#help-0
1 messages · Page 216 of 1
no worries. Yeah it couldn't be a number because you didn't know theta. If you knew theta, then you would've found a number
inverse trig functions
may you enlighten me 🙂
Broken
this turns into $\Theta =tan^{-1}(\frac{x}{5})$
Broken
yes
thanks mate:)
np
This isn't law of sines this is just a trigonometric equation
gotchya
i mean you could do law of sines
You can equate a trig function of theta to your base a and the height against the building and solve
You could but, law of sines can give you triangles that don't exist it's best to avoid it
Especially for something as direct as this
could u show an example?
Because this is a right triangle we don't need to use law of sines
Broken
where a = 6 and theta is 80
Nah you don't need the hypotenuse if you use the appropriate trig function
Broken
In general for problems with right triangles the trigonometric functions themselves are defined as ratios of sides of the triangle relative to a particular angle in the triangle so you can use them to solve for the entire triangle
You won't need arctangent here
you could just calculate tan(80)
and then multiply both sides by 6
oh yes lol mb
Broken
34 feet
you could also see how they do it in another example when you practice another
if thats available for that question
it's more off a review right before an exam
I've done all this before but it's so much
and I couldn't comprehend the differences between questions when there was so much
I think the next one though is law of sines
the Asa or ssa etc
sinA/a = sinB/b
ahhh okay I'll try this one on my own for a sec
fuck lol
I even have notes I replicate but I've no idea why I did what I did
different problem that I did
what's with the x^2? on the right?
yeah I've no clue
not sure
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Can someone do this?
,rotate
Someone can do this but someone that is not u should not do this
Someone that is not u can help u do this
If you are so inclined to be inclined
What have you tried
bro Stephen my man, what are you saying? lol 💀
I tried 1 way but it was hella confusing and hurt every brain cell I had that I took a 30 minute break
The moment you said straightforward integration
I didn't even bother 😭💀
"
" 😂
anyways
your idea was pretty good, expanding then integrating each term via the power rule of integration
were you getting confused on the expanding?
The fractions were really annoying to deal with and took way too long
This shouldn't take more than 3 minutes
try writing it all out and doing is slowly rather than going on algebra autopilot
right?
You just solved it for them
Wdym
were you getting confused about the expanding?
Is it correct
Yeah specifically the fractions part it got really annoying
they're integrating I don't think expanding two linear terms would be considered solving it for them, but eh I'll relax it a bit
But I have to expand first right?
so try to expand $(x^3-3)(\sqrt{x}-1)$ first
XxMrFancyu2xX
,w integral of \frac{(x^3 - 3)(\sqrt{x} + 1)}{x^2}
well he was right
F
Wait so I did it right 😅😅
Why did it feel like I did everything wrong
I feel like my steps were too messy
Cause I do most of the work in my head instead of write it down ig
Which usually makes me mess up on the easy stuff
Alright thank yall 🙏
yw! 
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,rotate
You can find the area of this trapezoid
All you need is the formula
Do you know it
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I got y=@^3sec(@) + @^3
but it should be
I dont get where the negatives game from
Can you make you work a bit cleaner and show one step per separate line
ok
open it in browser for full res
brother this room is occupied
you need to post in open rooms
Oh, sorry 0.0
pls delete and use the ones above
anyways I still dont get why it should be negative
@willow wraith Has your question been resolved?
@willow wraith Has your question been resolved?
damn hello?
you think so
cause i just dont see where the negatives would come from
let me get a second opinion if someone else thinks the same ill just close it
.close
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How would one go about solving these? Surface area is being asked (on the first 3)
I have no idea about how I'd go about the second one
On the first and third ig I'd just calculate the rectangles then add the pyramids on the first and the half cylinders on the third?
But since some 2 sides of the rectangles are covered idk what to do
the second one you can just find the area of the whole rectangular prism then subtract 1/2 the area of the cylinder
np
Anyone know about the other ones?
- surface area of rectangle = 2(wl+hl+hw)=2·(18·45+22·45+22·18)=4392
4392 - 2 sides of the rectangle = 45x18 = 4392 - 810 = 3582
surface area of cylinder = 2πrh+2πr2=2·π·9·45+2·π·92≈3053.63 - the 2 sides of the halves glued to the rectangle = 810 x 2 = 1620
3053.63 - 1620 = 1433.63
surface of rectangle 3582 + surface of cylinder 1433.63 = 5015.63
<@&286206848099549185>
shouldn't it be 3528+3056.63
for what
TSA for 3
with tsa meaning?
total surface area
did u make any typos?
i dont see me writing any of those numbers
what did i do wrong?
..
what
you have written in the last line
i wrote 3582 not 3528
oh yeah 3582*
is the 3056.63 also a typo
main thing is you don't have to subtract the 2 surfaces of cuboid from cylinder
yeah sorry for that
makes sense didnt think it through that much
is this correct?
like take complete surface area for cylinder
and add cuboid surface area with subtracting two surfaces
could i also just not change the rectangle and remove the 1 side that is touching the rectangle on eac hhalf cylinder?
u said to remove 2 sides from the cubod
yeah that are touching half cylinder
im asking if i can remove 1 side from each half cylinder
that will eventually be same
any other?
whys he subtracting 2 sides?
1 from the pyramid one from the cuboid?
O = surface area G = the base side of the pyramid
yes it's right
if you take pyramid area you will get that rectangle area also with it but we don't need it
same for cuboid
surface area is area of visible surfaces like you dont have to include the rectangle which is between pyramid and cuboid
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determine the angle formed by the two vectors geometrically
and represent it geometrically.
do you know in general how to find the angle between two vectors?
do the words "scalar product" ring any bells
bad notation
one, don't use the letter x as a multiplication symbol
two, NEVER denote the scalar product with the letter x or even ×
I use as '×' but my X is curvy, hence I don't get confused
hey i got the airplane question now 😃 thanks
with vectors × denotes cross product
never the scalar product, which is always written with a dot · or with angle brackets <u, v>
but wait how am i supposed to know the magnitude of each vector
There's a formula
wait
√[ (x component)² + (y component)² + 2 ab cos (angle between them. 90° here if it's components on axis) ]
i dont know if ive seen that yet tbh
that looks a lot like cosine law
You have to find c, isn't it?
yes
Wait
well
"determine the angle formed by the two vectors geometrically"
i need the angle between both vectors
and to represent it geometrically
now i am unsure ;-;
You can find the last bit, as your wish.
If they need to be approxed, you can.
I left it for you to adjust according to your question
it says the answer is 55.8
what is this part from
☺️ you're welcome
Your book needs exact values.
My textbook never asked for exact values, my questions were mostly that cos (theta) came out as 1 and hence, theta = 0
mine never specified
so i guess its just 0 from now on haha
anyways it probably wont be long until im back with another question but thank you so much :)
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fucked up here
you cannot multiply both sides by (1-4x) because (1-4x) is not sign-constant
an expression or function is sign-constant if its value is always the same sign for all admissible values of its input variables
i.e. if it is either always positive or always negative
then you can tell whether or not to flip the inequality sign when multiplying through by it
oh so x can be both postive or negative so the inequality may change i get it
but what now what should i do
oh so x can be both postive or negative
no, it's (1-4x) that can be both positive or negative.
well, you could visualize the graph of y=1/x and notice that 1/(1-4x) ≥ 7 is equivalent to 0 < (1-4x) ≤ 7
or if you want to go more formal you could rewrite 1/(1-4x) ≥ 7 as 1/(1-4x) - 7 ≥ 0 and then (1 - 7(1-4x))/(1-4x) ≥ 0 and do a sign analysis (after cleaning up the numerator)
(1 - 7(1-4x))/(1-4x) ≥ 0
what are u doing here?
..
@vale wigeon
$$ (1 - 7(1-4x))/(1-4x) ≥ 0$$
JXHN
i combined the fractions into one
$$ (1 - 7 + 28x)/(1-4x) >= 0 $$
JXHN
$\frac{1}{1-4x} - 7 = \frac{1-7(1-4x)}{1-4x}$
Ann
this is what i did
oh, so i just have to simplfy this? let me do in latex here : PP
$$\frac{1-7-28x}{1-4x} \geq 7 $$
JXHN
$$ \frac {-6-28x}{1-4x} \geq 0$$
0 not 7
oh oh right
JXHN
so i can use recporical property now ?
of inequality
a > 0
1/a > 0
$$ (1-4x)(-6-28x) \geq 0 $$
JXHN
@vale wigeon is this right?
You know about wavy curve?
nope
no bro it's in my course but it's little bit farther away
this is from the section of basic stuff
I want to learn this way too
if this is right should I solve it with zero product rule?
@vale wigeon
What did the rule say?
ab = 0
either a = 0 or b = 0
Both can be 0 too?
yeah i used "or"
or is logical operator(it's true when one statement is true or other statement is true or both statement is true)
You're right for the operator
The last part is generally done by wavy curve.
@stone gulch I need help i couldn't solve can you redo the solution the process that Ann recommended ?
I'm trying
okay ping me okay gonna take a lil break
you're gonna need that but it is not enough
yeah i am completely lost after i didn't get the right answer
@
can u solve it for me ://
x <= 1/4 and x <= 3/14
yeah i am completely lost
@vale wigeon
sorry, am busy
okay
@real cipher Has your question been resolved?
She did with wavy curve too
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On the second line isn’t there supposed to be a minus at the front
Can I have some help understanding this problem
Yes, but doesn't matter since it will be set to 0 anyway
Ah that’s why the 2 disappears on the next line as well
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10 - 12 + 17 x 10/5
I dont know where I am stuck
$10-12+17 \cdot \frac{10}{5}$
Oogy Boogy
Like this
wha
how
Whats 10/5
2
Oogy Boogy
?
Now what do we do
uh multiply?
bc that equation looks very scary
34
$10-12+34$
Oogy Boogy
46
No
I suggest doing the addition first
12 + 34 is 46 correct?
Yes
YayaayYAYay
No
120
With + or -?
I added
22
Oogy Boogy
32
Yes
But why do we add?
You just answered that
I asked you
22 or -22
And you said 22
Which is the same as +22
So we basically just added again ,with the ten?
$10-12+34$
Oogy Boogy
add
And whats that
-2
And whats -2+34
Yes
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can anyone help me figure this out as an equation? thanks
how far did you get?
!status
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
1
just doing some revision but for this type of question i have probably forgetton
try rearranging so that all terms involving x are on one side, and all terms not involving x are on the other side
ok will do
@normal flicker Has your question been resolved?
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can anyone please help me with this
<@&286206848099549185>
Is this a test
(25 marks): do I even exist
25 marks: so I'm a thing of past, alright
bro read the rules
electronic exams
no dude
if this was an exam there would be option or smthn
literally a pdf of exam questions
sounds believable my teacher also gives past papers
Problem is a or b?
a)
well then just find where they are and use pythagoras?
draw a diagram first
Find the displacement travelled by ship A and ship B individually after 30 minutes
where will they be
This is step 1
so ship A will be 7.5km out and b will be 15km out
and then you find that from port b ship a is um 82.5km out
and then yeah you have 15km and 82.5km use pythag
alr so this is what i have
to find displacement
correct if im wrong
75/2 for ship A is 7.5km
30/2 for ship B is 15km
so whats the next step
draw a diagram
alr
Do 90-7.5 then use pythagoras
if you connect the new point A and B
This point will be clear if you show diagram
alr
can you see the triangle
yes
okay so do the pythagorean theorem now
ok so this is where i am
inside square root is
(90-7.5) square + (15)square
ans:83.86km
@rocky atlas question
why did you find the displacement first
no cos your pro
We find displacement first to find the targetted triangle for using Pythagoras theorem
Not really
We see that the there are two ships and they are moving perpendicularly to each other so as long as we find the displacement done by both ships individually, we can trace a triangle where hypotenuse can be the distance between the ships
ohhh okkayy
makes more senes
actually
i dont get the hypotenuse triangle part
the one to sketch that
how do you work that out
That's related to geometry
proof of past paper
wait but could you sketch a triangle of this
so i can understand
Well when there is a triangle whose one angle is 90 degree, there will always be a hypotenuse and we use Pythagorean theorem there
In this case both ships move 90 degree to each other so I figured out that it's hinting us to make a 90 degree triangle
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✅
oh so 15 on vertical
Yes
82.5 on horizontal
wait so last question
why take away 90-7.5
why cant it just be 7.5
It's 90 on horizontal actually
The ship moved 7.5
And the point at which you can see a triangle
So the horizontal of our triangle is 90-7.5
Even thou total horizontal is 90
is this where B is then
Yea
alr i'll send you what im seeing
Sure
I see
How do I trust it's not a virus?
After all you send me a file
It could be risky for me
@copper pendant
Trust me it's a pictur
If it was just a picture you would screenshot and send it here
Alr I ll show you
You sending it in file format is suspicious
Yeah that's the thing basically
Told you now click that file above
Wait no
What
Ohhh
Alr got you
So we calculating the distance
Yeah
90 is distance overall
15/2 gives us displacement BUT NOT distance
Yes
So in order to find the distance 90 which is overall distance-7.5 which is the partial distance
But to get the distance from port a to where ship a is 82.5
Yeah
Alr thanks calamity
Wait
Your a real one
Thank you
Port a to where ship A is 7.5
Not 82.5
Wait so what is 82.5
I told you
The image you posted
Just exchange the position of 82.5 and 7.5
That's their true position
Wdym find distance 90
Distance 90 is already given!!
We got 7.5 by multiplying velocity of ship A to 30 minutes
At the start ship A was at Port A
Yes
It then moved by some velocity for 30 minutes
We multiplied that velocity to 1/2 hour to get us 7.5km
Right
So that's where 7.5 came
We then substracted 7.5 from overall distance 90
To get us the required side of the triangle
@copper pendant think of it like a story
Ship A is the hero who travels at a speed of 15km/hr towards right
alr so this is what i dont get
ship a travelled 7.5km correct?
Ship B is the cindrella who travells vertically downward at a speed of 30 km/hr
alr so 82.5 is amount of km needed in order to finish correct?
as you said required side of triangle
82.5 km is the length of the required side of the triangle
since it said 30 minutes after they sail in the question
and it asks to find the distance
It traveled after 30 mins yes
Yes
So see geometry
The distance between ship A and ship B after 30 minutes will be the hypotenuse
so ship a travelled 7.5km after 30 mins correct?
and ship b travelled 15km after 30 mins correct?
Yes
What is it
so why do we use 82.5km when thats how much km is needed to finish
Because
instead of 7.5km
alr bet
lol nice
WOW
dude i've been so stuck on this for the past hour
alr now it all makes sense
Nice

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Can someone help me solve this
@paper sage Has your question been resolved?
I should just calculate this integral
Where gamma is the over half of the ellipse from (1.0) to (-1,0)
@dry fern
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A company produces cocoa powder. The random variable x describes the filling weight of the packs in grams (g) and is assumed to be normally distributed. The expected value of the filling weight is 125g. The standard deviation is 2g. All weights are in grams, down to one decimal place. A manufacturer checks his filling machine. To do this, he examines 500 packs that were filled by this machine. The filling weight is too low if it is more than 4.5g below the expected value. Show the validity of the following statement using a binomial distribution: The probability that more than 2% of the packs have an insufficient filling weight is about 4.6%
@haughty plank Has your question been resolved?
<@&286206848099549185>
<@&286206848099549185>
what have you tried so far
what's the probability a particular packet has insufficient filling weight
i know the insufficient weight is 120.5 gs but i dont know how to determine the probability of it weighing less than 120.5gs
normally distributed
p(x<120.5)
so
125-x*2=120.5
x= 2.25
(z(2.25))= 0.9945
1-0.9945= 0.0055
the probability of packets weighing less than 120.5 gs
what do i have to do now
@haughty plank Has your question been resolved?
@haughty plank Has your question been resolved?
@haughty plank Has your question been resolved?
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help
lemmes ee
yes
?
i was not sure with the answer
,w abs(4x-3)<=11
Well it is correct
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What are you trying to solve?
can you send your original question? from the textbook or online or wherever
It looks like the bottom inequality is easiest
start there
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not sure what went wrong. i did these exact steps for a previous problem and it worked
the vectors should be 3x1
ohh
so should my 3rd row have 0's
oh the extra row should be the first row right?
so [0, 2, 1] and [0, -3, 0]?
Yeah you forgot to set x3=x3
wouldn't this be no solutions?
there are more variables than equations
you can't get a pivot for every column so it's impossible to be consistent
there are infinite solutions
no, because there must be at least 1 free variable; in this case there are 2
I don't know why they are insisting on saying x2=x2 and x3=x3. better to do something like x2 = s, x3 = t. but you'll get the same combination of vectors anyway
i'm not really sure how parametric vector form works
you write $\begin{pmatrix} 2x_2 - 3x_3 \ x_2 \ x_3 \end{pmatrix}$ as a combination of vectors. in this case, as x2 times something plus x3 times something
cwatson
where do c1 and c2 come from?
@ruby frost Has your question been resolved?
you said times something
so i made the something c1 and c2
you're saying it's this
but idk why
I didn't say it was that, the first vector is wrong
it would be [2 1 0]
to see that it's right, combine them into 1 vector
i don't understand how you're getting these numbers
there just isn't a 3rd row
in the equations
this gotta be right
imma drop this class and throw the computer out the window if it's wrong
yes that looks right
oh good
so basically just don't forget that if a column doesn't have a pivot, then it's a free variable
which must be included in the system of equations
yes
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need some help in part a plz
show that (u+w,v) = (u,v) + (w,v), there isn't really much of a hint to give you that isnt the answer
<@&268886789983436800>
use A1 and A3 in literally the only way you can
ok
(thats only additivity, you also need (au,v) = a(u,v) )
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i dont understand the question
try “tan 6 = h/132”
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did i draw v -2u correctly?
no ig
what did i do wrong?
direction of u vector you have shown is upward right?
oh
is this right?
Not yet
v is indeed right and -2u is right too now
But v-2u is wrong
head will be pointed towrds -2u
@jaunty sierra Has your question been resolved?
roughly, would it look something like this?
No
You have to find v-2u = v + (-2u)
And you have drawn v and -2u
So you have to add them
However this is not the way vectors are added
how do i do it?
Don't you remember how to add two vectors?
i thought i did..
Like this
You have done something similar but in the wrong order
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this is a stats question, im trying to prove the pdf of Z=X+Y but i cant wrap my head around how that double integral for the cdf was formed:
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i dont get what im doing wrong
cos has a range between -1 and 1
-sqrt{3} is outside that range
you have the right idea
no, how did you get that
idk
oh ok
so it’s magnitude is 1
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im trying to prove the pdf of Z=X+Y but i cant wrap my head around how that double integral for the cdf was formed:
i just really dont understand how the outer integral is -inf to inf
if you let y be whatever you want (the outer integral), then to have x + y <= a, you need x <= a - y
i see, that makes sense
then to get the pdf from the cdf
u just differentiate right
from cdf to pdf you differentiate
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is the answer 2403
Volume of the total solid is the volume of the rectangular and triangular prisms
yeah
i know that?
that's why the volume is 2403
because that is the sum of the rectangular and triangular
unless ur question is on calculating those volumes.
i dont think you understand im just asking for a check if the answer is correct i think i know what to do
ohhh
gotchu
i don't think 2403 is correct
but then again it's kinda late where I am so I could be wrong 
ill tell you what i did
aight
I found the volume of the rectangle which was 9 * 15 * 12 then I found the volume of the triangle which was 7.8 * 135 I added both volumes then I subtracted 135 twice
i forgot to add the sums 9 * 15 * 12 =1620 7.8 * 135=1053 1053+1620=2673 2673-135x2= 2403
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how did they get from left to right
$A \neq [c_1 \mid c_2 \mid \cdots \mid c_k]$ right
TheWhiteShadow
c1,...,ck are pivot columns of A
that's how you define matrix multiplication
cuz c is the pivot column
how?
$\begin{bmatrix} v_1 & v_2\end{bmatrix}\begin{bmatrix} a_1 \ a_2\end{bmatrix} = a_1v_1 + a_2v_2$ where $v_1$ and $v_2$ are vectors.
Zybikron
no i get that but
hol on
lets say this
the pivot columns are colum 1 and 3
$\alpha_1\begin{bmatrix}2\2\2\2\end{bmatrix}+\alpha_2\begin{bmatrix}3\3\4\5\end{bmatrix}=\vec{0}$
TheWhiteShadow
so this is the same as
$\text{A}\begin{bmatrix}\alpha_1\\alpha_2\end{bmatrix}=\vec{0}$
TheWhiteShadow
TheWhiteShadow
@merry depot
ah. probably just some sloppy notation then
either they're taking A to be just the pivot columns (the other columns are lin dep on those, so they're unnecessary) or they got sloppy with the indices on the alphas

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is there a standard name to the operation of sum of vectors elements?
maybe youre looking for norm?
magnitude is the same as norm isnt it
sides touching the cuboid too?
Am I allowed to reply to an old convo
normal vector like
square root of the sum of the elements squared
thats a 2 norm
yeah thats magnitude
im looking for non-squared sum
i assume there's no special name for it
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Is this correct?
how are you getting 66?
when you change the bounds, you don’t undo the substitution
When I plug 6 into the equation in the bracket it gives me 4 root66 am I not supposed to do that
6 is the bound you derived for u
you can either: keep the antiderivative in terms of u and use the bounds 1 to 6, or keep the antiderivative in terms of x and use the bounds 1 to 2
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i got the same answers you did by law of sines
what do you need help with then?
how what works?
law of sines or other trig functions
trig functions like sine and cosine are just ratios
yes
i actually did the reciprocal but i got the same answers 
you also gotta know that total angle measure in a triangle is 180, so you find the other angles pretty easily since every triangle is a right triangle (has one angle of 90 degrees denoted by a square)
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$8e^-x -e^x = 2$
Bánh Xèo
