then u should check that ur result is working
#help-38
polar skiff
polar skiff
that will help u see too if u got a mistake
u put ur couples in the system and u see if there are solutions
and since those are the only possibilities
real saddle
-2 - 2 = 4 is true
polar skiff
u found them all
real saddle
and
-12/10 - 14/5 = -4 is true
polar skiff
this is standard procedure in math, so thats cool to take the reflex now
real saddle
alrighty did i do all the steps then?
real saddle
oh
polar skiff
but then ur done
real saddle
3x^2 + 2y^2 = 20
3(-2)^2 + 2(2)^2
3(4) + 2(4)
12 + 8 = 20
3(-12/10)^2 + 2(14/5)^2 = 20
both true cool
sigh... i forgot to simplify the x of 12/10 and got it wrong
damn site
polar skiff
damn site
??
everythings good but u should write 28/10 better to square it and then do the fraction calc
then u write
the solutions of the system are the couples from the set S = {your couples}
and then ur done
real saddle
it was all good but
it counted me wrong and gave me a new one cause i didnt simplify 12/10 into 6/5
alrighty ty for ur help!
got it all figured it now thanks
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lean crypt
Help solve critical points in this given interval
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Help solve critical points in this given interval
lean crypt
hey, I need some help with this question, kinda stuck. i found the derivative and made it = 0 . Trying to find Critical points now but need some help
desert osprey
Ok so 3cos3x=0
lean crypt
then i got cos3x
desert osprey
That means cos3x has to = 0
lean crypt
yea
desert osprey
so you know 3x = arccos0
lean crypt
hm wdym?
lean crypt
can I ask a quick question, so the given internval right now is
since our theta is 3x do we multiply this interval with 3 now?
high hearth
desert osprey
yes you can
desert osprey
or you could find solutions for 3x = arccos0
and then divide them by 3
And find which ones lie within the range
lean crypt
what do you mean by arccos0?
desert osprey
arccos is just inverse cos
desert osprey
hm?
lean crypt
cos^-1(0) = 1.57
desert osprey
well yea pi/2
lean crypt
I think we are talking about the same thing. its the accute angle after finding the inverse of cos 0
desert osprey
but there are other solutions
desert osprey
yea
lean crypt
ok so thats where im stuck at
desert osprey
cast diagram or from a graph
desert osprey
lean crypt
yea those two
my first answer i got 1.57 for the A quadrant
then the other is pi/2 - 1.57?
sorry i mean 2pi
which gives me 4.71
but there are other solutions
this is what my textbook says
desert osprey
Yea that's what I was saying,
So you know 3x = [...], pi/2, 3pi/2
then you can work out x
lean crypt
hm a bit confused srry man. so we solved for 3x not x huh
lean crypt
i see
ok il write it down here so u can see
this is what I have sofar, im not sure how to get the -pi/2
so the interval goes to the negative section so do we spin clockwise?
also this is our new interval right
old interval x3
i somewhat got the answer, just not sure about the negative rotation to getting -pi/6 after dividing by 3. Thanks for ur help tho
and frogman
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smoky sundial
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smoky sundial
0.09 rounded to the nearest second would be 0, so this just seems wrong to me but I'm not sure what I did wrong.
eternal adder
how did you move 2pi/150 fron the left to the right on the third last line?
smoky sundial
im not sure tbh, i just did arccos of -3/5 to get 2.214. i thought that left me with 2.214 = 2pi/150t
south latch
I think your fraction is upside down?
smoky sundial
its just asking for when she first reaches 16m so i thought i only needed the first solution
smoky sundial
I think your fraction is upside down?
yea it is
smoky sundial
so the only issue was that fraction part?
eternal adder
yeah
smoky sundial
omg
i literally JUST watched a video abt that
thank you
now i got 521.6, so would the answer be 522 seconds?
solid kilnBOT
smoky sundial
lmao alrighty
smoky sundial
im gonna end it all it was wrong
solid kilnBOT
smoky sundial
yup
eternal adder
it probably read it as (.../2)* pi
eternal adder
so it multiplied by pi rather than divide
hardy totem
What are the limits of accuracy for the amount $4500 when it is written:
a to two signifiant figures?
hardy totem
am i trippin lmao
worthy remnant
if you said "i've got about $4500"
hardy totem
yep
worthy remnant
when does someone call you a liar?
hardy totem
when you lie? lol
worthy remnant
like, if you have 2 grand
or 10
2 sf means it's just the limits of your credibility
hardy totem
nah i know the limits haha
worthy remnant
so the 45xx is the important bit
hardy totem
so the 45xx is the important bit
alrr
worthy remnant
nah man, that's too close. think bigger, they're rounding to hundreds
hardy totem
mb bro
worthy remnant
np, try again
hardy totem
sorry bro but what do u mean by too close?
worthy remnant
you have 1.20. how many dollars do you have?
hardy totem
1 dollar
worthy remnant
you have 1.98. how many dollars? roughly
hardy totem
2 dollars
worthy remnant
you have 3 dollars. how many thousand dollars do you have?
worthy remnant
right. you're thinking too small with your answer
hardy totem
too small?
worthy remnant
when does the x5xx become a 4, or a 6, in 4500?
worthy remnant
4449 is closer to 4400 than 4500, right?
hardy totem
yep
worthy remnant
see the 00's?
hardy totem
yep
worthy remnant
only the numbers at the front matter
hardy totem
alrr
chagpts explanation is this right
If you're considering it with two significant figures (rounding to the nearest hundred), the limit of accuracy would be ±50 units. In this case, 4500 could represent any value between 4450 and 4550.
i just dont understand this part
worthy remnant
pffhahaha, there you go mate
hardy totem
i dont understand it tho?
worthy remnant
what's to understand? it's given you the answer
hardy totem
like the steps
worthy remnant
significant means important
hardy totem
yrs
hardy totem
ahhhhhhhhhhhhhh
worthy remnant
when 45 becomes 46 or 44 you care
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peak perch
How do I solve this and why is it done that way if someone could explain please
low gazelle
Draw it on a circle with radius 5 (cos =adj/hyp) so radius is 5
There are 2 quadrants where cos = -3/5 but you are given an extra constraint so only one of them will fit
Then you can find sin using opp/hyp
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queen sleet
how do i do this
trim joltBOT
how do i do this
queen sleet
Q1
wicked trail
queen sleet
why "u"?
queen sleet
is it possbile to do it without substiuting (3x+4)/(5x+1)
sterile egret
is it possbile to do it without substiuting (3x+4)/(5x+1)
Yeah but cubic exp will be there
stiff locust
hi
knotty locust
(0,0) not right for what?
stiff locust
from (x + 3) ( x + 6) = 0
knotty locust
for a hole in the graph?
dense breach
f(0) is not 0
stiff locust
(x + 3) ( x + 6)
divided by x + 6
I set this rational function to zero right
then multiply by x + 6
no
ugh
what do I multiply with
I divide right
Shouldn't the numerator also get divided
or no
dense breach
You factor out the common factor in the numerator and denominator
Keeping in mind that it leaves behind a ghost: the hole now present in the function
stiff locust
can you show me the algebra
odd fractal
you can rewrite the function as
stiff locust
@dense breach im asking about x intercept
odd fractal
the (x+6) term cancels
stiff locust
right
odd fractal
then you just have x + 3 = 0
stiff locust
so -3, 0
is your point
ok ............
that usually didn't happen why is why am confused
I usually didn't cancel out the hole when finding the x intercept
odd fractal
yeah a good tip is to simplify as much as you can before doing any arithmetic
it can end up making the calculation much easier
stiff locust
I was just told your x intercept is the numerator = 0
which in this case is (x + 3) (x + 6)
odd fractal
x intercept is when the function is equal to 0
stiff locust
I was just told your x intercept is the numerator = 0
Yeah = 0
the logic was that you cancel out the denominator
and that just leaves you with numerator = 0
does that not work with holes or something
odd fractal
well when you have a rational equation, you should see if you can simplifiy it to a non fraction
if you can factor terms out, they can make it easier to determine what the graph looks like. for example, if you have (x^2 + x), you can factor it into x(x+1), which would tell you that when x is equal to either 0, or -1 for that equation, the y value will be zero.
thats important for rationals because you know that if anything is zero in the denominator, there is a hole
stiff locust
find the x intercept for this
2x(x - 3) /
(x - 3) ( x - 1)
you said cancel out the x - 3 right
2x / x - 1 = 0
??
odd fractal
yes
stiff locust
now what
odd fractal
well when you take the new equation, set it to zero and solve for x
it'll be the same whether you include the denominator or not
stiff locust
you mean whether I remove the hole or not?
or do I always have to remove the hole
so your saying its just 2x = 0
odd fractal
no the denominator will tell you if there is a discontinuity
in this case we can see that it's at x=1
when looking for the x-intercept, you can either take the entire equation or just the numerator, set to zero and solve for x
so you could either compute 2x = 0 or 2x/(x-1) = 0
you would get the same result, which is x = 0
odd fractal
its a factor so you would be getting x = -3, or x = -6
stiff locust
and not -3
odd fractal
you can either factor the top to solve for x or use the quadratic formula right? if you use the quadratic formula on that polynomial, you will get the same answer
odd fractal
generally when you write out (x+3)(x+6) = 0, it's implying the factors necessary for the function. you would take each section and solve for x separately. ex (x+3) = 0 -> x = -3
(x+6) = 0, x = -6
odd fractal
by looking at the denominator
when you find intercepts, you are looking for zeros. for x-intercept this means that we are finding values where y would be equal to zero. this could be at an intercept, or a discontinuity like a hole. you determine which zeros might be holes by looking at the denominator and checking which values of x would make it zero, which in this case is -6
stiff locust
Can you know how much x ints you will have
or do you have to solve the rational function to zero
and get all your factors
is that the only way to find out how many x ints you will have
odd fractal
idk if its the only way but probably the most traditional
you can tell alot about end behavior of a function by just looking at it
stiff locust
Can you explain why it doesn't matter if you include the denominator or not
let's say I have x + 3 / x + 6 = 0
odd fractal
well think about it,
stiff locust
I can just do x + 3 = 0
odd fractal
to simplify the equation you multiply both sides by (x+6)
you just have (x+3) = 0
and vice versa for dividing by (x+3)
the denominator doesn't matter because no matter what it will always be multiplied by zero
stiff locust
I'm confused why multiplying x + 6 doesn't impact both
odd fractal
maybe i can explain it in a simpler way:
You have the rational function, y = (x^2 + 9x + 18) / (x + 6)
right away you can see that when x = -6, the denominator will be zero resulting in a discontinuity.
you can either rewrite the equation and simplify it to just (x+3) = 0
or you can factor the top -> y = (x + 3)(x+6) / (x + 6)
you can calculate this many different ways. here is one example
1: (x + 3)(x + 6) = 0 * (x + 6)
(x + 3)(x + 6) = 0
you can see that when x is -3 or -6, the entire term will be zero
stiff locust
is multiplying and dividing different?
lets say I have multiple terms in the top
x + 6 - 3 / -3 + 4
and for whatever reason I wanted to divide by 4
EVERY TERM gets divided by 4 right
odd fractal
why would they all get divided by 4?
stiff locust
so they don't?
odd fractal
if you multiply the whole thing by 4, then the entire numerator would be multiplied by 4
odd fractal
ok if you have a fraction and you are dividing 4 from a fraction, that would be the same thing as the fraction multiplied by 1/4
stiff locust
so every term getting divided by 4 is false
odd fractal
technically they are, its just simplified into one fraction with the same denominator
like x^2 / 4 + x / 4 + 2 is the same as (x^2 + x + 2) / 4
stiff locust
$$\frac{x+3}{x+6}=0$$
solid kilnBOT
geoxcaliber
solid kilnBOT
geoxcaliber
odd fractal
no
stiff locust
since thats what happens with dividing
stiff locust
(1/4) * 4 = 1
is that showing how you can divide everything by 4
and it'll be the same
@odd fractal also for the x intercept why does it not matter if I keep or include the hole's factor
odd fractal
you dont have to
stiff locust
but why does it give the same answer
odd fractal
if you know that its a hole u can ignore it as far as intercepts go
stiff locust
why does keeping the hole still give you the right x int
odd fractal
x int process doesnt give u just the x-int
it gives u all zeros of the function
which is when either y = 0, or y DNE
u find out if any of those are holes, either set denominator to zero and solve for x, or plug in the zeros you found and see if any give an error
stiff locust
why does keeping the hole still give you the right x int
what about this?
odd fractal
think about it like this: you have two factors, x = a, and x = b. you also know there is a hole at x = b. therefore, out of the 2 factors we found, one of them is a hole, leaving the other to be the x-int
stiff locust
I see what you mean now
so at the end you'll get your factors
even if there is a hole it doesn't matter
bc the other will be x intercept
but
$$\frac{(x+3) (x+6)}{x+6}=0$$
solid kilnBOT
geoxcaliber
odd fractal
eh it depends on the question. if its an easier one, there will be factors available to let you cancel some terms out. but for harder questions, you might have to do a little more work simplifying.
it helps to practice determining end behavior of a function without graphing it, yk get used to visualizing it in your head based off the math rather than a picture. and that doesnt mean you have to know what the image will look like, but certain things like where it might be increasing,decreasing, etc'
stiff locust
can your zero in the numerator also be taken up by a vertical asymtote and not just a hole?
odd fractal
yes
when u set the denominator to zero, you are looking for discontinuities, not necessarily just holes.
so that includes the infinite approach towards an asymptote or a removed hole
(or the 3rd one that i cant remember)
stiff locust
Alright ty so much, I have been struggling a lot with rational functions
odd fractal
np! check out organic chemistry tutor for good practice stuff on yt
stiff locust
Btw
"The graph can only touch the x axis as many times as it has x intercepts"
this is only for x ints right
other zeros not included
holes, va
odd fractal
yes
zeros are when y or f(x) is equal to zero
x-int is when y = 0 and is contiunous
stiff locust
Last question
To determine the hole's y you REMOVE the hole and plug in the hole's x
Why do you need to remove the hole (e.g. x+6) from the function
odd fractal
if you wanna know the holes y, you would technically need calculus, because that value is undefined. instead, draw a line from x=-5 to x=-7
stiff locust
but how are we able to plot the hole onto the graph ?
odd fractal
you cant find the specific value of that y unless you use limits, which is more advanced and unnecessary
stiff locust
so whats the idea behind removing the hole from the function and then plugging it into that new function
the result of that is the 'y'
odd fractal
you dont remove the hole, it's just that when you solve for the zeros, both sides are being multiplied by (x + 6), and if u recall, we have the right side of the equation set to 0
and anything times zero is zero
on the left side, the term just cancels out
stiff locust
but when looking for the hole's y
you have to simplify before plugging in the 'x' (hole)?
or can you put in the hole into the function without simplifying
odd fractal
you would have to manually graph and draw the line. this function is literally just a straight line of (x+3) with a hole of -6
its impossible to mathematically determine anything divided by zero
stiff locust
you dont remove the hole, it's just that when you solve for the zeros, both side...
no heres the thing
the logic is that when you remove the hole
you get x + 3 = 0
then you plugin -3
wait thats not your hole
you plugin -6
odd fractal
oh right, yeah that would work
stiff locust
you get -3
odd fractal
which is correct
stiff locust
whats the logic behind removing the hole
you couldn't just outright plug in -6 right
into the function with the hole
stiff locust
from dividing by x + 6?
stiff locust
So we shouldn't look into it as multiplying by x + 6
but as canceling stead
instead
odd fractal
right because we arent setting y to zero for that. if we want to plug in the hole value, you need to simplify and rewrite the equation so you dont get a divide by zero error
in this case, our factors cancelled out leaving us with x + 3 = y
plug in -6
-6 + 3 = y
-3 = y
if you were to multiply x + 6 instead, eventually you would run into an issue, which is that y would be multiplied by zero - which doesnt make sense
stiff locust
if you were to multiply x + 6 instead, eventually you would run into an issue, w...
How would y be multipled by 0
Isnt it x + 6
oh cuz x is -6
But either way we still think of it as = 0 no?
x + 3 = 0 is valid
Why can we change the y to zero after
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rare temple
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rare temple
i'm thinking the domain would NORMALLY be (-∞,∞) but how would i write it as an inequality?
nvm i got it lmfao 😭
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floral lark
Hi, this is a formula related to a competitive programming problem, and I am not sure how to interpret it. I am particularly confused about what the 2*n over i=1 means. Let me know if more context to the problem is needed.
trim lichen
yes, more context is needed
gentle jungle
Solve | x-1 | < 4 graphically.
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Solve | x-1 | < 4 graphically.
gentle jungle
I don't understand the concept behind absolute value functions and their relation to inequalities. Like it is rlly confusing for me.
wispy sparrow
absolute value function turns negative values into positive values, yes?
gentle jungle
yes
wispy sparrow
Solve | x-1 | < 4 graphically.
and graphically identify where it's less than y=4
wispy sparrow
yeah
gentle jungle
so how do I write down the value of x in terms of inequalities?
so using the greater than or less than sign..
wispy sparrow
you should've gotten x between -3 and 5 right
gentle jungle
right
gentle jungle
so how do I know it is not -3 included or 5 included?
lethal sparrow
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lethal sparrow
Hello! How do i find the coeffecient in front of the brackets?
ive identified the factors which are (x+1)(x-2)^2(x-5)
nvm i got it xD
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royal remnant
How would you compute this?
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How would you compute this?
wispy sparrow
i thought someone would've had solutions for cambridge integration bee but ig not
wintry stag
If you change sin(3x) to sin(kx) and differentiate under the integral sign, you get xcos(kx) and then you can integrate by parts.
royal remnant
If you change sin(3x) to sin(kx) and differentiate under the integral sign, you ...
oh shit yeah that makes sense
thanks
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lone mauve
to clarify, is this question just asking for the antiderivative of x^2?
"the derivative of a function that gives back x^2" <-- this is also called the antiderivative of x^2?
vapid lynx
it's a slight trick, but yes that's what they want
note that they ask for the equation of a curve
lone mauve
oh
vapid lynx
there are, of course, infinite curves that satisfy that
lone mauve
so this is still correct wording for antiderivative? "the derivative of a function that gives back x^2"
and the function happens to be the equation of a curve
vapid lynx
yes
lone mauve
would that mean that all antiderivatives are equation of curves? or not always
vapid lynx
the point is that when you integrate you get a +C, which could be any constant yielding infinite solutions
your intuition on how to solve is correct
lone mauve
I am reading online: "antiderivative is the area under the curve"
which feels a bit confusing to me
vapid lynx
it does have that property, but that's not the relevant one here
lone mauve
Oh right, because after you take the f'(x) derivative of the F(x) antiderivative, it gives back f(x) the original function, x^2
somehow, it feels like time traveling with antiderivatives
I gotta think about future and past to get back to the present
lone mauve
Oh right, because after you take the f'(x) derivative of the F(x) antiderivative...
Could all of this be summed up as F'(x)? Or not really
it's taking f'(x) of F(x) to get back f(x)
lone mauve
your intuition on how to solve is correct
F'(x) = f(x) but I don't know if that really applies here for this question, as per above. I don't know if you can just merge all of this f'(x) of F(x) into this F'(x), as they are separate steps
what would you say?
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wraith hinge
hi
wraith hinge
can someone help me with this?
forest egret
solid kilnBOT
WhereWolf(ping if needed)
pastel current
How do I go about solving this?
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How do I go about solving this?
west nest
Have you heard about the Vertex of a parabola
pastel current
Have you heard about the Vertex of a parabola
Yes
pastel current
Just that it's the "base" of the parabola. That may not be the best way to refer to it
Or the start?
I'm not sure what to call it
west nest
Hm, no
You can think of it as the point of the intersection of the parabola with its axis of symmetry
pastel current
That makes more sense
west nest
It tells us the maximum or minimum value of a quadratic function
pastel current
Yes
west nest
Do you know what determines whether it is the maximum or minimum value?
pastel current
Not exactly
pastel current
I know what the equation is, I'm not sure what you mean by definition
Do I have to turn the function above into vertex form to solve?
west nest
$f(x) = ax^2 + bx + c; a, b, c ∈ ℝ$ and $a ≠ 0$
pastel current
Okay good
solid kilnBOT
USS-Enterprise
west nest
**USS\-Enterprise**
Have you seen this
pastel current
I've seen the first half, not the part after the ';'
west nest
That part just tells us that a, b and c are Real numbers and that a can't equal 0, because then we don't have a quadratic function but a linear one
pastel current
I see
west nest
Anyway
pastel current
What does the E looking thing mean
west nest
Means "belongs to" in math
pastel current
Gotcha, thank you
west nest
Whether the vertex represents a minimum or maximum value of a quadratic function is determined by the leading coefficient
The leading coefficient is the coefficient next to the variable with the largest exponent
In this case this is a
Let's set b and c = 0 because we only care how a affects the parabola (and the vertex)
We are left with this:
$f(x) = ax^2$
solid kilnBOT
USS-Enterprise
west nest
Are you following till this point?
pastel current
Is it listed in the order of c,b,a? So -30t would be a, 240t =b, etc. ? I'm just wanting to double check since it's "backwards"
solid kilnBOT
USS-Enterprise
pastel current
The leading coefficient is the coefficient next to the variable with the largest...
So -30, correct?
west nest
This is now in the form of $f(x) = ax^2 + bx + c$
solid kilnBOT
USS-Enterprise
west nest
We just replace x with t, this doesn't matter
west nest
So -30, correct?
Correct, in this case a is -30
But let's leave this for a moment
We need to see how a affects the parabola in general in order to understand this
pastel current
I believe I am following still
solid kilnBOT
USS-Enterprise
west nest
We already know a≠0 because then this isn't a quadratic function
So let's look what happens with a parabola when a<0 and when a>0
Let's first pick a=1
$f(x) = 1x^2$ or $f(x) = x^2$
solid kilnBOT
USS-Enterprise
pastel current
When the a value is positive, the parabola opens upward, and vice versa
west nest
Yes, this is what the parabola looks when a is positive
Do you see where the vertex is in this case?
pastel current
Yes, (0,0)
west nest
Correct
And does this represent the maximum or minimum value of a function?
(We have to look at the y value of the vertex for this)
pastel current
Min
pastel current
Then (0,0) is still the vertex, except now it's the maximum since it opens downwards
west nest
And in this case the minimum value of our function is 0
So we have learned
When a > 0, the y-coordinate of the vertex is the minimum value of the quadratic function
And when a < 0, it is the maximum value
So in your case
We've got a=-30
Does this mean the vertex will represent the maximum or minimum value of our function?
pastel current
Max
west nest
Good
Now we only need to figure out the value
Do you know how to calculate the coordinates of the vertex of a parabola?
pastel current
Not without turning it into vertex form
west nest
Okay, turns out there's a formula to find each coordinate
Let's say the Vertex has coordinates (h, k)
The formula for h, or the x- coordinate is:
$h = -\frac{b}{2a}$
solid kilnBOT
USS-Enterprise
solid kilnBOT
USS-Enterprise
west nest
We are looking for k, correct
So just insert a, b and c
And you've found the maximum value of our function
pastel current
Ohhh I have seen that, I didn't realize it was applicable here. Could you also just plug the x coordinate into the original equation and solve to find y?
west nest
Ohhh I have seen that, I didn't realize it was applicable here. Could you also j...
You can do that too, of course
pastel current
That seems easier, for me at least lol
solid kilnBOT
USS-Enterprise
west nest
That you have in the numerator of the formula for k
Is actually the discriminant of a quadratic equation
It is crucial in solving quadratic equations (and determining the number of solutions)
Which I am guessing you'll be learning soon
Anyway, what did you get for k?
pastel current
I don't mean to cut you off, but I have to head to my next class now. I tried solving for k, but I think I did something wrong because my answer was very big lol. I'll look over this chat again after class and go back through to see if I can spot what I did wrong. I'll also try your method instead of plugging in for x haha
west nest
I don't mean to cut you off, but I have to head to my next class now. I tried so...
Hehe, no worries. Just mention me once you are back
pastel current
Will do, thank you!!
west nest
K is actually pretty big in this case (it's a natural number though)
pastel current
I'll close this for now
west nest
👍
peak wren
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peak wren
what should I do to find where the tangent line is parrelel
vapid lynx
what should I do to find where the tangent line is parrelel
parallel = same slope
vapid lynx
the line is y= 4x+2
peak wren
ye
peak wren
what should Ido then
vapid lynx
you should solve 2x=m to find the x coordinate of where this is true
peak wren
2x = m
m is the slope?
WAIT
do I do 2x^2 = 4x + 2?
and solve for x
<@&286206848099549185>
im confused
what do I do to test what value makes both slopes equal
wtf why did you delete your message now I look stupid
ok lol
ok ok
I thought you dipped
?
@sterile night
what are you doing
stop deleting yooru messages its weird
what does that mean
how did you get to that
?
\
but thats not a coordinate point
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@peak wren Has your question been resolved?
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wanton nest
uh
delicate jasper
boomerang
tacit quest
concave quadraliteral
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@wanton nest Has your question been resolved?
wanton nest
no
wraith hinge
@wanton nest , A Concave Kite
ashen lark
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nimble stone
ashen lark
I need to find the rational solutions to this but I'm stuck
nimble stone
what have you considered trying?
mellow tendon
Did you think of multipling like 2 different numbers to both equations ?
ashen lark
what have you considered trying?
I substracted and added the equations
ashen lark
Did you think of multipling like 2 different numbers to both equations ?
Not really, gonna try that now
marble wharf
I think subtracting should do something
ashen lark
Not really, gonna try that now
I multiplied the first equation by 5 and the second one by 4
Then substracted them
And got this
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@ashen lark Has your question been resolved?
zenith flame
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@zenith flame Has your question been resolved?
twilit kraken
I think you have substituted $\theta$ wrongly in last line.
solid kilnBOT
Enemagneto
twilit kraken
It should be $\cos^{-1}$.
solid kilnBOT
Enemagneto
zenith flame
you've lost me
secant is 1/cos and i would be dividing by this value on the other side of the equation to isolate theta right?
would that not make it cos rather than cos^-1?
twilit kraken
Damn.
How would dividing by sec(theta) isolate theta?
Are you familiar with trigonometry?
Because you seem to be botching it badly.
Also, ping reply if you want an immediate response.
zenith flame
i want to find theta's equivalent value yes?
so i am taking the inverse of secant from x=5sec(theta) after dividing both sides by 5 leaving the inverse of sec(x/5)=theta
zenith flame
Also, ping reply if you want an immediate response.
if thats the wrong process ive been missing something from every example ive seen thus far
twilit kraken
It seems so.
If you have $\sin x = a$, it becomes $x = \sin^{-1}{(a)}$ for x in the principal domain. Not because we divide by $\sin$. We make use of inverse function for that.
solid kilnBOT
Enemagneto
zenith flame
ok hold on
zenith flame
you are like honing in on something i didnt really articulate correctly
when i say divide by secant i am talking about putting the inverse function into the equation
which you seem to agree with
twilit kraken
Yes. You can't say divide by secant. It's a horribly wrong way of putting things.
zenith flame
but even if i had said it in the way you like more, it still feeds the wrong answer
twilit kraken
Dividing by sec(theta) would be fine but that doesn't isolate theta.
zenith flame
so im doing it wrong in some way
twilit kraken
but even if i had said it in the way you like more, it still feeds the wrong ans...
Because you did it wrong.
zenith flame
ok, so can you help me understand how i did it wrong?
twilit kraken
You had sec(theta) = x/5
zenith flame
yes
twilit kraken
Now, elaborate what you did.
zenith flame
wait
sec(theta)=x/5 is just from the trig sub
this one is sqrt x^2-a^2 which gives x=asec(theta)
and a is a constant so i can move it to the other side by dividing both sides by a
thats all fine?
.close
torpid shuttle
My answer was wrong can i get some help
trim joltBOT
My answer was wrong can i get some help
wispy sparrow
be careful with where you put your brackets
it looks like you have $(3\cos\theta)^3$
solid kilnBOT
chlamydia
wispy sparrow
which turns into $(12\cos\theta)^3$ by the end when it should be $12(\cos\theta)^3$
solid kilnBOT
chlamydia
torpid shuttle
But otherwise its fine?
wispy sparrow
you don't need the -3 on the end, it's just -sin theta
think of it this way: $\frac d{d\theta}(3\cos^4\theta)=3\frac d{d\theta}(\cos^4\theta)$ and just differentiate the cos^4
solid kilnBOT
chlamydia
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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wraith hinge
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nimble stone
why so urgent
night zodiac
<@100178473804394496>
Please do not ping specific people
wraith hinge
Oh sorry sorry mb
I’m helping a friend out and I don’t know the answer to this as I’m past gcses and in A levels and don’t study maths anymore
So I would appreciate the answer asap
night zodiac
Yeah we're not here to give out answers
wraith hinge
I mean I wouldn’t mind tryna solve it with u guys but it would be pretty pointless for me
But idm, let’s solve it
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crisp lance
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crisp lance
equate them in your head and you might see why im so confused
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@crisp lance Has your question been resolved?
tropic smelt
equate them in your head and you might see why im so confused
Hello. Then maybe no answer exists (?
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@crisp lance Has your question been resolved?
zinc ginkgo
equate them in your head and you might see why im so confused
Show your work if you want help
trim joltBOT
https://gyazo.com/ada12db36f1fd639535665bafe349810
lost trout
im just trying to formulate the equation for DF
dF
sorry
Force is (area)(density)(depth)
torpid shuttle
Was doing product and chain rule and got it wrong, dont really know what i messed up on
trim joltBOT
Was doing product and chain rule and got it wrong, dont really know what i messe...
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dim prism
how do i make y the subject in y = 4 / (2x-1)ˆ2?
trim joltBOT
how do i make y the subject in y = 4 / (2x-1)ˆ2?
wraith hinge
how do i make y the subject in y = 4 / (2x-1)ˆ2?
it is the subject
wraith hinge
ok then how do i make x the subject
make it x= ... with alg
dim prism
yeah thats where im stuck
wraith hinge
what have you tried
dim prism
bringhing the denominator to y's side, expanding it
wraith hinge
can i see your work please
dim prism
3 minutes im gonna have to get discrod on my phone
wraith hinge
y(2x-1)^2=4 like this
dim prism
yeah
wraith hinge
3 minutes im gonna have to get discrod on my phone
sure
wraith hinge
then i expand the (2x-1)ˆ2 and multiply it by 'y'
no you leave those for later since you'll need to square root both sides
you want it like (2x-1)^2 = blah
dim prism
Middle Colton
Ok lemme try that
i got x = (4 / √y) + 1/2
is this valiud
is this certified
wraith hinge
i got x = (4 / √y) + 1/2
(sqrt(4/y)+1)/2= sqrt(4/y)/2 + 1/2
cobalt sapphire
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cobalt sapphire
I’m stuck im trying to set the last part = to the original integral but i can’t like figure out how to neatly do it
for the integration by parts problem
| e^(2x)cos3xdx
sorry for the scribbles 💀
did i start the problem wrong?
<@&286206848099549185>
.close
heady talon
This is circuits related
trim joltBOT
This is circuits related
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@heady talon Has your question been resolved?
heady talon
any help ?
crimson briar
Having trouble solving this problem
trim joltBOT
Having trouble solving this problem
crimson briar
When changing the 1/9 to 1/3 do i also have to change the exponents?
delicate jasper
Ofc! Hihi
trim lichen
you don't just "change the 1/9 to 1/3"
you change 1/9 to (1/3)^2 perhaps
and then apply exponent laws (namely (a^p)^q = a^(pq) here)
rather than attempting some kind of synchronous change that is easy to fuck up
molten crest
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molten crest
the answers are both constants so why is only one convergent?
im so confused
<@&286206848099549185>
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full dock
Did I do anything illegal/wrong here?
trim joltBOT
Did I do anything illegal/wrong here?
trim lichen
but you DID write the dx.
trim lichen
anyway this looks ok assuming i didnt miss any arithmetic fuckups.
full dock
full dock
anyway this looks ok assuming i didnt miss any arithmetic fuckups.
Am I good to plug in my upper and lower limits now?
full dock
you have not yet actually integrated the thing
would it help to convert it to this form
$\int_{1}^{49}u+15\cdot\left(\sqrt{u}\right)^{-1}du$
solid kilnBOT
water beam
trim lichen
yes you should
full dock
$\int_{1}^{49}\frac{u}{\sqrt{u}}+\frac{15}{\sqrt{u}}du$
solid kilnBOT
water beam
full dock
$\int_{1}^{49}\frac{u}{\sqrt{u}}+\frac{15}{\sqrt{u}}du=\int_{1}^{49}u^{\frac{1}{2}}+15u^{-\frac{1}{2}}du$
then i get that
solid kilnBOT
water beam
full dock
and im allowed to do that right?
exotic pike
yup
full dock
nice
oh i almost forgot
theres 1/2 multiplying the integral
$\frac{1}{2}\int_{1}^{49}u^{\frac{1}{2}}+15u^{-\frac{1}{2}}du$
should be dis
solid kilnBOT
water beam
exotic pike
Should be in a much better place to solve now
full dock
yep
$\frac{1}{2}\left[\left(\frac{2\left(49\right)^{\frac{3}{2}}}{3}+\frac{15\left(49\right)^{\frac{1}{2}}}{\frac{1}{2}}\right)-\left(\frac{2\left(1\right)^{\frac{3}{2}}}{3}+\frac{15\left(1\right)^{\frac{1}{2}}}{\frac{1}{2}}\right)\right]$
solid kilnBOT
water beam
full dock
did I integrate something wrong
exotic pike
Looks alright to me
full dock
exotic pike
the leading 1/2, 2’s, and denominator 1/2’s can all cancel
full dock
o yeah
exotic pike
$[(\frac{(49)^{\frac{3}{2}}}{3} + 15(49)^{\frac{1}{2}})-(\frac{(1)^\frac{3}{2}}{3} + 15(1)^\frac{1}{2})]$
Didn’t bother with the left right stuff lol
solid kilnBOT
M. Frost
full dock
lmao
trim lichen
$\frac{1}{2}\left[\left(\frac{2\left(49\right)^{\frac{3}{2}}}{3}+\frac{15\left(4...
may i suggest some lubricant
full dock
is it gonna be to simplify the exponents
trim lichen
no, it's to go about your thing in a slightly different order
full dock
sure
trim lichen
$\frac12 \int_1^{49} u^{1/2} \dd{u} + \frac{15}{2} \int_1^{49} u^{-1/2} \dd{u}$
solid kilnBOT
Ann
trim lichen
and then write the antiderivatives of $u^{1/2}$ and $u^{-1/2}$ as $\frac23 u^{3/2}$ and $2 \sqrt{u}$ resp.
solid kilnBOT
Ann
full dock
is this that like linearity property
trim lichen
it's not "like" that, it is that
trim joltBOT
@full dock Has your question been resolved?