Melody

921 Questions
34315 Answers

+1

1

1742

2

+118725

Mathigon website

I just discovered a site called mathigon

https://mathigon.org/dashboard
mehr ..

Melody 02.04.2022

-8

609

1

+118725

Reporting problems.

There are a number of people having problems at the moment.
If you lodge an error can you please give all relevant information that you can think of.
Where you are in the world - the city or the country - is often very important information. mehr ..

Melody 16.03.2022

-2

8

1459

5

+118725

How to make an empty rectangle in Latex

I just worked out how to make an empty box of various horizonal size easily in LaTex.
This is not a recommended method, but other methods that I have tried here have not worked.
This coding is really simple. Just put letters inside mehr ..

●●●●●

Melody 15.03.2022

-3

871

3

+118725

HAPPY ANNIVERSARY CHRIS! (CPhill)

I just realized that you became a member here exactly 8 years ago today!

It has been great to have you here all that time

Off-Topic

Melody 13.03.2022

-4

849

3

+118725

WELCOME BACK CPHILL !

Melody 11.02.2022

-5

717

2

+118725

Very interesting question. No high level maths required.

This question was posted a couple of days ago.
https://web2.0calc.com/questions/geometry_73561

I think it is really interesting. It looks much more difficult than it really needs to be. mehr ..

Melody 01.02.2022

-7

889

11

+118725

Members have a better experience. Their questions get more attention.

Almost everyone is posting as a guest.
If you post as a member your questions will have a far greater chance of a timely and helpful response.
If you are a genuine learner and interact with us, you will become known and answerers will do mehr ..

●●●●●●●●●●●

Melody 09.01.2022

-6

1

996

3

+118725

HAPPY BIRTHDAY CHRIS!

Melody 20.12.2021

+5

16

5552

9

+118725

Some guidelines for question askers.

Please note:
1) Ask only one question per post.
2) When asking a question talk about what you have tried for yourself. Then people will take you more seriously and will be more able and willing to help.
3) If you get an answer mehr ..

Off-Topic

●●●●●●●●●

Melody 04.11.2021

-9

1091

1

+118725

Remeniscing - a little historical humour.

I just found this old post that some of you, who have been around for a while, might find amusing.

https://web2.0calc.com/questions/look-at-the-new-leader-board

Off-Topic

Melody 29.10.2021

+118725

0

(3n^4)^2

=(3*n ⁴) ²

=3 ² * (n ⁴) ²

=9 * n ⁸

=9n ⁸

Melody21.10.2013

+118725

0

Melody21.10.2013

+118725

0

Firstly my last entry had an omission in it that added to your confusion.
I have now added it in red. I have also changed +-2pi*k to just +2pi*k because since k can be a positive or a negative integer the - was not necessary.
Sorry about the confusion.

You had
theta = +-pi/6 + pi*n
I had
theta = +-pi/6 + 2pi*k OR (pi+-pi/6) + 2pi*k

These are both the same. I just seperated them because they would give different answers for cos.

Your logic is fine. You simply didn't think about cos(5pi/6)=cos(-5pi/6)= -1/root3
Hence you missed the second solution.

Now for some English terms
Even numbers are 2,4,6,...
Odd numbers are 1,3,5,.....

An even function is a function which is symmetrical about the y axis. (The axis of symmetry is x=0)
Hence f(-x) = f(x)
For example y=cos x OR y=x ²

An odd function is a function where f(-x) = - f(x)
For example y=sin x OR y=x ³
Odd functions are said to have point symmetry because if you rotate the the function 180 degrees about the origin (0,0) then it sits back over itself. I hope that makes sense to you.

You taught me a new word too. I had to look up what homogeneous equations were. I don't know where the word homogeneous comes from, I guess it refers to the fact that they all end up the same ratio, that is tan.

Melody20.10.2013

+118725

0

http://www.mymathforum.com/

I'm sorry but I don't know the answer to this question.
I would like to suggest that you post this question in a more advanced forum.
the link above is one such forum.
It has high school questions but it also has uni questions.
The questions are divided up into different sections
Try to find the most appropriate section in order to maximize your chances of a good answer.

If you get an answer I would be interested in seeing it.

Melody20.10.2013

+118725

0

What is the fifth root of .00032?

The 5th root is a power of one fifth
0.00032 ^ (1/5) =

Melody20.10.2013

+118725

0

f(x) = sin ² (x)* cos(x)

Are you familiar with the product rule?
the product rule says that if
y = uv
then y' = uv' + vu'

let
u = sin ² (x) = (sin x) ²
u' = 2* sin x * cos x (I have used composite function rule or chain rule to get this derivative)

v = cos x
v' = -sin x

so
y' = [ (sin x) ²]*[-sin x] + [cos x ] * [2* sin x * cos x]

y' = -(sin x) ³ + 2 *sin x * (cos x) ²

y' = 2 *sin x * (cos x) ² -(sin x) ³

y' = 2*sin x*cos ²x - sin ³x

Do you understand what I have done?

Melody20.10.2013

+118725

0

If it was a rectangular prism the volume would be
V=l*b*h
V= 48*8 = 384 cm ³

But this is a pyramid not a prism.
The volume of a pyramid is 1/3 the volume of the corresponding prism
so

V = 1/3 * 384 cm ³

V = 128 cm ³

Melody20.10.2013

+118725

0

Google translation (original was in Indonesian)

area bounded by the following curves rotated around the X axis rotating objects specified volume occurs.
y = x ²-4x +4, X axis and Y axis

My translation
Find the volume of revolution when the area bounded by y = x ²-4x +4, the x axis and the y axis is rotated about the x axis.

This is a concave up parabola, the vertex is at (2,0)
I think now it would be easier to do it in an attachment.

Ini adalah cekung up parabola, verteks di (2,0)
Saya pikir sekarang akan lebih mudah untuk melakukannya dalam lampiran.

I hope this helps Florin
Saya harap ini membantu Florin

Volume of revolution.jpg

Melody20.10.2013

+118725

0

e is just an irrational number with special properies, a bit like pi.

to get an approximate value for e on my calculator (casio) I would press

shift e ^x 1 =

It is approx equal to 2.718281828

This is an approximation because e is irrational and therefore cannot be written exactly.

I hope this helps.

Melody20.10.2013

+118725

0

-(1/3)(-6y)(3x)(-3)(-1)=

Well, if you are multiplying 2 numbers together
If both numbers have the same sign, both positive, or both negative, then the sign of the answer will be positive
If one of the numbers is positive and the other is negative, then the sign of the answer will be negative.

From this you should be able to work out if the answer is positive or negative

now it is just
(sign that you have worked out) 1/3 *6 * 3 * 3 * 1

1/3 of 6 is 2
Can you do the rest?

Melody20.10.2013