - a function which we can draw without lifting our pen
And the ...
dawg...
solemn basin
**uniformly** continuous
Isn't continous and uniformly continous the same 
zenith raft
no
zenith raft
look it up
native gale
uniformly continuous is more like that the slope is bounded
solemn basin
Nvm fck what is this 
solemn basin
uniformly continuous is more like that the slope is bounded
Slope at a point?
solemn basin
1/x in (0, inf) is continuous but not uniformly
Why?
zenith raft
generally you need two serieses Xn, Yn where Lim|Xn-Yn| = 0 but Lim|f(Xn)-f(Yn)|...
looking at sequences $(\pi n)$ and $(\pi n + 1/n)$ or something like that might work
warm shaleBOT
:bending_skull:
zenith raft
yea. i think $\lim_{n\to\infty} |f(x_n)-f(y_n)| = \pi$
warm shaleBOT
:bending_skull:
native gale
looking at sequences $(\pi n)$ and $(\pi n + 1/n)$ or something like that might ...
with these sequences?
zenith raft
yes
native gale
yea. i think $\lim_{n\to\infty} |f(x_n)-f(y_n)| = \pi$
as I see, this limit doesn't exist
zenith raft
does it not? for any $n$, $$f(x_n) = \pi\cdot n \cdot 0 = 0$$ and for large $n$, $$|f(y_n)| = |(\pi n + 1/n)\sin(\pi n + 1/n)| \approx (\pi n + 1/n)(1/n) = \pi + 1/n^2$$
warm shaleBOT
:bending_skull:
zenith raft
the \approx may look sketch but i think it's good
one second
https://www.desmos.com/calculator/cflnhzkswg this should be pretty convincing too
zenith raft
**:bending\_skull:**
this is pretty much the proof. just have to make the \approx more rigorous
you could do that with an error term for the approximation
native gale
https://www.desmos.com/calculator/cflnhzkswg this should be pretty convincing to...
so this basically converges to pi?
zenith raft
**:bending\_skull:**
this does yes
you don't even need to prove that
you could prove that, e.g., |f(y_n)| >= 1 eventually
since the limit just needs to be not zero
to prove what was asked
zenith raft
you could prove that, e.g., |f(y_n)| >= 1 eventually
i'm not saying this is any easier, just a note
native gale
yeah i see, thx
zenith raft
at least the problem is just a limit computation now. you want to show $$\lim_{n\to\infty}|(\pi n + 1/n)\sin(\pi n + 1/n)| \neq 0$$ somehow
warm shaleBOT
:bending_skull:
zenith raft
oh
ok maybe you'll like this better
eh nvm
$$\lim_{n\to\infty}|(\pi n + 1/n)\sin(\pi n + 1/n)| = \lim_{n\to\infty}|(\pi n + 1/n)\sin(1/n)| = \lim_{n\to\infty}|(\pi n + 1/n)(1/n)\cdot \frac{\sin(1/n)}{1/n}| = \lim_{n\to\infty}\pi + 1/n^2$$
warm shaleBOT
:bending_skull:
zenith raft
ugh
\begin{align*}
\lim_{n\to\infty}|(\pi n + 1/n)\sin(\pi n + 1/n)| &= \lim_{n\to\infty}|(\pi n + 1/n)\sin(1/n)|\
&= \lim_{n\to\infty}\left|(\pi n + 1/n)(1/n)\cdot \frac{\sin(1/n)}{1/n}\right|\
&= \lim_{n\to\infty}\pi + 1/n^2
\end{align*}
fluid lake
what the
warm shaleBOT
:bending_skull:
obtuse pebbleBOT
@native gale Has your question been resolved?
karmic hedge
https://www.desmos.com/calculator/cflnhzkswg this should be pretty convincing to...
This is the sickest album cover I ever saw
Reminds me of arctic monkeys or something
sullen prawn
obtuse pebbleBOT
sullen prawn
Is my answer correct?
Ms has taken -19 common from the direction vector of line l
obtuse pebbleBOT
Available help channel!
inland dagger
How to show that
obtuse pebbleBOT
How to show that
inland dagger
f(x)=sin(3x)-x
Has only one root in the interval (pi/6,pi/3)
By IVT it is clear that it has at least one root
worn yoke
we would expect it to only have 1 root if it is monotone (increasing only or decreasing only)
gilded needle
did you look at the derivative?
inland dagger
we would expect it to only have 1 root if it is monotone (increasing only or dec...
Can you elaborate
If its monote that would imply one root
Oh ok because monotone => injective
inland dagger
did you look at the derivative?
3cos(3x)-1
gilded needle
3cos(3x)-1
yea, what can you say about the sign of this?
(on the interval of interest)
inland dagger
cos(3x) is negative in (pi/6,pi/2)
So it is negative
Derivate negative means rhe function is decreasing
so done
gilded needle
yep
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
glass marlin
obtuse pebbleBOT
glass marlin
i dont understand where i went wrong
clearly v wrong tho
delta y over delta x
i plugged in the numbers and it is way off
versed wadi
so derivative = 5 cos (pi t) - 2 sin (pi t) (times pi)
Derivative at 1 = -5 pi
Derivative at 2 = 5 pi
Presumably the average is 0? no?
did i mess up somewhere?
@glass marlin
obtuse pebbleBOT
@glass marlin Has your question been resolved?
glass marlin
@versed wadi i ended up getting the first one right at 4 cm/s
the other ones i am clueless on
versed wadi
oh i get it
okay
so
the "average"
can be found by taking the integral of the derivative
and dividing by the length
so you just plug in the values in the initial function
and divide by the length
(5 sin (2pi) + 2 cos(2pi)) - (5 sin (pi) + 2 cos(pi))
is the first answer
versed wadi
basically just use the function as an integral between the two points
and divide by how big the gap is
glass marlin
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
zinc oxide
im so lost rn
obtuse pebbleBOT
im so lost rn
@zinc oxide Has your question been resolved?
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@zinc oxide Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
violet igloo
obtuse pebbleBOT
violet igloo
what is an extraneous solution
junior granite
what is an extraneous solution
a solution that you got while solving manipulated equation, but it is not the solutions of the initial equation
violet igloo
a solution that you got while solving manipulated equation, but it is not the so...
?
so is it not any of the 2 solutions that I listed above next to simplify
junior granite
so is it not any of the 2 solutions that I listed above next to simplify
to check it you have to plug it in the original equation
and see if those satifies or not
violet igloo
and so if it satisfies it it will be the extraneous solution?
junior granite
and so if it satisfies it it will be the extraneous solution?
if it "does not"
then it will be extraneous
violet igloo
oh ok
but the calculator does not have a customizable log base
can I just go with log base 10
junior granite
can I just go with log base 10
erm, can't you just do it yourself
junior granite
i'm just asking if that works
if it is not the intended solution then calculator, will give no output
not valid output
or something like that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hoary kraken
Why can the mc^2 term be suddenly ignored in the inequality near the end?
hoary kraken
if its bigger than stuff+mc^2, then its also bigger than just stuff
Ooooh I am stupid sorry thanks for the help
Another small question: where in this proof is the fact that $c \geq -1 $ used?
,, c \geq -1
warm shaleBOT
thijs2725
kind hawk
you are multiplying the inequality from the induction hypothesis by 1+c
if c<-1 then you would be multiplying by something negative
honest flicker
idk how 3
honest flicker
obtuse pebbleBOT
@honest flicker Has your question been resolved?
honest flicker
<@&286206848099549185>
junior granite
just plug in the that thing
honest flicker
the bottom will equal zero idk wat to do after that
i didn't pay attention in class omg
junior granite
i didn't pay attention in class omg
bro
junior granite
the bottom will equal zero idk wat to do after that
what will be the numerator?
0 or something else?
honest flicker
30
junior granite
yeah so it is 30/0 thing
honest flicker
ok it does not exist
junior granite
ok it does not exist
uhm, something/0 is not always DNE in limits
you have to show your work by finding both Left and Right hand limits
woven pulsar
idk how to 4
plug in pi to the equation
dealing with limits you should always plug in first to see if the value exists
honest flicker
idk wat do after
woven pulsar
not exists necessarily idk the correct term
sin^2(pi) - 3cos(pi) = ?
the value you get from that is the answer
since it isnt an indeterminate or undefined value
honest flicker
sin^2(pi) - 3cos(pi) = ?
idk how to do that
woven pulsar
how familiar are you with the unit circle
woven pulsar
okay so, you know where 0, pi/2, pi and 2 pi would be located right
and that cos is the x value of the circle and sin is the y value basically
honest flicker
wat do I do Abt sin squared
honest flicker
0
woven pulsar
and sin^2(pi) would also be 0 because sin^2(x) = (sinx)^2 and since sin(pi) = 0, it would be (sin^2(pi))^2 = (0)^2
woven pulsar
OK my final answer is 4
close but its not right
honest flicker
WHAT
woven pulsar
and sin^2(pi) would also be 0 because sin^2(x) = (sinx)^2 and since sin(pi) = 0,...
does this make sense
woven pulsar
yes
honest flicker
ummm wouldn't the bottom of that be 0 idk
oh wait
nvm
the top is 0
so like is the answer 0
righttt
@woven pulsar
woven pulsar
its not 0
honest flicker
help
woven pulsar
if you were to find the tan of pi/3 you would do the opposite over the adjacent
honest flicker
I'm blind
woven pulsar
ohh
honest flicker
wat do I do Abt the bottom
obtuse pebbleBOT
@honest flicker Has your question been resolved?
junior granite
is this right
which part is that?
honest flicker
wat
junior granite
is it 6?
honest flicker
Oh
umm 9√3/π^2 ???
light work
OK NUMBER 7
I do like the conjugate right
top and bottom
junior granite
I do like the conjugate right
yup
junior granite
I got √5/10
you can verify yourself too
on wolframalpha
,w limit x goes to 0 [sqrt{x+5}-sqrt5]/x
this mf
warm shaleBOT
junior granite
seems alright
junior granite
yeah
timid silo
obtuse pebbleBOT
timid silo
uh help
timid silo
wdym there's 4 options
waxen mirage
2 nd one
timid silo
oh ok
waxen mirage
Angle 1 supplementary to both 🙂
timid silo
u sure?
obtuse pebbleBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
waxen mirage
NVm i failed as a helper
timid silo
nah u the best helper fr
timid silo
Do you understand why?
Nah i didn't read the lesson i just had to submit this
i'll read it tmr morning
dw
waxen mirage
Goodnight!
timid silo
gn
waxen mirage
You seem to be from some asian country
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stark vortex
Am I starting this correctly
obtuse pebbleBOT
Am I starting this correctly
stark vortex
So assuming ive gotten the correct heights after the amount of time passed what is the next move
rose scroll
so you can find the average speed = distance travelled / time taken
versed wadi
Am I starting this correctly
the next value needs to be 4.01, 4.05 and 4.01
not .1, etc.
stark vortex
the next value needs to be 4.01, 4.05 and 4.01
wait
youre a genius I just realized thats what it wanted
stark vortex
the next value needs to be 4.01, 4.05 and 4.01
so does this look correct
ok how would I set up the equation for average velocity now
stark vortex
so for 4.1 seconds its 6.04ft / 4.1 sec ?
versed wadi
how much distance did the rock travel?
stark vortex
6.04 ft no?
stark vortex
oh ok so 19 - 6.04 its be 12.96 feet right
versed wadi
yep
stark vortex
ah ok I get it
so our average speed = 12.96/time taken
and time taken is just the 4.1 seconds or would it be 0.1 seconds
versed wadi
well, i think you should answer that
stark vortex
nvr mind thats a dumb quesiton obviously its the 0.1 lol
so the average speed for (i) is -129.6 ft per second
versed wadi
Seems right
slender sluice
Am I missing something? Is this obvious?
obtuse pebbleBOT
Am I missing something? Is this obvious?
timid silo
at least |exp(itheta x)-1| ≤ 2 is obvious to me
obtuse pebbleBOT
@slender sluice Has your question been resolved?
slender sluice
at least |exp(itheta x)-1| ≤ 2 is obvious to me
Well, you're right
triangle inequality + |e^(itheta x)|<=1
Think I got it, you can pull the |...| into the integral.
river garden
obtuse pebbleBOT
river garden
How would I find the larger or smaller x calue if u just plug 0 in
teal turret
its not plugging 0 in
u found that
y' = sqrt(3) - 2sin(x)
set y' = 0
and solve for x
river garden
True
I forgot a lot of trig
Hold on
How would getting the arcsin find both x values
teal turret
because theres 2 values that correspond to arcsin(sqrt 3/ 2)
on the unit circle, sin is equal to sqrt(3) / 2 in 2 places
river garden
Pi/6 and 2pi/3?
obtuse pebbleBOT
@river garden Has your question been resolved?
lusty sentinel
im not sure how to solve this
obtuse pebbleBOT
im not sure how to solve this
lusty sentinel
the answer is c. 6 btw
obtuse pebbleBOT
@lusty sentinel Has your question been resolved?
brave junco
and from there you establish the rest
lusty sentinel
and from there you establish the rest
Thank you. how would you know its x/7?
it seems that distance is being subtracted from both the left and right?
like as in how do you know the ratio is x/7
brave junco
no
because the one on bottom was 8 and we have that blue line is exactly 1 into the bottom line
lusty sentinel
ok yea that makes sense ty
brave junco
no problem there is a lot more calculation after this if you get the idea then tht is it, else i can just go through calculations with you
lusty sentinel
yea do you think you can explain the calculations?
brave junco
so the goal is to calculate these these
or to calculate the area in between
both ways will lead to the desired answer
now we know , the blue line is 7* (6/8) = 7 *(3/4)
same way we can calculate the one on the bottom
which will lead to x/5 = 8/6
which mean x= 20/3
now we know both
they are respectivly -1+21/4 and -1+20/3
( 17/4 ) and 17/3
through Pythagoras we can calculate hypotenuse
whic will lead to root square of ( 18.06 + 32.11 )
which is about 7.08
now we have a rough estimate of the area
the area of red triangle is ( 17/4)* (17/3) /2
which is around 12
so we know that the blue small triangle
area is more than 12-7
=5
and we know it is less than [(17/4)-1 ] [( 17/3) -1] /2
lusty sentinel
ah ok I see
brave junco
because the red and yellow segements are both more than one
se we and up on this estimate of above 5 and less than ( 3.25*4.6 / 2 )
which is above 5 and less than 7.47
and the only option in this range is 6
brave junco
np
it is definitely possible to calculate it exactly
but we can get through with just an estimate calculation
lusty sentinel
yea makes sense. This method was also pretty fast. without the typing and all
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fading tree
help
timid silo
help
as MN is 4.6
therefore ON is also 4.6
as they are equal
therefore MO is equal to 4.6 + 4.6 = 9.2
fading tree
so
timid silo
and the same case goes for 29
fading tree
the total length would be 9.2
timid silo
yes
timid silo
it goes the same as 28
just that the numbers are different and its reversed
no you do 8.8 divided by 2
cause its just 2 segments
check the grey vertical thin lines
they represent the number of equal segments
so WY is 8.8/2 = 4.4
fading tree
alr
timid silo
ping me if you need help i will be going across different help servers
fading tree
alr thanks man
timid silo
dw
fading tree
yo @timid silo
would
32 be DE=-9.5
like i turn that into an equation solve it and then divide into two
timid silo
but to get DE you are supposed to substitute the value of x to the original value
timid silo
no no
2x+7 = 4(x-3)
expand it
2x+7 = 4x - 12
do some swapping
2x - 4x = -12 - 7
therefore
-2x = -19
and hence
2x = 19
therefore x = 19/2 = 9.5
you substitute the value of x into the equation for DE
so you substitute x = 9.5 into 4(x-3)
and youll be able to get the answer
fading tree
u mean distribute 4 into 9.5 and -3?
fading tree
yes
timid silo
now you substitute the value of x into 4(x-3)
you get 4 times (9.5-3)
which is 4 times 6.5
and you will get 26
timid silo
no you dont need to divide by 2
cause as per your question the equation 4(x-3) is already only for DE
not the whole line
timid silo
yes
fading tree
would 33 be 3x+1 = 4x-6 = 2x+8
timid silo
would 33 be 3x+1 = 4x-6 = 2x+8
yes that is right