math-help

[atomic gazelle]

good luck bro

[left knoll]

Thank you

[dense fog]

@drowsy matrix

[granite kraken]

i have 23 days until my SAT

idk what the hell to do i need to get a 1500 or above

does anyone have any tips

[swift lake]

how and why is this equal to the bottom screenshot

[strange rampart]

using this property if u equate lhs by multiplying by 2 and dividing by 2

U will get 2logrootx/2log2 which is the same as rhs which is logx/log4

[left knoll]

can smn pls tell me if my limit is correct?

[copper heart]

Please help me with this 6,7,8

[maiden epoch]

How is there a -1 in -2? if we take out the module we're getting 1/x-3( x>0) and -(1/x-3) (x<=0), and the graph on the left is -(1/x-3), if we put -2 instead of x we won't get a -1, so how's there a -1 in x=-2?

[supple island]

if you "take out" the module it's 1/((-x)-3) and for x=-2 that's 1/(2-3) =-1

[tawdry bramble]

Ik its basic but I’ve always struggled with slope can anyone help?

[cosmic kestrel]

how much he drank at 0 seconds? He drank nothing, 0, so make a dot in (0,0) point of your graph. How much he drank at 1 seconds? 5 milliliters, so make a dot in point (1,5) and etc...

[maiden epoch]

I just understood that it’s gonna be -(-2) and not just -2, guess I just was too tired yday, ty anyway!

[bold atlas]

how to solve, a inequality involving a quadratic equation whose D<0

x^2 -x + 4> 0

[cosmic kestrel]

if d<0 then your parabola never equals zero, it means it is all above zero or all under zero, you have just to put any value (for example x=0) and then see that your parabola is always positive

[bold atlas]

like it would be a upward open parabola and >0 for every value of x
and if the inquality would have been x^2 - x + 4 < 0 , then x has no solutions, am i right?

[cosmic kestrel]

doesn't care if parabola is upward or downward. If D<0 then x has no solutions. And then, starting from this fact, we can find out that this parabola is always positive. If it is always positive then there is no way it can be downward or otherwise it will fall to -infinity, crossing y=0 on it's way

[supple island]

Np

[sweet karma]

now i can see it better and it's correct

[copper heart]

Help please

[tacit vine]

Who knows how to solve irrational equations

[left knoll]

I’m not to that level but what are these a little bit of info would help

[tacit vine]

Nvm, I know how to do them now

[quaint talon]

Inexpensive graphing calculator recommendations?

[swift lake]

sorry this is a very basic question but i can calculate the first value of x for 1(a) but how would i go about finding the second one w/o graphing it

[left knoll]

sjfjdjf lessgoo thanks<3

[supple island]

sinx=1 when x=pi/2 so pi/4 is the obvious answer, but since we have 2x we also have to consider that the period is halved, sinx=1 is true also for x=5/2 pi, this isn't in [0,2pi] for sinx, but we have sin2x so x=5/4 pi is the other one

[sand python]

thank u <3

[rain solstice]

y=0 not y=2

but yeah true

[left knoll]

jfhjfh not its y=2 cuz f(x) is 2+ the limit i calculated

[left knoll]

so in the end the solution of the limit is 2

[rain solstice]

lim f(x)=0 u did it ur self why u wrote 2?

its 0

[left knoll]

the og function is 2+8(x-2)²(ex-4)/x²

to make the calculus ez i only calculed the part after 2

and its 0

so 2+0 = 2

[rain solstice]

ooh i thought the og one is the one at the top

so yeah its true

ur major is physics and chemistry science right?

[left knoll]

yeppp

wait ur moroccan?

[rain solstice]

yep

[left knoll]

yours was pc science or maths science?

[rain solstice]

pc

[left knoll]

oh nicee

is someone good w the drawing of the curve (of a function) pls ToT

im struggling w this

[copper heart]

Guys anyone can solve this

[rain solstice]

this the full playlist i watched i used it will help u + its both french and arabic and its short 10 videos and all of them are under 5 min
https://www.youtube.com/watch?v=4chVEDDbv7A&list=PLd3kGW4dP7kN_Y9ialGh6xSOHzEDe0iHY&ab_channel=profAbderrahimmaths

watch from 1 to 10 alright?

[left knoll]

OMG DUDE THANK U SM

I WILL

[rain solstice]

np

[lilac vigil]

How does one become better at math contests?

[left knoll]

practice

study for 6h+ a day

thats what i personally did

[lilac vigil]

I see

[lilac vigil]

about how long before the contest did you start studying roughly?

[left knoll]

tbh i just started 2 weeks ago

today i revised 9h30min im kinda proud

[grizzled dust]

yo can someone check over my answers to see if im right

[rain solstice]

can i ask u how u can study that much while fasting

[left knoll]

man i just resist

i have no choice but to tryhard

when i have classes i study like ~4h a day

but during weekends its 8h+

i wake at 7am and stay till 10 pm

but yeah now ive been studying 7h and ngl i feel sooo tired and hungry

[rain solstice]

yeah i think that push you to try harder thx for the advice

[ancient pine]

bicycle go to A to B with V = 20 km/h ,after 1 hour a car go to A to b ,know S A to B = 250 (km) and after 1,5 they meet each other . V car = ?(km/h) ?

[rain solstice]

could u rewrite it its a little bit confusing

[ancient pine]

a wat make u confus?

[rain solstice]

know S A to B = 250 (km) and after 1,5 they meet each other . V car = ?(km/h) ?
this part

[ancient pine]

distant A to B is 250 ( km) and after 1,5 h bicycle and car meet each other:

need to find out what is V car = ?(km/h)

[rain solstice]

Let's first calculate the distance the bicycle travels in 1 hour:
distance = speed x time = 20 km/h x 1 h = 20 km

[ancient pine]

it seems to be
error title
right?:

i mean can t find the V car

[rain solstice]

Now let's calculate the remaining distance between A and B that the car needs to cover after 1 hour:
distance = total distance - distance covered by the bicycle = 250 km - 20 km = 230 km
and distance covered by the car = V car x 1.5
and we also know distance covered by the car = 230 km

Now we can combine the two equations:
V car x 1.5 = 230
Simplifying this equation, we get:
V car = 230 / 1.5
V car = 153.33 km/h (rounded to two decimal places)
So the speed of the car is approximately 153.33 km/h

[ancient pine]

hm ok:

[cosmic kestrel]

how to find x here?
3sin(a)cosx-cos(a)sin(x)-4cos(a)=3sqrt(3)
any tips

bcs I can't get anything beautiful

[rain solstice]

seek help from chat gpt

i would like to help if i was into trigonometry

i typed it and he stopped cuz its too long long

[pearl iris]

This is simple v s t physics but i havent studied this field for 4 years

[left knoll]

how can i get better at maths? i work really hard but it just doesn't come naturally to me, and i get a good mark for me, although always less than most in my class. what can i do in order to naturally improve

[cosmic kestrel]

After some time working with pupils I can say that:

1. don't ever just read or remember solutions, it's ok and even necessary to think for 1-2 hours(days) about problem and then ask smb for clue not whole solution
2. solving one complex problem urself is more valuable than 100 easier ones, don't think that quantity of solved problems will ever help you
3. be critical to knowledge you get in school. Question urself why 1+1=2 or exp(ia)=cos(a)+isin(a)
4. if you are preparing for some exam and have a lot of time it's good idea to train with one step harder questions that exam usually has. After solving hard problems you'll feel exam questions very easy.

[left knoll]

thank you so much🙏🙏 i really appreciate it

[left knoll]

np !! :)

[static quest]

[maiden epoch]

How do we get |x| graph if they say that final result is just x? When sqrt(x^2) supposed to be |x|

[nimble wedge]

when something like that is a power, then the power and 1/2 are multiplied and it turns out that x^2/2 is x^1

[nimble wedge]

the rule in scaling is that the steps are multiplied with each other

[maiden epoch]

But we can’t get that graph with y=x

When with sqrt(x^2) we can

D(f) is R{0}, but at the same time there can’t be a negative value under the rute

[nimble wedge]

can be a negative value, because one value is always positive and the other negative

[maiden epoch]

Yeah but when y=x they will be same -2;-2, 2;2

So I’m yet to understand how they’re getting |x| graph with y=x function

[nimble wedge]

because x is equal to 0 and then by definition -x is equal to 0, that's why the graph starts from 0 and goes to infinity

[maiden epoch]

There can’t be a 0 value

We can’t divide by 0

[nimble wedge]

no, I wouldn't, because they only look at xa, not x^2

[maiden epoch]

0 doesn’t exist

[nimble wedge]

it cannot be divided by zero, yes, but it cannot also be x=1 and -x=1, because the graph would be deformed

[maiden epoch]

I still don’t get it, the only explanation for me is that there should be y=|x| and not just x, then it makes sense

[nimble wedge]

no, it shouldn't exist, because even if you write that, it's the same as ix if you just wrote it

[maiden epoch]

Why it shouldn’t exist? sqrt(x^2) is basically a module

[nimble wedge]

but it's the same for you when you write x or |x|.

[maiden epoch]

If it’s y=x graph will exist only in the right part, as the values under the rute can’t be negative

[maiden epoch]

It’s not

|x| makes every y value positive

with “x” when x will be -2 y will also be -2, there’s no magic way it’ll change its sign to +

That’s how it’ll look with y=x

Answer in the book says it should be “a half-line without a starting point”

[cerulean elbow]

Is it right?

[left knoll]

does anyone can help me with a physics assigment?

[cosmic kestrel]

I can

if it's not big, otherwise better after 8 hours of my sleep

but definitely better to just send assignment here and not to wait if somebody would make you so much attention several times

[left knoll]

i nedd to know the values of the ammeter and voltmeter

[left knoll]

okay :V

thanks for helping tho

[cosmic kestrel]

can you find the equivalent resistance of the whole circuit?

[left knoll]

to be honest i dont even know the subject, i zooned out in class for a whole trimester

[cosmic kestrel]

watch first 11 videos if you are serious person https://youtube.com/playlist?list=PL0o_zxa4K1BV9E-N8tSExU1djL6slnjbL
otherwise if you just need the answer you need to find total resistance (10 ohms) using parallel and series connection formulas. Find current then using Ohms law (12V/10 Ohms=1.2 A) and then find out that ammeter will show (1.2/2=0.6 Amperes) and Voltmeter will show (1.2A*5 Ohms=6 Volts). You can use this simulation https://phet.colorado.edu/en/simulations/circuit-construction-kit-dc-virtual-lab to solve such a problems

[left knoll]

thanks!

[frozen skiff]

Does anyone know a good source (with examples) for learning about graphing functions using transformations

[cosmic kestrel]

google desmos if I understand you correctly

[frozen skiff]

thx

[cosmic kestrel]

I can also recommend some sources for learning about graphing functions using transformations.

1. Khan Academy: This online learning platform offers free video lessons and practice exercises on graphing functions using transformations. The lessons include examples of how to graph linear, absolute value, quadratic, square root, and cubic functions using translations, reflections, and stretches.

2. Mathisfun.com: This website provides clear explanations and interactive examples of graphing functions using transformations, including translations, reflections, and dilations. The website also includes step-by-step instructions for how to graph linear, quadratic, cubic, and reciprocal functions using transformations.

3. Purplemath.com: This website offers a detailed guide to graphing functions using transformations, including translations, reflections, and vertical and horizontal stretches and compressions. The guide includes examples of how to graph exponential, logarithmic, and trigonometric functions using transformations.

4. SparkNotes: This website provides a straightforward guide to graphing functions using transformations, including translations, reflections, and stretches. The guide includes examples of how to graph linear, quadratic, exponential, and logarithmic functions using transformations.

I hope this helps!

[brave wing]

How to find the max value ?

[orchid horizon]

The answer would be 0 ≤ m ≤ ∞

[alpine mauve]

why does the limit change to 0 to pi/2

[orchid horizon]

[That limit represent the theta as shown in the solution.]
The angle "theta" represents the angle between the positive x-axis and the line from the origin to the point of integration. Since we are integrating over the upper half of the circle, the angle "theta" varies from 0 to pi/2.

Note: In a double integral in polar coordinates, the first integral is taken with respect to the angle variable "theta", and the second integral is taken with respect to the radial variable "r".

[brave wing]

I thought the same but the answer is opt A

[orchid horizon]

oh sorry

[maiden epoch]

Why does sinx has period of just “2pi” but if it’s sin(x)=0 it’ll be “2kpi”

[latent tinsel]

hello, is anyone good with ANOVA?

[cosmic kestrel]

Distance between zeros is period=2pi. But every zero has coordinate 2kpi

[maiden epoch]

so for 3,14 for example it'll be this "pi"?

[cosmic kestrel]

what is it?

period is distance between two repeating points

do you see this distance in the graph?

[maiden epoch]

0 and 3,14 is the first distance

[left knoll]

can someone help in qst 3 pls?

[cosmic kestrel]

no, graph is different in 0 and 3.14 points. In point 0 it goes up in point 3.14 it goes down. Think again

[maiden epoch]

so pi and 2pi will be the first distance? then 2pi and 3pi?

[cosmic kestrel]

why pi

let's look at point 0 again

[cosmic kestrel]

where the same picture repeats

[cosmic kestrel]

no, graph is different in 0 and 3.14 points. In point 0 it goes up in point 3.14 it goes down.

[cosmic kestrel]

so in points 0 and 2pi graph behaves the same. That's why period is 2pi

[maiden epoch]

so if in point 3,14 it goes down, next time it'll go down will be 3pi?

[cosmic kestrel]

and distance between those points is 2pi

this distance is called "period"

[maiden epoch]

got it now, but still don't get the matter with "k"

[cosmic kestrel]

do you see in which points sin=0?

pi, 2pi, 3pi, 4pi, 5pi and etc

to write it in general, they say kpi where k is whole number

[maiden epoch]

I was solving 8.a problem, and there it said that x!= 3pi/2 (which I get why, because in -1 it’ll be 3pi/2) and then +2kpi

and I don’t get what’s the “k” and why its there

[maiden epoch]

So 3,14, 6,28, etc. etc.?

[cosmic kestrel]

yes

[cosmic kestrel]

they write it because shifting by 2pi doesn't change your graph

as we already discussed

[maiden epoch]

Also the thing is that if I’ll put any number in that x!= here I’ll get 0

[cosmic kestrel]

and even if you shift two times nothing will change

[cosmic kestrel]

why any? k is whole not any at all

k can't be 3/4

[maiden epoch]

any whole number* my bad

[cosmic kestrel]

so, does moving by 2pi change this graph somehow?

[maiden epoch]

Still be 0 if be moved by 2pi

[cosmic kestrel]

if I move two times by 2pi?

[maiden epoch]

still 0

[cosmic kestrel]

depends on what point are we talking

but nothing will change

if we move by 2kpi

that's why any solutions for problems we write with assumption that we can change it k times by 2pi (or +2kpi)

[maiden epoch]

But what if I would’ve wrote just x!=3pi/2, without adding “+2kpi”?

[cosmic kestrel]

чел

это будет значить что ты не все ответы учёл

потому что 3pi/2+2pi например тоже подходит ведь как ответ

сдвиг на 2pi же не меняет ничего а значит тоже удовлетворяет уравнению

you got it?

[maiden epoch]

Вроде понял

[cosmic kestrel]

надо не вроде а полностью

синусы и косинусы это функции от углов. Если ты провернешь угол на 360°=2pi радиан, то это будет тот же самый угол и ничего не поменяется

[maiden epoch]

Ну меня с толку сбило «k» которое там появилось

[cosmic kestrel]

сколько раз я могу поворачивать угол на 360 градусов? Сколько угодно. Поэтому пишут k раз

[latent tinsel]

can anyone help me with this?

[left knoll]

thank u smsmms<3

[reef prairie]

can someone explain to me these 2 steps?

[onyx void]

How is the shaded area calculated?

[lilac vigil]

Hard question

[simple knoll]

any1 good at 12th math care to help me for 30 mins ? i got 25 questions

[cosmic kestrel]

draw a height in the center and then you'll get a lot of rectangular triangles

[cosmic kestrel]

1. f(1/3×0)=1/2×f(0) so f(0)=0
2. f(1-0)=1-f(0)=1
3. f(1/3)=1/2×f(1)=1/2
4. f(2/3)=1-1/2=1/2
5. f(1/9)=1/2×f(1/3)=1/4
6. f(1/3^n)=1/2^n
7. f(1/2)=1-f(1/2) so f(1/2)=1/2
8. f(1/6)=1/2×f(1/2)=1/4
9. f(5/6)=1-f(1/6)=3/4
10. f(8/9)=1-f(1/9)=3/4
    As we know:
    5/6<6/7<8/9
    and also
    3/4=f(5/6)<=f(6/7)<=f(8/9)=3/4
    that's why f(6/7)=3/4

[left knoll]

bro how r u this good at maths

[cosmic kestrel]

you will be taught everything in high school and uni

I am just old

[left knoll]

hes teacher

[minor plume]

How would you solve B) ?

[left knoll]

How can I cram calculus?

I don't know anything

[surreal flint]

https://quicklatex.com/cache3/30/ql_6e6eccd5550569d55621ae3c65d9fb30_l3.png

just put t=sinx back

[left knoll]

@limpid scaffold what am i looking at

[limpid scaffold]

Thats integrals

Part of it at least

U dont have book u study by?

[left knoll]

I do need to learn derivatives to do them ryt?

[left knoll]

yes

[limpid scaffold]

U need to memorize few rules

[limpid scaffold]

Try finding them there

[left knoll]

this was given by teacher as what to expect for test

[limpid scaffold]

U cant borrow ur friends notes?

[left knoll]

I have notes

I just don't understand anything

[limpid scaffold]

Try understanding it by looking at same examples in book

Like which rule was it calculated with

Chapter 5 is integrals

[limpid scaffold]

https://www.fd.cvut.cz/department/k611/pedagog/K611GM_A_soubory/GMliteratura_soubory/Stewart_Calculus_6ed.pdf

Id sent u my notes but they arent in english 🥲

[scarlet umbra]

Hi

Can someone tell me if this is an improper fraction or not?

nvm i figured it out thank u

[cosmic kestrel]

you should urgently find calculus lessons in YouTube or other places and train yourself to pass graduate exams and etc. Also if you need a precise study plan or list of knowledge sources you can use chatgpt for an advice

[left knoll]

I have made zero progress

Just sunday remaining now

[cosmic kestrel]

what prevents you from studying?

[cosmic kestrel]

until what

[left knoll]

I watched lectures I don't understand

Test on monday

[cosmic kestrel]

do you have program of the test?

[left knoll]

and I can't watch full playlist too they are hour long physically impossible

[left knoll]

wdym

[cosmic kestrel]

list of topics the test requires to know or problem examples

[cosmic kestrel]

better to study something than nothing

don't be upset and just look what you can and what you have to do in this situation

[left knoll]

@cosmic kestrel given by teacher

can i skip derivatives and just learn integrals

or are they connected

[cosmic kestrel]

yeah, integral is the opposite of derivative

you can try to learn formulas but I think better to learn derivatives

[left knoll]

i just have single day

[cosmic kestrel]

also complex numbers in the last part of file are easy to study

[left knoll]

only till q5 co and if

[cosmic kestrel]

it depends on you really

I don't know maybe you can't add numbers then day is definitely not enough

[left knoll]

huh

resource recommendation?

[cosmic kestrel]

If you're having trouble understanding derivatives, don't worry, you're not alone. Here are some of the easiest resources to learn derivatives from:

1. Khan Academy: This is a great resource for learning any math concept, and their calculus section is excellent. The videos are easy to understand, and the website includes interactive exercises that allow you to practice your skills and track your progress.

2. Mathway: This website provides step-by-step solutions to many calculus problems, including derivatives. It's a great tool for practicing and checking your work.

3. Derivative Calculus by MIT OpenCourseWare: This is a free resource that provides detailed explanations of derivatives, along with examples to help reinforce the concepts.

4. Paul's Online Math Notes: This is a comprehensive resource that covers all topics in calculus, including derivatives. The explanations are detailed and easy to understand, and there are plenty of practice problems to reinforce the concepts.

5. YouTube: Videos can be an excellent tool to help clarify concepts you're struggling with. Search for "derivatives" on YouTube, and you'll find plenty of great channels, such as The Organic Chemistry Tutor, Khan Academy, and PatrickJMT, to name a few.

Remember to take your time and practice regularly. Try to understand each concept before moving on to the next. If you're still struggling, don't hesitate to reach out to a tutor or teacher for extra help.

it's not that bad idea to try rewriting the test if you don't know anything. If it's very important like it threatens you by expulsion, you can try to simulate your sickness

[left knoll]

[cosmic kestrel]

everything will be ok, especially if you make right conclusions from this situation to prevent similar ones in future

[left knoll]

Hopefully

[cosmic kestrel]

try to watch some videos about derivatives and ask here if you don't understand some specific moment

or you can dm me with questions but I don't guarantee that will answer instantly

[vapid sedge]

I know how to prove isosceles, but im too lazy. Hint - look at the parallel a ,b and all the angles they make with lines

[fringe moss]

Pls help 25

[wise crown]

A and B together can do a piece of work in 10 days, B and C together can do it in 15 days while C and A together can do it in 20 days. They work together for 8 days. C alone will complete the remaining work in?

[cosmic kestrel]

1. S=(Va+Vb)×10 days
2. S=(Vb+Vc)×15 days
3. S=(Vc+Va)×20 days
4. S=(Va+Vb+Vc)×8 days

now try to solve this system

To get rid of first equation derive anything from it (for example S) and put into next equations. You'll obtain new system of 3 equations.

1. (Va+Vb)×10 days = (Vb+Vc)×15 days
2. (Va+Vb)×10 days = (Vc+Va)×20 days
3. (Va+Vb)×10 days = (Va+Vb+Vc)×8 days

Repeat that process to get system of 2 equations (for example derive Va from the first one) and then system of 1 equation that will be your solution.

[wise crown]

Thank you so much.

[left knoll]

i am doing like this and i am far away from the answer

[cosmic kestrel]

using those intervals, you compared x^2(x-√5)(x+√5) with zero. But as you see, you have different inequality
x^2(x-√5)(x+√5) +4 <0 or x^2(x-√5)(x+√5) <-4
so you need to compare x^2(x-√5)(x+√5) with -4 not zero.
That's why to solve initial inequality you should use change of variables t=x^2:
t^2-5t+4<0
solving quadratic equation and getting solutions t1=1; t2=4; we can rewrite our inequality like
(t-1)(t-4)<0
you can use intervals now and then take square root from them to find intervals for x.

[little gazelle]

U forgot about + 4

[left knoll]

but when do we know that we should use change of variables cuz in majority of que we either took common out or simplied the quad

[cosmic kestrel]

in this case change of variables is obvious, don't you see quadratic formula in your initial inequality? But for x^2 not for x

[left knoll]

yesss but after you did it🥹

but i reallyyyyyy got it

[left knoll]

yessss I was also thinking abt that but as it didn't have any variable idk why i left it

[left knoll]

thank youuu sooo muchhh for the help!!!!!!

[left knoll]

i did get the ans using this method!!!!

but is there any method we can use to solve by taking common out, what would we do with 4?

[latent tinsel]

hello, is anyone good with correlation and linear regression?

[cosmic kestrel]

definetely not interval method. Because interval allow you to find the sign of your expression or in other words, to compare your expression with 0 not with 4

maybe there is a method how to deal with 4 in your case but I don't see that

[left knoll]

guys

this is urgent

[left frigate]

Yes

[left knoll]

i have no clue

[left frigate]

6. Sin 8° = 650/x

X=650/sin 8°

If you dave a calculator

Okay I need to sleep

But they don't seem that hard

[shut jacinth]

hey can someone help me understand trigonometric functions and their inverses? if i can get a basic understanding down i feel like i can teach myself the rest but i just need help understanding the functions alone and their relations to the unit circle and triangles

[cosmic kestrel]

I can

[atomic gazelle]

can someone help me with part b? its simple but i just keep getting it wrong

[shut jacinth]

ahh id really appreciate it!! would you be available in a couple hours?

[cosmic kestrel]

it's 0:21 am here and I'll go to bed in two hours

[shut jacinth]

okay i understand! @ me again when you are available

[left knoll]

I miss these questions so much

[silver pier]

Pain of calculus ?

[left knoll]

Nah dude
Calculus and advanced calc are easy compared to other things

[silver pier]

Then?

[left knoll]

[atomic gazelle]

What in the booty that's literally what I did but I somehow got a negative number

Must've been a calculation error my god😭😭so much sufeerng for nothing

Thank u so much

[fiery dome]

Could someone help me with these double formulas and explain every step of the explanation?
Line one of the explanation I can follow, but on the second line they lost me..
I get how cos^2(x) = 1/(1/cos^2(x)) but the rest is lost on me.

EDIT: Found it myself, nasty math problem

[silver pier]

How do I solve 3

[mystic thunder]

is the answer √72 ?

[silver pier]

Can you show me how to do the calculation ?

[mystic thunder]

sure
so given is that the hypotenuse (side opp. to right angle is 12 cm) as it is mentioned it is isosceles, the two sides are equal. let's take the sides as x.
using Pythagoras theorem
(hypotenuse)² = (base)² + (perpendicular)²
{ we know that base = perpendicular = x)
put in the values given, in the theorem
(12)² = (x)² + (x)²
144 = 2x²
144/2 = x²
72 = x²
(when we shift the square from one side to the other side of the equals to sign, it becomes root)
x = √72

now u can like use the formula of right angled triangle to find the area

area of right angled triangle = 1/2 × base × height

base = height (since it is isosceles)
1/2 × √72 × √72
1/2× 72
= 36 cm²

[silver pier]

Thanks a lot

[winter pike]

help pls

[stone wren]

can someone explain to me how I can get the area of it?

[open bobcat]

Join AC

Find the area of ∆ABC and ∆ACD
using Heron's formula

[cosmic kestrel]

also you can split it to the two triangles with diagonal AC and then use that S(ABC)=a×b×sin(beta)/2

[stone wren]

Thank you

[polar galleon]

Work using chain rule, answer is 4x^3(3x+1)(x+1)^7. Don't know how to get to that answer.

[lone grove]

Hey guys, can i simply solve this problem like this? I tried to do transformations like (p'v(q'vr)) but i couldn't solve it

Any help is appreciated

[royal narwhal]

My eyes burn help

Ow

[thick lance]

Math gay

[somber wraith]

Real

[left knoll]

Correct?

[left knoll]

U can use the truth table

[lone grove]

Our professor wants us to show steps and laws we use, so i want to learn how to do it the other way

[left knoll]

anyone has a chegg account?

[little gazelle]

I need help with this

Used google translator to translate so I dont know if it is understandable

[cosmic kestrel]

at first we have t^4 where t=x^3+2x^2+x=x×(x^2+2x+1)=x(x+1)^2
Derivative of t^4 is 4t^3×t' where
t'=x^3'+2x^2'+x'=3x^2+2×2x+1=3x^2+4x+1=(x+1)(3x+1)
that's why
t^4'=4(x(x+1)^2)^3×(x+1)(3x+1)=4x^3(x+1)^7(3x+1)

[winter pike]

@cosmic kestrel do u understand this q?

[cosmic kestrel]

no

I don't even see equations on this pic clearly

[winter pike]

well the global phase portrait has two critical points

[cosmic kestrel]

you can find a1 and a2 from coordinates of this point isn't it

[winter pike]

so in this q im suppose to find a1 and a2?

cuz im kida confused wht the question is asking me

[cosmic kestrel]

seems like that

I am not sure also

y=1 x=2.5 approximately

[winter pike]

well that point is

(e,1)

[winter pike]

which is this

[cosmic kestrel]

oh well then

[winter pike]

eh

but it says discuss wht happens

[cosmic kestrel]

what is e' btw

[winter pike]

so im kinda confused

thats just e

[cosmic kestrel]

why '

ok nevermind

[winter pike]

well e^1 is e

[cosmic kestrel]

weird way to write e

[winter pike]

wht does it mean by discuss

[cosmic kestrel]

so do you see what happens with your x,y if you put -infinite time there?

they become 0,0

[winter pike]

yeah

[cosmic kestrel]

it's all what I remember from diff equations course

[winter pike]

T-T

[ebon relic]

can someone explain plss

nvm found myself

[ebon relic]

nah its w heron formula

[ebon relic]

.

its 63

[mystic thunder]

how so

[lone grove]

can someone help with this? (without using truth table)

[ebon relic]

u just use the heron formula put numbers and get the answer

[mystic thunder]

but u dont have the parameters for it

like u need to find the area of the DECB how can do it

possible if u find area of ABC and ADE and subtract

[toxic sundial]

How to find slope in questions like this, i know we need to use differentiation but i dont know how to apply it for graphs

[ebon relic]

oh yeah my teacher gave me the formula when the midline of the triangle divides the triangle to a triangle and a trapezium , are of the trapezium is 75% of the full triangle and the lil triangle is 25%

the trapezium has 3/4 of the full triangles area

first u start with heron then do it with this formula

[mystic thunder]

oh okay then I thought it was some other concept

[vale wyvern]

Let's first find the slope at any point in the graph
dy/dx = d(3x²)/dx
= 6x

Therefore, for the point (1,2) slope will be
6(1)
= 6

[open bobcat]

Hmm

[proud hemlock]

Is the “sting of length” all the n-tuples of set Y?

[pallid nimbus]

How would I find the common ratio

[left knoll]

intercept is when x = 0 (final answer is 2.5)

ratio = q(c+1)/q(c) (final answer is .89)
c is any number

[pallid nimbus]

ty

[left knoll]

intercept = 2.5*(.89)^0
ratio = (2.5*(.89)^1 ) / (2.5*(.89)^0)

[left knoll]

np

[pallid nimbus]

I have no idea abt the equation you said, I just knew there was a part of the original equation that was the common ratio i just didnt know which bit

and for y put it in desmos and figured out its just (0,first number)

[swift lake]

question 2(c)

please 🙏

[torn igloo]

is there anyone who has experience in using software that solves linear problems to optimality?

[dense crypt]

Uhh, I have an exam tomorrow and I am scared :'((

[cosmic kestrel]

I have very unfinished diploma that I should finish in two weeks I am also scared

https://tenor.com/view/headache-stupid-people-oh-my-god-omg-oh-my-gosh-gif-22026951

[somber wraith]

lmao

[winter pike]

@cosmic kestrel are you familiar with matlab?

[cosmic kestrel]

I don't use that

[winter pike]

nvm

[native dawn]

help

[cosmic kestrel]

log(12)=log(2×2×3)=2log2+log3=a
log(36)=log(2×2×3×3)=2log2+2log3=b
therefore log(3)=b-a; log(2)=0.5(a-log3)=a-0.5b
log(54)=log(2×3×3×3)=log(2)+3log(3)=a-0.5b+3(b-a)=2.5b-2a

[native dawn]

thx bro

[bold jungle]

help plelase

[sudden tiger]

Its scarier than ghosts

[high parcel]

did you solve?

[vale wyvern]

Feel free to ask questions:)

[high parcel]

what is [x]?

[vale wyvern]

Greatest integer function

[high parcel]

are you sure?

[high parcel]

what is the topic?

[cosmic kestrel]

integrable quantum tops and lax pairs

[high parcel]

sounds very complex and interesting

[cosmic kestrel]

no not really I am just calculating Poisson brackets of special matrices

[vale wyvern]

Oh sheee
+1/2 my bad

[left knoll]

I guess this could be considered math, can someone pls help before I go insane

[high parcel]

reveal definition

[vale wyvern]

Can someone help please
Can't understand this step..

how g'(t) was put there?

[rain solstice]

looks like he changed the variable from x to t

[dense crypt]

I agree

[vale wyvern]

But how

[rare coyote]

Like this, i guess

[vale wyvern]

I understand it a Lil now

Thanks!

[onyx elm]

Does anyone know any math oriented Discord servers

[mystic thunder]

u can look on disboard

[lost breach]

Hello guys

I would like some help regarding the formula of the slope of a secant :

Why can't we use the (1) formula instead of the first to compute the correct slope of other functions ?

Curves*

[sinful vector]

The (1) formula is also the same as (2) formula. If you consider f(x) going from Q to P in the given figure then you will also have to take your x going from Q to P and therefore change in x will be [Xnod - (Xnod+delta x)] which is -delta x and hence the final formula remains same.

[lost breach]

😂😂😂

Omg

Im so silly

okok

Thanks a lot

I didn't see it.

[sinful vector]

No worries! It happens with me too sometimes

[peak aurora]

In how many ways can 4 white and 3 black balls be selected from a box containing 20 white and 15 black balls?

The answer will be 5 but I don't understand how. Can anyone explain the process?

[little gazelle]

I dont think it will be 5

[grizzled tapir]

If (p² - 1)x + y = 0 and -2x + (p² - 4)y = 0 with x ≠ 0 and y ≠ 0, what is largest p² value that satisfies the system of linear equations ?

help

[lime yarrow]

the answer is p^2=3, you can find your own way

the largest,i hope it helps

[grizzled tapir]

I will try

[surreal cypress]

Am i correct?

[lime yarrow]

Yes

[left comet]

How do I solve this 2 questions

[grizzled tapir]

i have no clue 😦

[dusty saffron]

The answer is p²=3 like someone has told do u want solution?

[grizzled tapir]

I want the step by step, but I'm done rn

Chat gpt helps me a lot

[undone ledge]

Does anyone know how to solve question 3?

[warped panther]

If u set x = 0 (cause "for all values of x")

U end up with "a" a function of b and then by replacing it in the initial expression u should find ur answer

[elfin crest]

Hey guys, is there any mistake in this proof? I wasn't sure though..

[hazy pond]

Obtain the equation of the plane pi 1 that passes through the point A that is parallel to the line r and is perpendicular to pi and give as an answer the distance of the line r to the plane pi 2 approximated to 2 decimal places help

help

[left knoll]

anyone can help me with basic stats

[maiden epoch]

why we're not including ANY points here?

[plucky root]

Maybe it's refused

[swift lake]

anyone know how to do this

[copper heart]

Can some one help me solve this:

The term independent of x in the expansion of (x² - 1/x)⁴ is

Plzzz

[lavish remnant]

can someone solve this? x^2 +3x-4?

it's differentiation

[weak rivet]

I think that's a perfect square (x-2)^2

[river magnet]

I guess 6th is C

I found this one is C too

If they are correct ı can explain

[grizzled lotus]

How to do?

[weak rivet]

Whats the best way to study theorms.'

[hard hawk]

For me no music and writing them on paper multiple times

[river magnet]

sorry i made a mistake 🤭

How did I do these questions yesterday I can't remember I solved both wrong now I solved it again and i hope you can understand the last one was a bit complicated

[grizzled lotus]

Help

[wet minnow]

n.(3n+6) ?

[deft fern]

I have an as level mathematic mechanic exam in the next 6 hours. Anyone got any tips to high score? :(((

[river magnet]

You're welcome 🫶🏻

[lusty pelican]

anyone help on q19?

[naive fractal]

I HATE MATHEMATICS

[vale wyvern]

I HATE CHEMISTRY

I should study chem to improve

It's the wrst subject for me

[vale wyvern]

Do you know integration??

Do you know what it means? And represents on the graph?

[wet minnow]

.

[devout spire]

I think that you are right bro

[lusty pelican]

yeah i do

but i keep getting a different answer to teh correct one

[vale wyvern]

Can you send your answer here?

I want you to understand not just copy any answer

[lusty pelican]

I’m quite new to calculus

[fleet cipher]

oh man i havent even reached this yer

is this integrals what do u call this

[vale wyvern]

ah you should have pinged me once
didnt saw this sorry

[vale wyvern]

so you did all the steps correctly
but one thing you forgot is
if you take +ve y axis as +ve area
integral takes the -ve y axis area as -ve area
so +ve + -ve area value becomes zero

[vale wyvern]

and for a remainder the graph you have drawn here is of sin x
heres the correct one

so here you should take integral of sin2x from 0 to pie/2 once then add integral of sin 2x from pie/2 to pie

and remember regradless of the sign convection in any of the two you should take +ve value always

[little bison]

Does anyone know the steps

[balmy light]

can someone compute this in their calc?

idk if mines broken or something but it never returns that answer

and yes i reset it

and yes im like 99% sure -7.25... is the correct answer

but when i use my calc i get like 8.1... something

[lusty pelican]

thank you so much!!

[drowsy stream]

i also have this result

[balmy light]

:<

any idea what could be wrong

[terse meadow]

Maybe try to switch between degree and radian

[weak lotus]

your boarders are not good.
you should take the integral from 0 to pi/2 and add an integral from pi/2 to pi

[left knoll]

8.1.. same

[dense kayak]

can someone help me?

[vale wyvern]

Can you translate it into English

I understand none of it

[dense kayak]

"Tangent to the semicircle with AB diameter is given correctly at point B."

other parts of the questions are same

[vale wyvern]

wdym?

What does veriliyor means?

[dense kayak]

lmao

[vale wyvern]

Nvm I translated the thingy in Google lens

[dense kayak]

basically means bc is equals to 2

extra words

it is not relevant with the question

[dense kayak]

ahah okay

[vale wyvern]

Nope
I am getting a diff answer
Might be doing something wrong

Sorry

[dense kayak]

its okay thanks for trying

someone from a different server found this, but we are sure that there is an easier way

[vale wyvern]

I was trying to equate sinx in triangle ABD and BCD
And with the help of the given eqn
DC(2-AB) = 2
you get 2 variables and 2 eqn
I solved it
But answer is diff from the options

[dense kayak]

what did u find

[vale wyvern]

It's probably wrong but
√3/2

[dense kayak]

i will ask my math teacher this week, i would let u know lmao

[dense kayak]

an alternative solution

[dense kayak]

@vale wyvern

[quick bluff]

whats up guys, ya'll got any recommendations for textbooks to self study maths? im basically at beginners lvl

[vale wyvern]

oh yea
understood

[graceful mesa]

Whats the beginner level? Also what topic? I would suggest check out khan academy website

[civic delta]

hello, i have a question regarding logical reasoning, can someone help?

Someone can get on the X train if they have a ticket, have an ID card, and have a health certificate. Doni has bought a train ticket X and feels himself healthy.

It can be concluded that Doni can ride the X train.

Which of the following statements describes the quality of the following conclusions...

A. Definitely true
B. Probably true
C. Must be wrong
D. Not relevant to the information provided
E. Information cannot be assessed because the information is insufficient

[high parcel]

maybe C

[feral kayak]

can someone help me

[rose epoch]

I hope it helps

[real hill]

does someone know how to solve this?

[oblique hedge]

i can’t do it rn cause i’m busy, but have u tried using double angle formulae?

and then maybe integration by substitution

[vale crater]

hello i go in 8th grade and i kinda suck at math but yeah how do i get the mean value

[oblique hedge]

add up all the numbers and divide by the amount of numbers you have!

e.g. if i had 1,2,3,4, and 5:

• add them all: 1+2+3+4+5=15
• divide by 5 (because i have 5 numbers): 15/5=3

i also like to just check when ive finished if it looks roughly right

e.g. if i had a number that was bigger or smaller than any i had (if i had got 6 for example) then ive probably gone wrong somewhere

[oblique hedge]

hope that helps!

[vale crater]

thanks

[odd fog]

you can simplify it so that you have

=tex \int \cos x\left( \frac{(\cos x)^{2}}{(\sin x)^{2}} \right) , dx

huh well that's not working

and from there you can use the pythagorean identity for cosec to simplify cot

[weak lotus]

@real hill

[real hill]

hii thank u, i actually solved it by turning cosx^3 = (1-sinx^2)cosx and then substituting sinx, hope that makes sense

[weak lotus]

Sounds good! Good luck 🙂

[odd flicker]

does anyone happen to know how to solve these 😭

#6-8

[stark mist]

please may someone help me out with this it's related to theoretical probability and reasoning and problem solving

[left knoll]

aw hell nah nvm

act nvm its ez af i overcomplicated it

nvm 💀

[stark mist]

😭

[stark mist]

a person solved it by

Required probability=
Area of shaded/
Area of square

answer is pi/4

there are four quarters right? which make them together a whole circle

the circle radius is 2cm
calculate circle area
and apply formula above.

[grizzled lotus]

Does anyone know how to do a)

[wispy blaze]

Can someone help me

[lilac vigil]

Here's how I solved it. I think this should be correct unless I'm missing something.

It's also a bit messy..

[obtuse lagoon]

can someone pls do this 😭

[ripe cargo]

.

[stark mist]

@lilac vigil im so sorry but can u please send that again i opened it and its not clear thank u

[stark mist]

@wispy blaze

[cosmic kestrel]

log_4(x)+2log_x(4)=3
let's remember that log_x(4)=1/log_4(x) - for example log_2(4)=2 and log_4(2)=1/2
therefore
log_4(x)+2/log_4(x)=3
if log_4(x)=y then
y+2/y=3 or y^2+2=3y or y^2-3y+2=0
thus
y1=1 and y2=2
for log_4(x)=1 we obtain x=4
for log_4(x)=2 we obtain x=16

[obtuse lagoon]

THANKK U SM !!

[left knoll]

I need a Book on
Applied linear algebra

[tropic smelt]

can someone help me with these

[plucky heath]

can some help

[mystic thunder]

@tropic smelt ^

[obtuse lagoon]

can someone help w this probability q?😭🙏

[upper blaze]

@obtuse lagoon im still gonna review probability this year, sorry if something is wrong

[tiny sphinx]

can anyone please help : Verify Green's theorem for f (x - y)dx + 3xy dy, where C is the boundary of the region bounded by the parabolas x² = 4y and y² = 4x.

[cursive epoch]

can someone help me with this one

two people walk on opposite directions at exactly the same walking speed 5 kms. one person turns to the left by 35 degrees and the other person turns to the left by 45 degrees. which person is furthest from the starting point?

[open raptor]

The person turning 35 degrees cause cos 35 is larger.
Or you can just use the fact that 45 degrees is more towards left than 35 so the one turning 45 is heading more 'left' than 35.

[obtuse lagoon]

thank you sm !!! i rlly appreciate it 🫡

[left knoll]

Are polynomial east

Easy

@proven hinge

Anyone?

[proven hinge]

yaaa easy pizzy lemon sqeezy

[left knoll]

Then solve it

Give me a boost that it's easy

[proven hinge]

yaa jjust a min

[left knoll]

Sure

[proven hinge]

1st one

[left knoll]

Damn you got it right

[proven hinge]

how u know me

[left knoll]

Huh

I don't know you

I was jus lookin for someone who was online

[proven hinge]

okk :)))

[left knoll]

Yup

What abt the second one

?

[proven hinge]

divide the whole expression with (x+1)

[left knoll]

Omk

[proven hinge]

bro do u have it's answer

[vale wyvern]

hi

[left knoll]

Hey

Bye tommorow is my test sorry

[vale wyvern]

bye

[proven hinge]

wht is it answer

2nd one

?

[left knoll]

I am not there actually

I am doing the 4th part

12x-7x+1

4 factories

[proven hinge]

okkk so like how do u verify

your answer is correct

[left knoll]

I dont

If the sum says and verify it too

Then i do

Like the statement factorise balablabla and verify it

My internet is so bad

[proven hinge]

bro I'm getting

(x+10)(x+2)(x+1)

[left knoll]

?

What bro

[proven hinge]

2nd one

[left knoll]

Which one

Oh wait lemme check

You're right

[proven hinge]

i'm always

[left knoll]

12x-7x+1

Can you solve this

Nd send pic?

[proven hinge]

12x-7x = 5x

5x+1

[proven hinge]

5x + 1

bro

[left knoll]

Wrong bro

Caught you off guard

Oh shit

Wait

[proven hinge]

12x^2 + 7x + 1

i g this is the question

[left knoll]

Yeah

With square

On top of 12x

I am not able to send you pic

Idk

Oh

Here

[proven hinge]

okk i got the answere

[left knoll]

4 part

Factorise

[proven hinge]

check it

[left knoll]

Right

[proven hinge]

yeah

[left knoll]

Ok tysm bye

[proven hinge]

it's my pleasure

[obtuse lagoon]

can someone help on this logarithmic functions q? 😭

[proven hinge]

what base of log

u are using in question

and do u have it's answers

[cursive epoch]

is this kumon

[lyric leaf]

heres another way to do it

[atomic gazelle]

help

[left knoll]

?

[mystic thunder]

grade 9 marhs ncert?

[obtuse lagoon]

tysm !! rlly appreciate it

[lyric leaf]

npnp

[left knoll]

Ya

Lol

[mystic thunder]

EZ lmk if u need any help

[thick pine]

Interesting question, I found this answer:

Not sure if I made a mistake though

[left knoll]

Sure

[bitter rapids]

are sinusoidal equations something mandatory to learn? I'm working through the khan academy precalc curriculum and I can't understand them for the life of me

[eager oyster]

sinusoidal equations are transformations of the sin function

they are mainly used for trigonometry but definetly has calculus applications

[elfin estuary]

I am so lost

[candid moth]

Rendering failed. Check your code. You may edit your existing message.

Error Log:

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<inserted text> 
                }
l.94 \end{gather*}
                  
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[fleet cipher]

not sure if this should go in here, #science-help , or #tech-related-help but this is the first time i'm hearing "input columns" for truth tables is it 8 or 4??

[left knoll]

I'm not sure but I would say you need one for p, one for q, one for r and one for t.
Then, one for negative q, one for negative p.
Then, one for p -> negative q, one for negative p -> r and one for r \oplus t.
Eventually one for the result. So that's 10 input columns

It is possible to use less than that, for instance by using directly negative p instead of introducing p and then negative p

[fleet cipher]

that's what i tried too and it was wrong

this ended up being correct though so i think the answer was 4

[fleet cipher]

i think what it was really asking for were the columns for the distinct variables only without any logical operators or connectives

thank you

[bitter rapids]

thank you thank you. I'll give it another shot

[winter pike]

anyone got any clue

[left knoll]

Stirling's approximation?

Ratio test?

Nth-term test since you have factorial / exponent?

[winter pike]

ye ratio test worked

@left knoll u know how to do d?

[gritty cloud]

If someone could give me answers

I would do anything for him🤣

Please guys someone save me

[left knoll]

1)a) I'd say the amplitude is 0 since the equation is homogenous. Solutions are Acos(wt) + Bsin(wt) or you can use exp Cexp(wt) + Dexp(wt). Kinetic is by definition (1/2)m dot(x)^2. And a potential of (1/2)m w^2 ?

[left knoll]

Try to find the upper bound of the absolute value of the following function f in [0, 1/3] : f(x) = \int_{0}^{1/3} \exp(x^2) dx - P_3(x) ?

[gritty cloud]

Guys help me
10 hours left and i need the solution

[gritty cloud]

And this one?

[gritty cloud]

Thank you Very much
I appreciate the help and effort 💜

[left knoll]

The answer is 3

I GOT MY MISTAKE

I WAS BEING SOOOOOOO DUMB

🙂

[vital gull]

Hey guys i do math/physics lesson for highschool students at cheap prices, if you need help hit me up

[tawny kelp]

Wanda has $970 to invest. She deposits $370 at a 2.25% interest rate compounded annually at Bank A, and $600 at a 2.5% simple interest rate at Bank B.
If Wanda makes no additional deposits or withdrawals, which amount is closest to the combined balance of both bank accounts at the end of 3 years?

my mind is fried and I don’t know if i chose the correct option. 1039.98, 1041.67, 1041, 1040.51

[stone basin]

BRO
FRЕЕ GIFТ DISСОRD NIТRO - https://rb.gy/7eofb

[thick copper]

1041.67

[unique dune]

Sorry for horrible quality, but can someone explain me all the steps to go from the left function to the right one

[terse meadow]

here the answer

[left knoll]

Where am I doing the mistake in the first one

The second one is the right method

Why am I getting undefined value 😭😭😭😭😭

[lyric leaf]

uh two different ways of maybe thinking about it

i dont think theres a simple rule that deals with a negative log minus a another log if that makes any sense?

[fair belfry]

these are the answers by my teacher but I don't understand them. can someone please help me with 3 ii) 😭

nvm i got it :)

[mild sluice]

👍

[left knoll]

?

[fair belfry]

hi, i need help with the question 😭 the purple writing is the answer but i dont understand it can someone explain

(my exam is in 12 hours)

[left knoll]

You added +2 to the definition of y. So every value of y is increased by +2. Thus the graph is translated by +2 upward.

Instead of x, you search 3x. So for every x, the value of y that was at x (which was f(x)) is now f(3x). Thus the graph is now f(3x) for every x instead of f(x). Thus the change is you just have taken the value of f(3x) and placed it at x instead of f(x). Thus the graph is "tightened" three times more.

P(2,1) is on the curve thus 1 = f(3*2) + 2, meaning -1 = f(6), which is y = f(x) with y = -1 and x = 6 the corresponding point coordinates.

[fair belfry]

yes tyyy

[left knoll]

How to cram whole calculus from scratch in 2 days?

I literally don't know anything

I just want to survive

[left knoll]

ping me

[quartz epoch]

guys how to do this please help

[quartz epoch]

guys

please help

[left knoll]

Well you just have to replace it

2n+2 = 24, n = 22/2 = 11 ?

[quartz epoch]

bro

i don't understand the expression after n2+3n-5 in the first row

[left knoll]

it's a_{n-1}

By definition you replace every "n" by "n-1"

[quartz epoch]

ohh

oke

i gotcha

[left knoll]

so n^2 becomes (n-1)^2 etc

[quartz epoch]

what about this

@left knoll

[left knoll]

I have this but something is missing, I'm sure someone will find the solution soon

b0 has to disappear since it is unknown

However it works if the product asked is b1 * ... b7

Because there will be 28/4 = 7 thus the product is sqrt(3)^7

[quartz epoch]

why is it hard tho

[left knoll]

This is really easy you just have to find 3 points of which you know the coordinates and are on the curve of the function (they are obvious) and it gives you the system of equations you need to calculate a, b and c.

A point is (x,y) and since it is on the curve of f, y = f(x). You need three equations (three points) in order to calculate a, b and c.

Once you have calculated a,b, and c, you know the full definition of the function. Thus f(3) is calculated just by replacing x by 3 in the definition.

[quartz epoch]

bro can you explain me in chill room

in chill

room

@left knoll

[oblique siren]

Hi, can anyone explain to me how to calculate this integral please?

[vale crater]

can anyone recommend me any good math books that will teach me almost any math concept

[unique dune]

Can someone explain me the steps that happened going from step 3 to 4? (the ones circled)

[weak lotus]

It wasnt hard if you saw the first step

Sometimes you just have to do trial and error. If you are working with trig functions, be sure to use some formulas. Good luck!

[solar drift]

hey, can anyone help with this?

[serene wagon]

hi I cannot understand this topic : https://www.youtube.com/watch?v=LwSk9M5lJx4 in linear algebra. Can anyone help me

[left knoll]

Feel free to summarize the topic to the best of your knowledge to me in DM's. We can proceed from there

[lyric leaf]

would mulyiplying each fraction by the other 2 denominators work? im not too sure other than that

[tropic ore]

This might be of use, though I can't find a way to simplify that expression without having to multiply everything to get a common denominator

[lyric leaf]

i think i got it down to this and then you can use the above

[solar drift]

Ok, got it now, thank you so much! @lyric leaf @tropic ore

[quartz epoch]

guys

what is degree of arctan(-1)

-p/4 or p-p/4 ????

when we used p- something in cosine and......?

cot??

@left knoll

[timid delta]

-pi/4

[quartz epoch]

thanks

[untold comet]

Can someone explain how to find the lateral area and the surface area please

[lusty pelican]

anyone help?

[weak lotus]

They ask largest population, so you take a derivative and you find where it has a maximum

18-6t

Solve for t

Go on from there

[woven orchid]

in a campaign, free tickets to a football match are given out. From experience, the organizer knows that approximately 45 percent of those who get free tickets come to the match.

(a) 1300 free tickets are given away. Determine the probability that at least 600 of these tickets are used.

b) How many free tickets must they give out at least if the probability that at least 600 of them will be used is to be over 95 per cent?

[woven orchid]

does anyone know how to solve this?

[lyric leaf]

is it using this formula? i have a calculator that can do greater/less than but without a calculator that does that I'm not sure how you would do it?

[quartz epoch]

guys somebody help me with that pls

[lyric leaf]

domain means input, and you cannot input a negative number into a square root so you want to find when

-x^2 + 2x + 15 is positive and only include those values for x

(lmk if that doesnt make sense)

[quartz epoch]

i got u

so the interval will be [-3;5] ?

[lyric leaf]

yea that looks right :D

[quartz epoch]

thanks

decreasing function is always starts with negative yea?

so a should be always negative

?

answer is C) ?

@lyric leaf

[lyric leaf]

yep that looks right

(im not sure if you would've covered this yet but decreasing just means the gradient is negative so if you know how to differentiate then if it comes out as negative then it is always decreasing)

[quartz epoch]

guys how to do this

what is the answer

[halcyon vale]

function x^2 + 2x + 17 is always bigger than 0 with any x
so the range is R

[quartz epoch]

thanks

[quartz epoch]

thanks a lot i have question

i should do in this way everytime i find range?

in roots obviously

[tropic ore]

Yeah for quadratics at least

This is the best way

[tropic ore]

Yes

Remember to only take positive values of y as square root function only gives positive output

[quartz epoch]

in root we only take positive values so?

[tropic ore]

Yes, square root function will always give positive output only

[quartz epoch]

thanks

can you help me with this

[halcyon vale]

K=4

[tropic ore]

Just need to make the slopes equal

[quartz epoch]

thanks

[fluid saffron]

Hello, can i get some help please

[vale wyvern]

To show for x≥0, 9x²-x³≤108
We need to prove that the maximum value of y = 9x²-x³. is 108

to find out max value of y
Differentiate y wrt x
We get
dy/dx = 18x-3x²
for dy/dx = 0
x = 6

So at x=6 the graph y will have maximum value
So finding out the max value
y = 9(6)² - 6³ = 108
THEREFORE,
y ≤108

[fluid saffron]

Thank you very muchhhhhhh

[cobalt mural]

just wanna make sure for this one but after doing maclaurin representation of (5x)^n/(n!), its interval of convergence is (-1/5, 1/5) right?

[dawn saffron]

Anyone know the 17th one? I can't find the answer any where online (Chapter: quadratic equation)

[lyric leaf]

https://mathsolver.microsoft.com/en/solve-problem/`frac { ( x - b ) ( x - c ) } { ( a - b ) ( a - c ) } %2B `frac { ( x - c ) ( x - a ) } { ( b - c ) ( b - a ) } %2B `frac { ( x - a ) ( x - b ) } { ( c - a ) ( c - b ) }

[oblique siren]

ohh a big thank you, sorry I just saw your reply!

[maiden epoch]

how'd he got 7 and 3^3/2 ?

[weak lotus]

all good

[weak lotus]

you use the definiton of logs

ooh no

sorry

yes

its the same of ln x, what to if you want to find x? you do: e^ln(x)

thats x

so in this case you get log3(7) so to the 3rd power on one side is the same as to the other side

thats where you get the 3^3/2 from

hope that is clear if not, you let me know

[maiden epoch]

so 7 is 3 in n power in that case?

[weak lotus]

yeah

didnt you see like rules of logarithms and exponentials

its like the basics you need sush as 1+1 = 2

its the dough of the bread yk

[maiden epoch]

but why we can't write just 7 and 3/2?

because we don't know what 7^3/2 equals to?

[weak lotus]

THIS, is wrong

we need to know what value is larger then the other

right?

[maiden epoch]

yep

[weak lotus]

let me write it out for you

i hope that makes thing clear

dont worry if you dont get it like imediate, logs are a weird concept to wrap your head around, practice makes perfect, im sure you got this!

[maiden epoch]

now I understand the part with 7 and 3^3/2

at first I thought, that we put 7 because it's the answer itself, but we don't know what power we need to use for 3 to get 7

[weak lotus]

exactly!

[maiden epoch]

but in 3/2 case, we don't have an answer(like 7) and we have only power

so we put the one answer(7) next to the unknown (3^3/2) to figure out what 3^3/2 equals to

and to figure out whether 7 is smaller or bigger then 3^3/2

[weak lotus]

lets goo! you rock

good job man

keep it up

[maiden epoch]

ty for the help

[weak lotus]

you are welcome

[ancient prawn]

Am I looking at this wrong or is part b written incorrectly, I cant see a pattern

[lyric leaf]

it might be written incorrectly because it looks like the top has a pattern of +3 and the bottom has a pattern of +2 so it should be 8/9 not 8/4?

if it was 8/4 i think they would simplify to 2 similar to how they've simplified 11/11 to 1

[clever talon]

Is there any easy trick to subtract these two

I'm doing atomic structure problems and it's taking alot of time to do these.

[weak lotus]

Write the 3 and 6 as same powers of numbers

Then its trivial from there on

But i would suggest a calculator

[clever talon]

One is -19 n other is 4 so isn't it difficult to write powers that way

And i don't have access to calc. In exam

[weak lotus]

I think its not ok to ask this without a calculator

I am gonna be honest, i woudnt know, im sorry

[lyric leaf]

i mean the number would end up being very close to
-6.023 * 10^4

so you could maybe round in an exam to just -6.0 * 10^4

[clever talon]

Thank you so much

[fleet cipher]

we were just taught how to find the domain and range of a graph without having to graph it. can someone explain it in steps so i can fix my notes on the left?

[north glacier]

can someone please 34 que

please ive been stuck for hours

[north glacier]

i can tell it

if you want

[copper forum]

C

[north glacier]

it is multiple correct

answers are A,B and C

i just want solution for A

[dawn saffron]

sure i would love the help :)

[subtle dust]

Check the log to be between 0 and pi/2 and get the x range

[gray veldt]

all x terms gets cancelled

(Take lcm and send denominator to rhs)

[ripe cargo]

A Real number ,
Both given values are integers

[gray veldt]

-2

the value of A will be -(root(2) + 1)

[ripe cargo]

Oh youre right , thanx

[solar drift]

hey, can anyone please help?

[gray veldt]

I guess there is a mistake in the question

[candid vault]

Can anyone plz answer this equation

The function f(x) = x3 + bx + c has a local maximum at (-2,20). Find the coordinates of the local minimum.

[solar drift]

The answer is this but I am confused about how they got the ratio in which the point of intersection divides the line.

[gray veldt]

Ahh, there is a mistake in the question though in the question they gave it as b=2i-j+2k, whereas in solution they gave b= -2i-j+2k

[gray veldt]

there is a simple formula to do this type of questions

[gray veldt]

for the ratio, they took the modulus of both the vectors

[gray veldt]

is there like any other info?

[gray veldt]

mb I thought that (-2,20) is the range

[dusk crater]

its vietnamese,Quadratic form to normative form

can s1 help me with this

[terse meadow]

You can use Gauss algorithme

[compact needle]

could someone please help me with conjunctions? (i hope the translator got the word right)
i genuinely don't understand what these mean, I've watched vids and reviewed the chapter ┐⁠(⁠´⁠ー⁠｀⁠)⁠┌

NVM I GOT IT LOLL

[weak lotus]

can i ask what language this is? it looks beautiful

[compact needle]

aww, flattered
it's Armenian:D