how would i get the answer to this if i wanted to?
#help-10
timid silo
timid silo
ohhh thats why the calculator websites didnt show anything
dark stirrup
Instead of terms, I prefer to call them variables or unknowns
Variable meaning "changing" or "the ability to change"
Hour it works is that you want to express some mathematical concept, but you do not know all the values
As an example, "I need to raise all my prices by $7"
That's just adding 7 to whatever your original price was
But if you have a lot of different items, it could be a lot of different values
So we choose some "variable" to refer to thie original price of whatever item I choose
Then the expression y+7 says exactly what I'm doing in short, concise math terms
And it works no matter what because y can be anything
So yeah, there's no definite value of y or a or b or any variable
At least in expressions like this
tawny sail
Instead of terms, I prefer to call them variables or unknowns
just be careful on teaching that idea, because x is a variable and a term, 5x is a term but not a variable in its entirety
dark stirrup
Does all that make sense @timid silo?
dark stirrup
just be careful on teaching that idea, because x is a variable and a term, 5x is...
I did not know 5x as a whole was considered a term. I don't really remember the beginning vocabulary
timid silo
so i can close this now
tawny sail
I did not know 5x as a whole was considered a term. I don't really remember the ...
A term is a combination of decimal numbers and variables multiplied/divided together.
Variables:
x, y, z, a, b
Numbers:
2, 3, 5, 1/2
Terms:
x, 2, 3y, 25.3, 1/2, xy^2
sage dagger
how would I do this 16^x = sqrt(2)
obtuse pebbleBOT
how would I do this 16^x = sqrt(2)
balmy mortar
hint: express everything in the same base
sage dagger
hint: express everything in the same base
so 16^x = sqrt(16^2)?
royal basin
16 is a possible choice but it is clunky
better to acknowledge that 16 = 2^4 and so 16^x = 2^(4x)
obtuse pebbleBOT
@sage dagger Has your question been resolved?
sage dagger
better to acknowledge that 16 = 2^4 and so 16^x = 2^(4x)
do we have to solve for x afterwards after 16^x = 2^4x
high lily
2^(4x) not 2^4x,
those parentheses aren't optional in text
well the end goal is to solve for x...
would you be able to express sqrt(2) in exponent form?
timid silo
how would I do this 16^x = sqrt(2)
do you know about logarithm?
obtuse pebbleBOT
@sage dagger Has your question been resolved?
carmine surge
obtuse pebbleBOT
carmine surge
im lost
obtuse pebbleBOT
@carmine surge Has your question been resolved?
obtuse pebbleBOT
@carmine surge Has your question been resolved?
quaint rampart
Should I differentiate this first and then integrate what's left or just simply cancel d/dx? I'm confused.
obtuse pebbleBOT
Should I differentiate this first and then integrate what's left or just simply ...
@quaint rampart Has your question been resolved?
fading quest
either works as they are inverses, the big thing is that you are gonna get a constant since the derivative is inside the integral and not outside $$\dv{x}\int\frac{x^2+3x\sqrt{x}}{x\sqrt{x}}dx=\frac{x^2+3x\sqrt{x}}{x\sqrt{x}}$$but$$\int\dv{x}\frac{x^2+3x\sqrt{x}}{x\sqrt{x}}dx=\frac{x^2+3x\sqrt{x}}{x\sqrt{x}}+C$$
warm shaleBOT
Duh Hello
fading quest
note that the 2nd term on the fraction is actually just a constant for all $x\neq 0$ so you can rewrite it to $$\frac{x^2}{x^{\frac{3}{2}}}+C_1$$ where $C_1=3+C$ and then you can again rewrite this a tiny bit further
warm shaleBOT
Duh Hello
lapis crest
The smoothie chain makes multiple $0.15 increases to the average prices of their smoothies. The table shows the average profit of the chain compared to the number of price increases. The data models a quadratic function.
Increases (x) Profit (y)
25 204
60 285
105 368
132 384
155 376
172 356
200 318
254 185
290 70
Use the data in the table to answer questions 3-5.
3. Use technology or hand calculations to determine the equation for the quadratic function modeled by the data in the table. Show an image of your final answer. (10 points)
4. Using the equation from question 3, determine the maximum profit. (5 points)
5. Using the equation from question 34, determine how many price increases will cause the smoothie chain to have zero profit. (7 points)
obtuse pebbleBOT
The smoothie chain makes multiple $0.15 increases to the average prices of their...
lapis crest
What like… 4th time is the charm? haha
tawny sail
What like… 4th time is the charm? haha
Let’s say I am selling something to you that I buy for $9
tawny sail
The market price is $16, but i sell it to you for $9.20, I might sell heaps but I need to sell a crap ton to make a good total profit. Similarly if I sell it for $25, I might make a good profit per sale when I sell one but I won’t sell enough for the business to profit overall. So yeah the 4th time the charm thing is just about the right price to maximise sales/profit margin. Let me know when you’re back, if I’m not asleep I’ll help
obtuse pebbleBOT
@lapis crest Has your question been resolved?
obtuse pebbleBOT
@lapis crest Has your question been resolved?
obtuse pebbleBOT
@lapis crest Has your question been resolved?
vague apex
still need help with this?
obtuse pebbleBOT
@lapis crest Has your question been resolved?
vague apex
alright, what do you need help with?
lapis crest
Not too sure yet, I haven’t been able to read anything the last guy said
obtuse pebbleBOT
@lapis crest Has your question been resolved?
obtuse pebbleBOT
@lapis crest Has your question been resolved?
fiery eagle
Let me check
obtuse pebbleBOT
@lapis crest Has your question been resolved?
lapis crest
I haven’t been able to do anything lately
granite eagle
People I hope y’all having a nice day and fun and enjoyment learning math! 😃
solemn osprey
What like… 4th time is the charm? haha
Wdym? Can you clarify what your question/problem is? (Unless you’re having trouble with everything for problems 3,4 and 5)
lost tree
I haven’t been able to do anything lately
well u r gonna have to try something
lapis crest
Been busy with work and everything
lapis crest
Ok I can finally continue on this
lapis crest
Wdym? Can you clarify what your question/problem is? (Unless you’re having troub...
I need help with 3 only haha
4 and 5 I don’t need I just accidentally included them
lapis crest
<@&286206848099549185>
I can finally work
Hey @lost tree are you free to help?
<@&286206848099549185>
fringe lake
The smoothie chain makes multiple $0.15 increases to the average prices of their...
what does that mean
lapis crest
Thats what Im trying to figure out lol
Thats just the information to the question
I only need question 3
I do have to finish this pretty soon
Yep
Nope xD
Im the worst at graphs
Fun fact, both of my algebra 1 and 2 teachers got fired after their first year
Yes yes
Mmmmmmmmmmmhm
I believe so
The middle or something
Highest/lowest point?
I cant remember
132, 384
Cool cool
Alrighty now were getting somewhere
Ope alright you did it for me thank you
Its all good
Not one bit as I have no idea what a symbolizes
Alright
And I need 3 points?
Oh cool
plugging them in now
Ew
-180/11449
Really?
Alright lets see
Uno momento
DUUUUUUUUUDE THANK YOUUUUUUUUU
I THINK ITS RIGHT
Ok so
Now I dont know either
Its going to be off by a little right?
This is what it looks like when I plug in all the points
Yea probably
I have no idea
How do I use the equation for this?
Using the equation from question 3, determine the maximum profit. (5 points)
lapis crest
Crap
lapis crest
Can you guide me through?
lost tree
this is assuming that there is a perfect parabola passing through all these points
if there isnt one you will have to use regression
lost tree
Can you guide me through?
okay pick any three points
lost tree
assuming that
y = ax^2 + bx + c
substitute in those values of x and y in this and find 3 equations
lost tree
okay
lost tree
yes y = ax^2 + bx + c
lapis crest
Ok wonderful
lapis crest
a=-1/25b - 1/625c + 204/625
a=-1/132b - 1/17424c + 8/363
a=-1/290b - 1/84100c + 7/8410
Ok
lost tree
a=-1/25b - 1/625c + 204/625
eq1
lost tree
a=-1/132b - 1/17424c + 8/363
eq2
lost tree
a=-1/290b - 1/84100c + 7/8410
eq3
lapis crest
Mhm
lost tree
u can see that LHS of eq1 and eq2 are the same
lapis crest
LHS?
lost tree
so -1/25b - 1/625c + 204/625 = -1/132b - 1/17424c + 8/363
lapis crest
Ah
lost tree
so -1/25b - 1/625c + 204/625 = -1/132b - 1/17424c + 8/363
that leads u to this
can u simplify this
bring all like terms together
lost tree
So it gave me b = -157/3300c + 276208/29425
okay lets call this eq4
now u can also see that eq2 and eq3 have the same lhs
lapis crest
yea
lost tree
so u can set their rhs's equal to each other
lapis crest
Mhm
lost tree
So it gave me b = -157/3300c + 276208/29425
and find another equation like this
can u do that
lapis crest
For c?
lost tree
for b?
lapis crest
Oh
lost tree
well it doesnt really matter
lost tree
So it gave me b = -157/3300c + 276208/29425
i said b coz u found for b here
lapis crest
Not too sure how to do that
lost tree
can u set the rhs's of eq2 and eq3 equal to each other
lost tree
yeah
u can do this coz their lhs's are the same
like for example, if u have a = b, and c = b, clearly a = c right?
u r doing the same thing here
lapis crest
Yea
lost tree
okay
lost tree
-1/132b - 1/17424c + 8/363 = -1/290b - 1/84100c + 7/8410
now simplify this
lapis crest
b = (7768680 - 16669c)/1512060
lost tree
okay im assuming ur numbers are correct
lost tree
b = (7768680 - 16669c)/1512060
and lets call this one eq5
lapis crest
Ok
lost tree
so now u have two equations eq4 and eq5
lapis crest
Equall them to eachother?
lost tree
in just 2 variables
lost tree
Equall them to eachother?
yes u can do that
lapis crest
Ok
lost tree
coz u have b on the lhs of both of them
lost tree
simplify this and u have a value for c
lost tree
This should help me find c
yes
put that value for c in either eq4 or eq5 and find a value for b
and finally put those values u find for b and c in one of eq1, eq2 or eq3 and find a
lost tree
u cant have 2 c's
lost tree
-157/3300c is this (-157/3300) * c
with c in the numerator?
ig u typed it wrong in ur calculator
lost tree
show me what u r typing in ur calculator
lapis crest
Im really tempted to give up
lost tree
-157/3300c maybe try typing this as -157c/3300
lost tree
this is wrong
lost tree
the 157/3300 thing is correct
lost tree
right
lapis crest
c = 116(110752/448009)
lost tree
,calc 116(110752/448009)
warm shaleBOT
Result:
28.676281056854
ah i see
lapis crest
How do I write that
lost tree
,calc 116 + (110752/448009)
warm shaleBOT
Result:
116.24720931946
,calc (7768680 - 16669(116.24720931946))/1512060
warm shaleBOT
Result:
3.8562988689959
So thats b
lapis crest
a = -1/25b - 1/625c + 204/625
Plug it in
Gets us
a = -1/25(3.8562988689959) - 1/625(116.24720931946) + 204/625
Is that plugged in right?
lost tree
well u want the b's and c's to be in the numerator
what u have written 1/625c there for example is actually (1/625) * c = c/625
lapis crest
So I didnt write it right?
lost tree
a = -3.8562988689959/25 - 116.24720931946/625 + 204/625
warm shaleBOT
Result:
-0.013847489670972
Is that a?
lost tree
Oh thats what I want?
yes
lost tree
Is that a?
yes
lost tree
so y = -0.013847489670972 * x^2 + 3.8562988689959 * x + 116.24720931946
lapis crest
Holy crap
lost tree
Whats the original equation again?
y = ax^2 + bx + c
maybe to see if it works try plugging in a different value for x from ur table
and see if it gives the right y
lapis crest
Its a little off but is that ok?
lost tree
by like a few decimal points ig?
that shud be okay coz we didnt put exact values for a, b, c
lost tree
Result:
```
-0.013847489670972
```
like the decimal points here might just keep going
we just stopped there
lost tree
now to find where the profits are maximized
u differentiate this and set the derivative equal to 0
lost tree
do u know how to differentiate?
lapis crest
Nope
lost tree
dy/dx ?
lapis crest
No
lost tree
so y = -0.013847489670972 * x^2 + 3.8562988689959 \* x + 116.24720931946
oh well in that case ur gonna have to complete the square of this
well actually a quadratic of the form y = ax^2 + bx + c reaches a maximum or minimum when x = -b/2a
do u know what completing the square means?
lost tree
like what we aleady had was ax^2 + bx + c
we can cnvert this to the form A * (x - B)^2 + C
the process of doing that is called completing the square
lapis crest
Ew
lost tree
when u do that, u shud find that A = a, B = -b/2a, and another value for C
lost tree
we can cnvert this to the form A * (x - B)^2 + C
okay can u expand this
lapis crest
No
lost tree
i mean remove the brackets
lapis crest
Oh
I’m not gonna lie my brain is literally fried
Wait the maximum profit would be 384.726 when the number of price increase is 139.242
lost tree
u know how to simplify (x - B)^2 right
lost tree
no
lost tree
say this is the parabola passing thru all the given points
D is the maximum point that u r given
but it is not the maximum that the parabola reaches
lapis crest
I’m not gonna lie my brain is literally fried
And that’s what I have here
I just plugged it into desmos and found the point
lost tree
we can cnvert this to the form A * (x - B)^2 + C
well to find it you can differentiate or u can do this
like if u have it in the form y = A(x - B)^2 + C, what u must notice is that everytime that x is NOT equal to B, (x-B)^2 is a positive quantity
if A is negative number, A * (x - B)^2 is then always a negative number
so A(x-B)^2 + C is always a number less than C, coz A(x-B)^2 is a minus something, and A(x-B)^2 + C is then like C - something
and A(x-B)^2 + C is maximum exactly when x is equal to B
lapis crest
I think... I got it
lost tree
okay so u got y = ax^2 + bx + c
and we want to find A, B, C such that y is also equal to A(x-B)^2 + C
u dont really want to find A and C, if we are interested in finding where the maximum is reached, we must only find B
so what u want is
ax^2 + bx + c = A(x-B)^2 + C
like u want to find A, B, C so that this equality holds
do u get it
lapis crest
Yea I think so
lost tree
okay so can u expand A(x-B)^2 + C
lapis crest
I think
lost tree
try
kindred oasis
.close
woven summit
If we have a relation which is transitive we have the definition:
aRb & bRc => aRc for all a, b and c
What is the definition of anti-transitive relation?
obtuse pebbleBOT
If we have a relation which is transitive we have the definition:
aRb & bRc => a...
royal basin
it appears that antitransitive refers to the property aRb & bRc => NOT(aRc)
woven summit
This is for all a, b and c right?
I have to show that if a relation is anti-transitive R is not symmetric or not antisymmetric
obtuse pebbleBOT
@woven summit Has your question been resolved?
obtuse pebbleBOT
light vortex
obtuse pebbleBOT
light vortex
I got an answer that i dont think makes sense
timid silo
show your steps
warm shaleBOT
StopTheSkap
timid silo
So
You have [
\f{(3^x + 3^{-x})^2}{4} - \f{(3^x - 3^{-x})^2}{4}
]
to consider. Do you agree?
warm shaleBOT
light vortex
yes
timid silo
Okay
So mind telling me how you went about doing
[
(3^x + 3^{-x})^2 - (3^x - 3^{-x})^2
]
warm shaleBOT
timid silo
yeah write it on paper and try it out
timid silo
well
you said it yourself earlier, but apply the difference of squares formula to make the calculations easier
Which would be:
[
a^2 -b^2 = (a-b)(a+b)
]
warm shaleBOT
light vortex
yes
light vortex
im just doing it by hand
timid silo
alright
light vortex
You have \[
\f{(3^x + 3^{-x})^2}{4} - \f{(3^x - 3^{-x})^2}{4}
\]
to consider. D...
from here
i got
$\frac{(2 * 3^{-x})(2 * 3^x)}{4} = 1$
warm shaleBOT
StopTheSkap
light vortex
its the same thing
bc you can cancel the two 2s on top and the 4 on the bottom
and get
$3^x * 3^{-x} = 1$
warm shaleBOT
StopTheSkap
light vortex
right?
light vortex
so unless its 0
is there an answer
actually wait
there are infinite answers
because a^x * a^-x = 1
regardless of what x is
no thats wrong
because you dont add the powersa
nah
have no idea
obtuse pebbleBOT
@light vortex Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
cloud saffron
obtuse pebbleBOT
cloud saffron
Stuck here. I know I need to apply the chain rule I’m pretty sure.
the negative exponents are tripping me up
cloud saffron
-t
ruby path
Also remember to multiply each term with dt/dx
cloud saffron
1/tˆ2 first then?
i came from that step though
the original problem was s(t) = 1/t + 1/tˆ2
short spruce
and your goal is to find s'(t)?
cloud saffron
yes
short spruce
well you simplified it incorrectly
cloud saffron
ok
short spruce
i'm not sure how you arrived to $(-t)^{-2}+(t^2)^{-1}$
warm shaleBOT
a disappointing son
short spruce
because that would be $\frac{1}{-t^2}+\frac{1}{t^2}$
warm shaleBOT
a disappointing son
cloud saffron
i took the rational expressions and made them negative exponents to clear the fraction
short spruce
how did you come up with two squared terms
short spruce
i agree that you should be changing them to negative exponents
short spruce
that i agree with
cloud saffron
and tˆ-2 on the right
short spruce
yes
now it's just power rule
don't get confused by the negative exponents
if you need to, write the power rule out
cloud saffron
ok
short spruce
just remember you're subtracting 1 from the exponent
but it's kinda unlike what you're used to
normally you'd go 4 to 3 or something
but your exponent is negative
cloud saffron
never mind i missed the negative sign in the second photo. the first one should be right
no forgot to move the exponent to the coefficent
coefficient
was not being careful
making stupid mistakes
o wait... using the power rule and multiplying the -1 * -t doesn't change the sign? it's just the coefficient that's moved, correct?
not sure how they came up with 2tˆ-3
i get 2tˆ-2
ah i see i have to multiply tˆ2 by -1 in the exponent first and then -1, correct? That's the only way I see it coming out to 2tˆ-3
.close
frosty valve
how do u find the range of a function
obtuse pebbleBOT
how do u find the range of a function
frosty valve
f(x)=5-7x-2x²
ruby path
Do you know what the range of a function is?
frosty valve
range is the image?
ruby path
Well its every value a function can output
ruby path
f(x)=5-7x-2x²
Do you have a general idea of how this function would look if graphed
frosty valve
no
ruby path
Can you identify what type of function it is?
frosty valve
no
blissful hollow
Whats the domain
frosty valve
Whats the domain
there isn't a given domain
blissful hollow
Yeah sry. Its a polynomial function
blissful hollow
Its a function in the form of the sum of powers of x
More specifically its quadratic
frosty valve
oh ok
blissful hollow
Because the maximum power is two
This particular function has two real roots
So the graph is like a curve that intersects the x axis at two points
And then it extends upwards or downwards indefinitely
frosty valve
does this question require factorisation?
blissful hollow
Not necessarily. If you imagine the graph, it either extends to infinity or - infinity
You have to find the minimum / maximum value
And thats the other end of the interval
frosty valve
i haven't learnt anything abt infinites yet
blissful hollow
Have you learnt differentiation?
frosty valve
no
blissful hollow
i did write it in the form p-2(x-q)² is it needed for this question?
Ah ok. In that case you can do this
frosty valve
11.125-2(x+2.25)²
blissful hollow
Y<=11.125 in that case
frosty valve
how do i find out that this is the answer
frosty valve
Y<=11.125 in that case
and the answer in my book shows x instead of y
blissful hollow
Is the question find out the range?
frosty valve
what answer does your book give?
x<=11.125
blissful hollow
so basically if you have an eqn of the form a(x-h)^2, the minimum / max value = 0 when x = h
because the square is always positive
so it either always positive or negative depending on the value of a
frosty valve
so basically if you have an eqn of the form a(x-h)^2, the minimum / max value = ...
what's h
blissful hollow
h is just some number written as a variable. In your case its 2.25
frosty valve
oh
blissful hollow
when you have an additional k (in your case 11.25) added to the equation, all the values shift by that amount
so your minimum / maximum becomes k
thats why you can say that this equation gives values >=k or <=k
in other words, your range
frosty valve
does this apply to other questions as well
blissful hollow
if you have an equation and you can bring it to the form a(x-h)^2 + k, then yes.
frosty valve
alr ty
obtuse pebbleBOT
@frosty valve Has your question been resolved?
ruby path
😔
timid silo
just
tawny bobcat
did i do smt wrong?
timid silo
go to a new a channel
trail cloak
Open a new channel
ruby path
Lol
high lily
you deleted the original message
tawny bobcat
okk
timid silo
its not that, you deleted your original message you posted here. Which results in the closing of your channel
obtuse pebbleBOT
Available help channel!
half quartz
Q: Given that: (m-3)x^2-(2m+2)x+61-9m = 0.
To what range of values can m satisfy the condition: r1*r2 > 8?
I got to the answer: m < 5
obtuse pebbleBOT
Q: Given that: (m-3)x^2-(2m+2)x+61-9m = 0.
To what range of values can m satisfy...
half quartz
But it isn't the right answer
high lily
show work
half quartz
Using Vieta's formula: 61-9m / m-3 > 8 ---> m < 5
supple granite
seems like you just multiplied m-3 on both sides
you can't do that unless you know for sure that m-3 is positive or negative
high lily
show everything you did between applying the initial prod of rots to the final result
half quartz
seems like you just multiplied m-3 on both sides
you can't do that unless you kn...
Could you please explain? I'm not sure I'm familiar with the concept
supple granite
for inequalities, if you multiply a positive value, the inequality sign stays the same, but if you multiply a negative value, the inequality sign switches
so you can't just assume that m-3 is positive and multiple it on both sides
half quartz
ohh
supple granite
either you split the cases into m-3>0 and m-3<0
or you graph (61-9m)/(m-3)
half quartz
high lily
or you can multiply both sides by (m-3)^2; a non negative value
and then solve the resultant quadratic
supple granite
yeah that's probably quicker
half quartz
Could you demonstrate using a very simple example, just so I could grasp the concept?
So far I've been solving inequalities like regular equations. I did know, however, that dividing by a negative number flips the sign though
supple granite
also, forgot to mention, but you probably should do the discriminant>0 thing since it has two roots
supple granite
Could you demonstrate using a very simple example, just so I could grasp the con...
let's say you're trying to solve this inequality
you can't just multiply both sides by m since you don't know whether m is positive or negative
so instead, you multiple m^2, which is always a positive number (m^2 can't be 0 since the denominator can't be 0)
so if you multiply m^2 on both sides you get
m(2m-1)>3m^2
2m^2-m > 3m^2
m^2+m>0
m(m+1)>0
m>0 or m<-1
half quartz
hmm, so you're saying that divison by a negative number always flips the sign regardless of if it's done only on one side of the inequation?
err not sure I understood
half quartz
You can't just multiply both sides by m since you don't know whether m is positive or negative
this 😅
If I were to attempt to solve this inequality (the way I understand it), I would've multiplied both sides by m to cancel the division
It's multiplication, not divsion 🤔
grizzled shore
you could... multiply by something that's always positive!
supple granite
If I were to attempt to solve this inequality (the way I understand it), I would...
you can't multiply an unknown if you don't whether if it's positive or negative
grizzled shore
what can you do to m to make sure it's positive... 🤔
supple granite
instead, you can choose to multiply the square of the denom, which you know for sure is always positive
half quartz
How come it's possible to do this in an equation, then?
supple granite
should I give you another example?
half quartz
Hold on, wouldn't it be entirely plausible to solve it this way if it were an equation though?
supple granite
whether you multiply m or not doesn't matter if it's an equation, not an inequality
half quartz
ah, I see..
So, please explain why
Sorry, I think I'm just missing some crucial information about inequalities that are hindering my understanding haha
supple granite
for an equation, you can multiply anything on both sides
for an inequality, you need to be cautious of what you are multiplying by, since you need to consider whether to switch the inequality sign or not
half quartz
I learned this only applies to division with negative numbers.. like /(-1) etc
So there are more exceptions?
I didn't know that
supple granite
the inequality sign switches when you multiply a negative number
supple granite
I learned this only applies to division with negative numbers.. like /(-1) etc
yeah
half quartz
Pfft well I didn't know that
supple granite
take this for example
half quartz
good to know.
supple granite
on the top equation, you can multiply -2 on both sides without considering anything
however, if you want to multiply -2 on the bottom inequality, you need to switch the inequality sign
so can you tell me what the bottom one would look like if you multiply -2 on both sides?
half quartz
x > -6 ? and so the correct solution is x < -6?
obtuse pebbleBOT
@half quartz Has your question been resolved?
half quartz
After more googling I finally understood. The more I learn, the more I realize how bad my high school teachers were ... thanks Jay, Frosst and Ramonov!
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cinder quest
Can someone help me
kind hawk
just ask. but in a different channel now. this one will close
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
All I need is a point in the right direction idk how to find X for this specific situation
If anyone could help that be great
gleaming ridge
,rotate
warm shaleBOT
gleaming ridge
Do you know how to find mean of data points
Hint: mean is same thing as average
@timid silo
timid silo
Yea but not when the x is alone or without equal sign
gleaming ridge
x is just placeholder for a number so treat x as a number,
obtuse pebbleBOT
@timid silo Has your question been resolved?
glass tartan
can someone help me to prove why is this true?
obtuse pebbleBOT
can someone help me to prove why is this true?
teal turret
fierce lagoon
Simplify the denominator as (a-b)/x
alpine raven
Simplify the denominator as (a-b)/x
no need
fierce lagoon
I mean yeah
alpine raven
^
fierce lagoon
That too I guess
fierce lagoon
My thought was the $\frac{\frac{a}{b}}{\frac cb} = \frac{a}{c}$ identity
warm shaleBOT
Umbraleviathan
obtuse pebbleBOT
@glass tartan Has your question been resolved?
glass tartan
i thought it was wrong because the denominator should be (a-b)/x
but i got it, thank you
timid silo
Please help me in solving this problem
obtuse pebbleBOT
Please help me in solving this problem
snow latch
Lol
obtuse pebbleBOT
@timid silo Has your question been resolved?
tardy epoch
Please help me in solving this problem
Did you try changing to polar coordinates
timid silo
Yes but it was not working
obtuse pebbleBOT
@timid silo Has your question been resolved?
next lantern
obtuse pebbleBOT
next lantern
could anyone help me through this proof by contradiction
wrong image >_<
i initially tried to start with letting x y and z be odd numbers
which i thought was the proper first step but i guess not 🤷
this ended up being the correct answer, but i thought in proof by contradiction we always assumed the first part is true, and just negate the second part of it
so i would actually be working with
no odd integer can be expressed as the sum of three odd integers
and then show it can
is my thinking wrong?
obtuse pebbleBOT
@next lantern Has your question been resolved?
radiant prairie
So for part a, I multiplied matrix A by vector b using the dot product to get <3, 12, 9, 19>. Is that it? I'm confused by what it means by "as a linear combination of the columns of A".
obtuse pebbleBOT
So for part a, I multiplied matrix A by vector b using the dot product to get <3...
gleaming ridge
Well, it's a bit hard to explain but Ab is basically the columns of A with coefficients of b
say Ai is the ith column of A and bi is the ith entry then
Ab = A1b1 + A2b2 + A3b3
I wish I could explain it more properly but I hope this helps
You can try writing the Ab in an expanded way and see the pattern
Or maybe take a general matrix A and b
@radiant prairie
radiant prairie
Ab = A1b1 + A2b2 + A3b3
So Ab = 1<2, 7, -2, 0> + 3<3, 1, 3, 5> + 2<-4, 1, 1, 2>?
gleaming ridge
yes
radiant prairie
=<2, 7, -2, 0> + <9, 3, 9, 15> + <-8, 2, 2, 4>
=<3, 12, 9, 19> would be my final answer? Assuming I added right
gleaming ridge
You just have to write them as linear combinations
radiant prairie
How do you do that
gleaming ridge
So Ab = 1<2, 7, -2, 0> + 3<3, 1, 3, 5> + 2<-4, 1, 1, 2>?
like that
just use whatever notation your text uses for column
radiant prairie
So for part a, I multiplied matrix A by vector b using the dot product to get <3...
Oh okay. Then for part b, would you just dot product like I did here?
gleaming ridge
Yeah it would be the ordinary matrix multiplication written as dot product
radiant prairie
Ok thank you!
timid silo
bro waited 0 seconds to tag
gleaming ridge
lamfao that was quick
warped fulcrum
Guess it's useful for them to know why it equals that 🤔
sharp pecan
.close
obtuse pebbleBOT
sharp pecan
it is
timid silo
23*2/100
gleaming ridge
next time just use calculator
warped fulcrum
Perhaps to confirm?
warped fulcrum
Yeah they should also read rules perhaps 😂
obtuse pebbleBOT
Available help channel!
timid silo
https://www.wired.com/2009/09/how-high-does-a-bullet-go/ so I want to replicate this article but I don't know how to connect these calculations together
obtuse pebbleBOT
https://www.wired.com/2009/09/how-high-does-a-bullet-go/ so I want to replicate ...
@timid silo Has your question been resolved?
burnt ore
how to calculate area of triangle
burnt ore
r is 6cm and theta is 0.55 radian
please help!
<@&286206848099549185>
please
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waxen sonnet
obtuse pebbleBOT
wanton isle
Looks good to me.
sour dirge
help 7 25.4 mg/mm3 a gr/m3
molten cosmos
obtuse pebbleBOT
obtuse pebbleBOT
@molten cosmos Has your question been resolved?
molten cosmos
<@&286206848099549185>
obtuse pebbleBOT
@molten cosmos Has your question been resolved?
deep ravine
What did i do wrong?
obtuse pebbleBOT
What did i do wrong?
timid silo
hey guys i just wanna solve this for my friend
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ancient fiber
How would I factor this polynomal
obtuse pebbleBOT
How would I factor this polynomal
daring rock
At a glance it looks like you could factor in groups if you rearrange a couple terms
ancient fiber
alr lemme try that
obtuse pebbleBOT
@ancient fiber Has your question been resolved?
ancient fiber
At a glance it looks like you could factor in groups if you rearrange a couple t...
im confused. What terms do I rearrenge them in?
daring rock
Notice that three terms have a factor of -y^3
ancient fiber
yea I factors those terms got -y^3(x+5)^2
ancient fiber
yea thats my mistake lemme fix it and I will get back to you with answer?
daring rock
sure
ancient fiber
I finished. Is this correct?. (x+5)^2(2x-y)(4x^2+2xy+y^2)
ancient fiber
thanks
daring rock
np
obtuse pebbleBOT
@ancient fiber Has your question been resolved?
wind magnet
Please help me answer these problems, these were my past worksheets that i forgot to answer. I really need to review for the test so please help me. Thank you.
obtuse pebbleBOT
Please help me answer these problems, these were my past worksheets that i forgo...
wind magnet
lemme find my worksheet
bold bane
For 5, try to disprove any of the 3 statements to eliminate A,B,C, or D.
delicate kettle
For 5, try to disprove any of the 3 statements to eliminate A,B,C, or D.
i think the answer is B
im not sure
im trying to compute
it
whats ur solution
wind magnet
there different
angles
so yea
1 is wrong
@bold bane 1 is wrong right?
<@&286206848099549185>
wind magnet
i think B is correct
bold bane
You just said I is not true so how could B be the right answer. 🤔
Is the second statement true or false?
bold bane
So the first and second statement are not true. What about the third statement?
wind magnet
correct
bold bane
So which answer should you pick?
wind magnet
C
bold bane
C says the first and third statement are true.
But you already said the first statement is false.
bold bane
Yes.
bold bane
wind magnet
uhuh
bold bane
Given that ST and SR is of equal length, what can you say about the angles STR and SRT?
delicate kettle
there also equal
bold bane
So if RST is equal to 80 degrees, what do STR and SRT equal?
wind magnet
160
bold bane
What is the sum of the angles in a triangle?
bold bane
The sum of the angles in a triangle is 180 degrees.
wind magnet
mhm
bold bane
You are given RST as 80 degrees, what must STR and SRT sum to?
wind magnet
50
bold bane
So you are trying to find angle QRS. You have one part of the angle. You now need to find the other part of that angle.
How could you do that?
wind magnet
ok
so
180-50
so that
its
130
on R
then U is 130
also
Q and T is 50
U and R is 130
right?
bold bane
Wrong vertices but you have the correct angle measures.
bold bane
wind magnet
no
bold bane
The opposite angles in a parallelogram are equal by definition of a parallelogram.
So Q and T are equal and U and R are equal.
We can use that fact to find the angle QRT.
Which you can add to angle SRT to find angle QRS.
wind magnet
Which you can add to angle SRT to find angle QRS.
whats the answer tho
bold bane
We don't give out answers on here. We try to teach you how to solve the problem yourself.
You have all the information you need.
wind magnet
You have all the information you need.
okay so the answer is 130
right?
because
Q is 130 leading to S
@bold bane
obtuse pebbleBOT
https://discord.com/channels/268882317391429632/1072343049843257494
valid palm
Hello
I need some helo with Transformations
We have had 3 and My schoolmates sent me this peace of paper
I’ve been sick and Don’t understand
The notation eay of it
If it’s described in words, it’s really simple, but like how can you tell when the function will be stretched or the other way around
This is what I got from them, but I can’t really do anything
<@&286206848099549185>
Please help me, I’m sooo desperate
Yes our math teacher is quite special indeed
But that’s not the point
Look at the exercises please
valid palm
The formula for vertex?
foggy idol
Bro
valid palm
Like I mean I know the Discriminant and that type of studd
valid palm
Yea, but like I just don’t really understand translations in general
valid palm
Vertex form is y=a(x-h)^2+k
yup that's understood
foggy idol
And you have the answer
valid palm
if We have the first excersise
y=x2+5, what does the +5 do to you function
like it either streches
or the opposite of it and I just don't know these kind of rules
valid palm
<@&286206848099549185> can you help me with this peace of paper, please
Can we start with the 1st one?
y=x2+5 and what does the +5 do in this case
zinc falcon
@valid palm +5 will shift the graph 5 points upward on the y-axis
zinc falcon
Yeah but how can we do that, can you please guide
valid palm
I made it so anyone with link can edit the page
zinc falcon
This will be the new graph
zinc falcon
Ok
obtuse pebbleBOT
@valid palm Has your question been resolved?
wind patio
im confused on how solve more
i am trying ACD ~ BCE through ~SAS
i have the one side, but unless theres a theorem that proves the bottom section proportional, it wont work
obtuse pebbleBOT
im confused on how solve more
i am trying ACD ~ BCE through ~SAS
i have the one ...
true granite
im confused on how solve more
i am trying ACD ~ BCE through ~SAS
i have the one ...
SAS doesn’t work here, since it’s asking for similarity, not congruency
SAS proves congruency
wind patio
no but theres a SAS similarity theorem
my geo teacher taught us
it requires proportional sides
true granite
yeah, congruent triangles are always similar, but similar triangles aren’t always congruent
wind patio
and congruent angles
true granite
oh yeah that works
