it said
#help-38
last junco
x,y are integer
x+y+xy=23
x^2y+xy^2=126
the question
i finally got the ans
but still thanks for these tips
last junco
x,y are integer
if the ans is 31522, x and y are not integer
tepid rock
Yes, mention every one of those details next time you ask any question.
last junco
thx
tepid rock
.close if done
last junco
`.close` if done
do u get any idea for this question
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pliant warren
how do i prove inequalities by induction?
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how do i prove inequalities by induction?
pliant warren
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mental lodge
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mental lodge
<@&286206848099549185> pleases'
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molten pollen
hi
molten pollen
idk how to attempt number 1
and im confused on whether I integrate for number 2 or something
cursive musk
might want to charge your battery
cursive musk
yep
so theres a neat trick you can do here
dx and dy can just be numbers
so you can multiply them
cursive musk
well thats the whole idea
dy/dt / dx/dt = dy/dt * dt/dx = dy/dx
now you know dy/dt and dx/dt
molten pollen
aight I got it
molten pollen
do you know abt this one
cuz its not given by a dy/dx but it says velocity vector and position
cursive musk
ah
so youre given v
and an initial condiiton
so you need to integrate from t = 2 to t = 6
and add that to f(2)
do each component seperately
molten pollen
and add that to f(2)
why this
cursive musk
because we are integrating from 2 to 6
the integral is the change in value
so it ends up being f(6) - f(2)
but we want f(6)
so we need to tell it to add the change in value to the original value of f(2)
cursive musk
ye
molten pollen
and the integral = to f(6)-f(2) so we add f(2)
cursive musk
ye
molten pollen
how did I never learn this tho š
cursive musk
how did I never learn this tho š
you'll be fine
are you surprisingly ahead
4 years of the average american student
cursive musk
you dont have to
itd be great if you did
but you can always retake the class next year
you have that cushion
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naive berry
Hi I have a trigonometric question specifically about finding the angle of a right triangle
naive berry
My teacherās answer for the angle is completely different from mine the answer being 49.6 degrees
I find the missing value for the opposite angle
wraith hinge
do you know what sin, cos and tan are?
wraith hinge
Let's first think about which sides of the triangle we know
opposite, adjacent, and hypotenuse are used in trig calculations
solid kilnBOT
naive berry
The teacherās answer was 49.6 degrees but I kept on getting 86 degrees
wraith hinge
so we have the hypotenuse and the ajacent side
you don't need to solve for the unknown side, there's a different trig function from sin that you'd use
sin cos tan, do you see which one it is?
naive berry
I donāt see one aside from sin
wraith hinge
ah
naive berry
So it would be
cosine theta = (24/37)
Theta=arccosine(24/37)
Iām still getting 0.86498
wraith hinge
Iām still getting 0.86498
change your calculator from radians to degrees
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weak orchid
how can i do this with angle sum and difference formulas
weak orchid
heavy lion
use $\tan (a - b)$
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bettim
stark bison
Note that 1/12 is just 1/3 - 1/4
weak orchid
ohh ok
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umbral maple
i know it science but it math
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i know it science but it math
umbral maple
(the one i ticked was wrong)
sweet hare
,rccw
solid kilnBOT
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fiery sleet
Can smn help how we achived this
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Can smn help how we achived this
fiery sleet
4xy, 0 <x< 1, 0 <y< 1,
hallow spruce
try drawing the region x<y on the xy plane
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fiery sleet
try drawing the region x<y on the xy plane
oh
is there a video resource or smth for it
i have no idea how to do so
hallow spruce
probably but I don't know one
just draw the line x=y and identify the region below that
fiery sleet
just draw the line x=y and identify the region below that
like this/
hallow spruce
yes
now try to convince yourself why that gives you the double integral given in the solution
fiery sleet
dx's lower limit would be 0 right but how come its upper limit is y but for y its 1 š¤
hallow spruce
for any value of y, x can take on values in the interval [0,y)
since that's what x<y means
(and obviously both x and y are constrained to (0,1))
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fathom meadow
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https://youtu.be/clC3ld6rJVU?t=299
fathom meadow
can someone help me on how he finds the B value
here
Like the 2pi/b = 8 -> B = PI/4
I replayed the part as much as I can
but can't understaand
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fathom meadow
2pi/B = 10/3
ya but how
what is that
like I dont understand what 2pi/B is
or 10/3
like I dont understand what he means by period
I thought period was the Y value(the thing he marked in dark blue)
that was average between the largest and smallest Y vlue
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surreal eagle
i know its a little messy but is this right?
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i know its a little messy but is this right?
surreal eagle
if it loads
specifically the last two steps
can i divide an n from (n/(n+1))^n
dusty hound
the last step is wrong
(1+1/n)^n doesn't go to 1
it's probably a limit you know though
surreal eagle
e?
dusty hound
yes
gleaming turret
Ive noticed that if you pick random vectors under magnitude x, and plot them out on a grid with a spacing of 1, with all of them coming from the origin, and you take the average amount of grid lines they pass through, call this f(x), if you then take f(x)/x and limit x to infinity then it converges to 8/(3*pi). Why would this be?
green sand
the number of grid lines the 2-d vector (x,y) passes through is floor(x) + floor(y)
in the limit we don't need to consider the floor functions
then paramaterise the vectors by their angle, scale them down to the unit circle to account for your division by x, and integrate over theta
sorta
gleaming turret
Unrelated but is there likely to be an elementary solution to f(x)?
gleaming turret
I mean f(x) as the average amount of grid lines vectors under magnitude x go through
Not the amount of grid lines an individual vector goes through
green sand
there's an integral expression for it
gleaming turret
I know, ive also found an infinite summation for it, but im just interested in seeing if there is a nicer solution
green sand
well since you're summing stuff like floor(ksin(x)) I very much doubt there would be
gleaming turret
Ah thats annoying
I found an infinite summation by doing an integral from a to a+1 of sqrt(x^2 - a^2) which is easily solvable, and then doing a summation mulitipled by a of that from 0 to infinity which real part is the amount of vertical lines it passes through in a quarter so you take away the imaginary part and then multiply it by 8 and divide it by the area
green sand
the annoyingness is self imposed as you're just looking at the x-distance and y-distance when you're looking at the number of gridlines
you're just looking at the area of a circle ultimately
gleaming turret
i forgot to type in multiplied by a
if you multiply each column by a which increases as the summation goes up then it works like the gridlines
so it works out each 1 wide columns area with the integral and multiplies it by a which goes up each time
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kind iris
Hello. How do I turn this
$$\frac{\left(x^{2}+x+1\right)^{2}-2x\left(x^{2}+x+1\right)}{\left(x^{4}+x^{2}+1\right)-2x\left(x^{2}-x+1\right)}$$
into this
$$\frac{\left(x^{2}+x+1\right)^{2}}{x^{4}+x^{2}+1}$$
solid kilnBOT
lmaowhat
kind iris
I am pretty sure they are equal
I just need to do some manipulation to convert it (the top one) to that (the bottom one)
severe wave
try and assign a new variable to each polynom and see what changes from top to bottom
and when you have a more visible fraction see if you can reverse what was simplified
silent canyon
why do you think they are equal?
kind iris
why do you think they are equal?
I substituted different values for both, they give the same output
It could be that it was a coincidence but I don't think so
This is not the actual problem
I have to prove that $\ln\left(\frac{x^{4}+x^{2}+1}{\left(x^{2}+x+1\right)^{2}}\right)$ is an odd function
solid kilnBOT
lmaowhat
kind iris
try and assign a new variable to each polynom and see what changes from top to b...
How would that work? That would just give me a weird fraction
(a - b)/(c - d)
kind iris
**lmaowhat**
@silent canyon
cosmic meadow
((x^2+x+1)^2 - 2x(x^2+x+1)) = x^4+x^2+1
((x^4+x^2+1) - 2x(x^2-x+1)) = x^4-2 x^3+3 x^2-2 x+1
is (x^4+x^2+1)/(x^4-2 x^3+3 x^2-2 x+1)
the same like:
(x^4+2 x^3+3 x^2+2 x+1) / (x^4+x^2+1)?
(x^4-2 x^3+3 x^2-2 x+1)(x^4+2 x^3+3 x^2+2 x+1) = x^8+2 x^6+3 x^4+2 x^2+1
(x^4+x^2+1)(x^4+x^2+1) = x^8+2 x^6+3 x^4+2 x^2+1
Yes, they are the same
Hint: When you want to know if 2 fractions are equal, cross multiply will give you the solution.
kind iris
I mean
I don't think you're supposed to do this
It can be shorter
It's an objective question and is supposed to be answered in around a minute
cosmic meadow
probably, but it doesn't take more than 1 minute
kind iris
That's true
cosmic meadow
i would do this way for sure, it's 6 lines
findng a way to make a transformation looks harder and would require to think more
i would call that more like a clean way to solve, not faster
kind iris
Oh
Lol
I'm done
I found a way better way
$\frac{x^4+x^2+1}{(x^2-x+1)^2} = \frac{x^4+x^2+1}{(x^2+1-x)^2} = \frac{x^4+x^2+1}{(x^2+1-x)^2} \cdot \frac{(x^2+1+x)^2}{(x^2+1+x)^2} = \frac{(x^4+x^2+1)(x^2+1+x)^2}{\left[(x^4+1+2x^2) - x^2\right]^2} = \frac{(x^4+x^2+1)(x^2+1+x)^2}{(x^4+1+x^2)^2} = \frac{(x^2+x+1)^2}{x^4+x^2+1}$
Wasn't that long after all
solid kilnBOT
lmaowhat
kind iris
Just had to multiply by its conjugate
kind iris
findng a way to make a transformation looks harder and would require to think mo...
Yeah I agree, but I was just finding a way to make this easier because I'm just practicing
If I get the hang of finding good manipulations then that would help me in the actual exam
Thank you for your help
.close
cerulean hearth
I don't get why E is a sub vector space of R^R and not just R
marble wharf
E consists of functions
cerulean hearth
ye and
cerulean hearth
because a vect is a vector space
marble wharf
and?
its a vector space spanned by those three functions
but that doesnt mean that those functions are suddenly numbers
cerulean hearth
and what would be the sub vector space then
marble wharf
hmm?
cerulean hearth
if a function is R -> R
the sub vector is R for me, seem logical
marble wharf
there is a copy of R inside R^R, the constant functions
but otherwise you are talking nonsense
do you mean that the vector space is over the field R?
cerulean hearth
well when i'm talking of sub vector space of R that mean that the vector space of E is inside R
marble wharf
for that it first would need to be a subset
which it is not
the element of E are functions
they are not numbers
they are not included in R
E is not a subset of R
verbal gulch
why are you calling it a sub vector space instead of a vector subspace
unless you actually don't mean it?
cerulean hearth
no i mean it
verbal gulch
are you talking about a vector subspace or something else?
cerulean hearth
hum e.g E = {(x,y,z)ā¬R^3, x = y +z}
are you calling that a sub vector space of R^2 or a vector subspace of R^2
marble wharf
thats not even proper set notation
cerulean hearth
now?
cerulean hearth
and what's a sub vector space then
verbal gulch
I don't even know what you mean by a "sub vector space"
do you mean vector subspace or not
that's what I've been trying to ask
cerulean hearth
that's what i'm trying to clear
cerulean hearth
that would be a subspace of R^3
then that's what i meant
verbal gulch
how am I supposed to know what it means
cerulean hearth
I'm asking you about the *definition* of some weird terminology you're using
that's why i give an example to know
verbal gulch
this tells you what a vector subspace is
is that the same thing as what you call a "sub vector space" or not?
cerulean hearth
yes
marble wharf
they clearly mean that
dont put too much attention on that word swap
could come from translation or something
verbal gulch
they clearly mean that
I mean I thought so, but then they insisted on calling it something else, which is weird
cerulean hearth
i used vector sub space on this serv and they were not any misunderstood so i thought that was the good term
verbal gulch
vector subspace or linear subspace or just subspace is common terminology
but sub vector isn't
sometimes people say things that seem like they're something, but they turn out to be completely different
in any case, a very succinct definition of a subspace is some set that is a subset of a vector space and is a vector space in itself
your E is not a subset of R, and therefore it cannot be a subspace of R
nova spire
eh, in french it's called "sous-espace vectoriel" so literally sub vector space
not every language is english-centered
verbal gulch
yeah sure, but if you say it in English, then it's weird
nova spire
so we must forgive him
cerulean hearth
your E is not a subset of R, and therefore it cannot be a subspace of R
then it's a subset of what
there must be something to refer to functions
marble wharf
you really are focusing on the wrong thing. I've seen some people mess terminology up way worse
R^R is the space of all functions R->R
that is what that notation means
civic basin
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civic basin
i started by x = sin theta substitution
then i got here and im stuck
need help on how to continue this integral
civic basin
try using u=(1-x^2)
hmm let me try this first
wraith hinge
what did you get to?
civic basin
what did you get to?
im not sure if it's even right but let me type it out
is it readable
solid kilnBOT
Toby
solid kilnBOT
granite cove
That looks much harder than x = cos u
civic basin
lol
wraith hinge
That looks much harder than x = cos u
yeah lol, do this instead 
civic basin
from here?
granite cove
Right from the beginning
civic basin
Right from the beginning
shouldnt i be using the first one
granite cove
shouldnt i be using the first one
There is a reason why I suggest this here
Can you try it?
granite cove
Yes. What's sin/cos?
civic basin
tan^2 theta / cos ^2 theta
granite cove
Note that (tan x)` = 1/(cos x)^2
civic basin
oooohh
wait let me see if i can continue from there
this makes this integral - u^2 du
is the final answer - (tan theta )^3 / 3
how to check
granite cove
Now you can sub back I think
civic basin
yup that's correct
echo jasper
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echo jasper
should i add the 3
on the other side first
and make it (x+1)^2+3?
btw i am graphing
knotty locust
Don't open multiple channels for the same question, next time stick to your original channel
hollow bloom
Add the 3??
echo jasper
other one because i change this question
echo jasper
I close the other channel
knotty locust
In the future I mean
echo jasper
Is ok
knotty locust
Anyways, if you are trying to graph this function you need to find its vertex
echo jasper
I wont make it again
knotty locust
do you know what vertex form of a quadratic function is?
Actually, I'll start by asking if you know what the vertex is
echo jasper
yeah we get the -k and h right
knotty locust
Where (h, k) is the vertex
echo jasper
yep
knotty locust
So for your question here, it is already in vertex form
can you find what the vertex is?
echo jasper
is -1,0
hollow bloom
That's just completed square form does it have 2 names then
echo jasper
is down
knotty locust
Yes
because "a" is -3, which is negative
so it opens down
Can you graph it now?
knotty locust
you just have to know some sample points to graph it
echo jasper
ok
knotty locust
so start with labeling the vertex
echo jasper
ok
knotty locust
which is at x=-1
echo jasper
ok labled that one
hollow bloom
You just plot points such as x intercept y intercept then draw a curve through them
knotty locust
yes
echo jasper
like if i picked -2 as an X i just plug it like this one -3(-2+1)^2
knotty locust
yes
and that tells you the y-value of the graph at x=-2
so you could then plot that point
echo jasper
Ok nice thank a lot for assist
rich mason
The number of students at a school increases by 40% in one year. The following year, the number decreases by 25%. The total increase in the number of students is 23. How many students were there at the school before the increase?
0.75 * 1.4x = 1.05x.
1.05x - x = 23
answer 460
x * (1 + 0,40) = x * 1,40.
x * 1,40 * (1 - 0,25) = x * 1,05
- 1,05 - x = 23
answer 437
which of these are right?
rich mason
Hi
plain slate
you're doing the same calculation
idk why you are getting different results
although you dropped an x here
harsh berry
you're doing the same calculation
plain slate
460 is right, how did you get 437?
rich mason
calculator from 1934
cursive night
your final eqns for both is the same, yet you have two different numerical values
rich mason
which should i write on my homework for a better grade?
harsh berry
first
cursive night
which should i write on my homework for a better grade?
you should write the right answer obviously
how did you get 437 anyway
rich mason
you should write the right answer obviously
i asked bing ai chat bot how they got 437 heres what they said
Let x be the number of students before the increase. After the first year, the number of students is x * (1 + 0.40) = x * 1.40. After the second year, the number of students is x * 1.40 * (1 - 0.25) = x * 1.05. Since the total increase is 23 students, we have x * 1.05 - x = 23. Solving for x gives x = 437 students.
So there were 437 students at the school before the increase.
cursive night
dont use such chat bots to do math, they're pretty terrible
rich mason
dont use such chat bots to do math, they're pretty terrible
nah we wanted to see if we were right we got 460 but how does the bot get 437?
@cursive night how?
cursive night
idk man its clearly wrong
limpid snow
The bot interpreted the question wrong
thorn grail
hii guys!!! im in year 10 and this question is really confuisng me? i asked my teacher about it and they said to work it out yourself :/ i already worked out that the first question is 1400pi over 3 + 1000m2 thanks in advance ā¤ļø
harsh berry
B?
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forest axle
Given a parallelogram with area 480 square inches, and side lengths 24 and 40 what is the measure of the obtuse angle?
crude blaze
Given a parallelogram with area 480 square inches, and side lengths 24 and 40 wh...
draw a picture
quasi wasp
<@&286206848099549185>
one can find the acute angle and then find the obtuse angle
you can find the acute angle using trig
forest axle
one can find the acute angle and then find the obtuse angle
Ok
forest axle
do you know how to do this?
I do not
quasi wasp
so one can find the height, and then solve for the acute angle using trig
forest axle
I don't know how to solve for the height either
forest axle
480/40?
quasi wasp
yes!
forest axle
12
quasi wasp
yup
forest axle
Would i do adjacent/opposite
quasi wasp
yeah sin theta = 12/24
quasi wasp
and then i suppose we do the inverse of sin (0.5)
yes, arcsin
quasi wasp
so its 30 degrees
correct
quasi wasp
answer is 150 degrees?
yes!
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quasi wasp
appreciate the help
no problem!
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mossy quarry
Why is it not C or D ?
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Why is it not C or D ?
severe wave
Why is it not C or D ?
c can't be cause on the specificed intervals the derivative is the opposite of the requirements
d isn't also cause f' of 2 exist
severe wave
c can't be cause on the specificed intervals the derivative is the opposite of ...
this also applies for d
mossy quarry
d isn't also cause f' of 2 exist
but its still continuous
severe wave
for a derivative to not exist there are 2 cases
non continuity that you mentioned and limit of f' being infinite
and that function is continuous since it's left and right limit on x =2 is the same
but the sudden change mimics undefined derivative basically
a function like that doesn't really exist tho unless it's a composite function @mossy quarry
mossy quarry
limit is not infinite tho
for c
and even tho theres a sudden change
it still touching
if i were to trace that line
with a pencil
my pencil will always be in contact
with the line
unless theres a hole
that i cant see
then sure
undefined
i think theres a hole there tbh
but u say its cause of the unexpected turn
severe wave
no it's not about a hole
there's no hole
going beyond the rule of
"sharp turns have no derivative"
I'll try and explain where it comes from
now before that, i said it's continuous and to prove that if we had the original function fx we would analyze the x=2 with left and right limit
and if both limits go to the same value it's a continuous function
now if we talk about derivative definition
it's limit for a small change
when we have a smooth curve, no matter how small you analyze this "small change" you will have values to compute this limit
but when you try and compute the limit of derivative left and right you will get different values
since the shape is not smooth the point literally has no small change it's sudden
severe wave
yeah
mossy quarry
when i wrote it out
the values
(-inf,-9)(-9,-5)(-5,8)
first and last set is negative
mind you this is the derivative
the graphs are just regular functions
not the dy/dx
so like
mossy quarry
first and last set is negative
u flip these signs right
severe wave
yes?
mossy quarry
and u get +, -, +
severe wave
wait wait
abcd are functions
for the given intervals
lets take first
inf to -2
it states that the derivative is negative
severe wave
that information means that the function values are heading towards negative values
severe wave
np
negative derivative means function is changing to lower values in respect with x
so y decreases
don't try and apply mechanic rules try and logically think what the derivative represents for a function
so when the problem states those facts
we imagine a graph going on a downward slope then upward and downward again
mossy quarry
sure
the derivative
not the regular function tho
those graphs
a-d
are y(X)
not y ' (X)
severe wave
yes and that's what I'm saying
mossy quarry
2x
severe wave
yes but derivative doesn't say that for a function it states the trend a function follows when you go through x values
which means
what happens to y values
and you increase x values
for plug in -2 it's -4
for -1 (increase x with 1)
it goes -2
we see for x increase y increases aswell specifically with number 2
and that's what the derivative said by being a positive 2
it's sign said the original function is positive trend
and it's number literally told us how y values increase/decrease
in your case you don't have any derivative value or function you are just told it stays positive
which assures you that for your original yx function when you move left to right on x axis
y values go down then up and then down
on those specific intervals
your issue is just miss understanding what derivative means for the function just watch some YouTube videos if what i said still is confusing and you will get the hang of it
mossy quarry
heres why im confused
you see this new problem here?
i fliped the signed they said
of derivatives
from "+ , - , + "
to the opposites
- , + , -
at (-inf,-9)(-9,-5)(-5,8)
severe wave
with your analogy then A should be your answer
mossy quarry
- -> x is min
severe wave
but it's not
mossy quarry
- -> - is max
severe wave
recheck the question
mossy quarry
true but the min
severe wave
it goes down then up and down again
this is A
severe wave
first derivative has no relation to min and maxes
it's just the slope of the line
idk who gave you the method of flipping but it's wrong and it won't teach you proper derivative notion
question is literally saying
what piece of line goes up and then down and then up and then down
A is not it cause it goes down first not up
same for B
D has only 3 states
where as the exercise specified 4
so it's just C
severe wave
yes but derivative doesn't say that for a function it states the trend a functio...
read all this again till it makes sense
I'm gonna go sleep
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dim jewel
Hey i have got a question
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Hey i have got a question
dim jewel
How do i define Sine function without triangles
I mean
Not like Sin x = that expansion
so here how do i define Sin A in second case ?
Because as long is its angle is acute we can make a right angle triangle then Sin = perpendicular /hypotenuse
But whag if angle itself is obtuse
frigid stump
sin x = sin 180-x
frigid stump
You can also calculate sin using the area of a triangle. A = ab* sin x/2
dim jewel
Ohh do we can define x or y coordinate
With its angles
So it was defined so right angles initially
frigid stump
Yeah, kind of
sage mural
How to solve for x?
trim joltBOT
How to solve for x?
cloud portal
How to solve for x?
It's in a triangle, which would have a total angle of 180. Find the two other angles in the triangle and you will find x.
sage mural
It's in a triangle, which would have a total angle of 180. Find the two other an...
How do I find those angles?
brave shell
39
cloud portal
For the angle in the bottom-right of the triangle:
- The 68 is on a line. The angle next to it would be 180-68
- The angle we just found is itself on a line. Find the angle on the opposite end and youve gotten the bottom-right angle.
For the anlge in the bottom-left of the triangle:
- the 107 is on a line. The angle next to it would give it.
@sage mural
It's a little hard describing it using text, lmk if that was clear.
brave shell
If two lines are intersecting opposite angles in between lines are equal
So left bottom of triangle is 68
cloud portal
Oh right, thats faster. I only remember the basic properties.
brave shell
180-107is bottom right
brave shell
Oh right, thats faster. I only remember the basic properties.
It's fine it only changes speed of output not the output itself
sage mural
180-107is bottom right
73?
sage mural
is x= 39 ?
brave shell
If you have further doubts DM me
brave shell
is x= 39 ?
Absolutely right you are great man
sage mural
Yay
brave shell
So umm close the help box and free it for others?
sage mural
thanks so much! Have a nice day, God bless! Jesus loves you :3
brave shell
Thanks man and welcome
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thick kayak
help
thick kayak
I couldn't understand why second sum is
ln(2)
also this too
I think reasoning behind these same can somebody explain thx
lavish hawk
I couldn't understand why second sum is
Comes from the power series of ln(1-x)
The 2nd one is just the above series without the first 2 terms
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upper panther
hii guys!!! im in year 10 and this question is really confuisng me? i asked my t...
a) Area = (2 x rectangle) + (arc length x 25) + (1 x sector) (find more about radians on TLmaths) = (2 x rectangle) + ( r x Īø x25) + (1/2 x r^2 x Īø) [Īø = Ļ/180 x angle in degrees ] = (2 x 25 x 20) + (20 x Ļ/3 x 25) + (1/2 x 20 x 20 x Ļ/3) [ arc length = r x Īø ] = 1000 + 700Ļ/3 m^2 [ area of sector = 1/2 x r^2 x Īø] (not 1000 + 1400Ļ/3, 'note that the top is open' in the question) b) Cost = 54 x (1000 + 700Ļ/3) =
trim joltBOT
a) Area = (2 x rectangle) + (arc length x 25) + (1 x sector) ...
@upper panther Has your question been resolved?
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brave oasis
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brave oasis
Basically im using modulo congruence to try to figure out the missing digit
using modulo 11
Basically:
a_mod_11 * a_mod_11 will be congruent to c_mod_11
So they have the same value i think
and since c is missing x, we can find x
but if theres both x and y, how do i find that?
like 2677xy53
where x is 7 and y is 3
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dense breach
Basically im using modulo congruence to try to figure out the missing digit
You have to use mod 9 as well I believe
for 2 missing digits
brave oasis
You have to use mod 9 as well I believe
Ah ok, could you elaborate?
I know the rule that adding up the digits of a number will give you the remainder of the number when dividing by 9
dense breach
yeah
so essentially you know what your two missing digits add up to (mod 9)
if you know their difference as well that should be enough to compute them, except for 00 and 99 which get confused with each other
brave oasis
if you know their difference as well that should be enough to compute them, exce...
Ah thatās smart, ok. Would I just find the difference using the mod 11 rule?
dense breach
yeah
sharp gull
Hello, I want to ask what does "floor" and "ceiling" means? I have polish education in my school.
harsh berry
4.1 floor = 4
4.1 celling = 5
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vagrant marsh
floor means round down
ceiling means round up
if its an integer already, do not round
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idle pewter
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sweet hare
what is your question
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gray quarry
!status
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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
safe yacht
Determine the center and radius of the circle if the equation of the circle is x^2+y^2-10y=0
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kindred pier
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azure pebble
how to prove this?
trim joltBOT
how to prove this?
azure pebble
using this
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vestal turtle
using this
do you know what en means?
azure pebble
and
vestal turtle
oh
azure pebble
yeah it's just in dutch haha
azure pebble
yeah but this doesn't need to be proved
azure pebble
how to prove this?
it's this that needs to be proved
vestal turtle
right, so when we sub, most of the terms cancel
we get a simple sum of a and b, and then we have to use the angle sum formulae
azure pebble
yeah i tried using the sum formula but i cannot get to the answer on the right side
vestal turtle
i think its better to do right side to left in this case
then literally just write your proof in reverse and you go from left to right
if you need a left to right
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knotty quiver
How do we solve problems like this?
trim joltBOT
How do we solve problems like this?
dire vortex
Solve $x + \frac{1}{x} = 5$
solid kilnBOT
Rub05
dire vortex
To find x
knotty quiver
I got the roots to be
knotty quiver
(15 Ā± ā21)/2
knotty quiver
You can transform the other expression to have the form of this one too
I didn't understand you there
dire vortex
**Rub05**
You can transform $x^3 + \frac{1}{x^3}$ to look like somthing similar to the other expression
solid kilnBOT
Rub05
knotty quiver
(15 Ā± ā21)/2
Do I just input the values into the next expression and solve them?
dire vortex
Do I just input the values into the next expression and solve them?
Yes
dire vortex
Could you help me do so or elaborate how should I do so?
That's more hard
knotty quiver
Yes
Oh okay
I just felt like things'd get messy if I do that
so was confused as to what to do
wraith hinge
Nope, there's an easier way
knotty quiver
Nope, there's an easier way
guide me messiah š
wraith hinge
Do you know the (a+b)Ā³ formula?
wraith hinge
Oh, nice, sharp!
knotty quiver
Thanks!
wraith hinge
I thought of aĀ³+bĀ³+3aĀ²b+3abĀ² and then factorise it later on
knotty quiver
okay man thanks
wraith hinge
(x+1/x)Ā³=5Ā³
wraith hinge
Got it already?
wraith hinge
110?
knotty quiver
yep
wraith hinge
Nice job brother
wraith hinge
Have a nice one!
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knotty quiver
Have a nice one!
šš»
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wraith hinge
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flat wing
Can someone help me out
trim joltBOT
Can someone help me out
onyx mist
!status
trim joltBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
since you do have something, could you show me your work to get that?
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flat wing
I tried using 200cos 35
flat wing
since you do have something, could you show me your work to get that?
But it says it a different angle
Not sure how I find it
onyx mist
do you remember the formula for the amplitude of transmitted light from incoming amplitude, angle of incidence, and transmission coeffecient?
from that, you just need the formula for trans coef, then its straightforward to solve
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onyx mist
<@489473096730935296> Has your question been resolved?
@flat wing , you forgot to react to the bot here
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proud tendon
Hi i need help with solving this
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Hi i need help with solving this
proud tendon
stark bison
Is this y = ax again?
proud tendon
Yea
stark bison
Ah, then you each if the products of x and y is the same everywhere
Because y = a/x can be rewritten as xy = a
proud tendon
I get it
The first one dosent have inverse dependence because the answers are different
And on the second one there is inverse dependence because they are all the same 0.24
A=xĆy
stark bison
Yup
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vale obsidian
Im just having trouble with part B of the question
trim joltBOT
Im just having trouble with part B of the question
vale obsidian
I dont really know what to do
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vale obsidian
<@&286206848099549185>
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@vale obsidian Has your question been resolved?
vale obsidian
someone help please
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solid kilnBOT
ilegosking
vague axle
I need to give my answers in scientific notation.
trim joltBOT
I need to give my answers in scientific notation.
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
I don't know where to begin, how do i start to simplify the process?
<@&286206848099549185>
rustic oxide
I don't know where to begin, how do i start to simplify the process?
you can reorder the multiplication so that you have (2.4*1.8)*(10^4*10^-2)
rustic oxide
For the divisions do i make two separate fractions? 4.6/2.3 * 10^8/10^-6?
exactly
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dark turtle
not sure how to treat this.
trim joltBOT
not sure how to treat this.
dark turtle
would i be correct to do the root test for x^n?
twin swan
yep, that should work
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scarlet goblet
Quick question what is Ī¼ in a T-Test? Is it the number I am testing on? I can't get a clear answer
scarlet goblet
Here's an example of what the equation looks like
what is the difference between xbar which is the sample mean vs mu
scarlet goblet
What if the data set I have is a sample of a population?
knotty locust
then xbar would be the mean of the sample
and mu would be the mean of that population
scarlet goblet
So hypothetically I have a population that is recording the years fathers spent in education, and there are two variables white and nonwhite. The sample mean is that of the variable I'm testing and the population mean (mu) is of all the fathers?
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@scarlet goblet Has your question been resolved?
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steep cypress
What's this?
trim joltBOT
What's this?
crude blaze
a limit
wise dagger
a picture
trim lichen
have you done anything with limits before?
steep cypress
Yes
trim lichen
so do you know, say, what 1/x goes to as x grows larger and larger?
crude blaze
@steep cypress no
inner orbit
Indeed
inner orbit
0
trim lichen
as x grows without bound, 1/x gets arbitrarily close to 0.
you might have heard something along these lines especially if you have been introduced to the formal definition of limits
(also whatever small but positive number you can think of, 1/x eventually gets smaller than that)
trim lichen
no
inner orbit
why just zero?
I love this analogy
Imagine you walking to a wall. You keep walking towards it but never actually reaching it. You are tending to that wall which has a definite value, but you may never reach that value.
trim lichen
that's a different matter