Melody

921 Questions
34315 Answers

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Mathigon website

I just discovered a site called mathigon

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

Melody 02.04.2022

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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

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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 ..

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Melody 15.03.2022

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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

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WELCOME BACK CPHILL !

Melody 11.02.2022

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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

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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 ..

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Melody 09.01.2022

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HAPPY BIRTHDAY CHRIS!

Melody 20.12.2021

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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

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Melody 04.11.2021

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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

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If theta is a fourth-quadrant angle such that sec theta= 4, use a trigonometric identity to find the exact value of tan theta. Decimal answers are not allowed. Use simplified radical form, if necessary.

I don't know about trig identities, I'd just do it with a triangle.
Draw a right angled triangle
label one of the acute angles theta,
Put 4 on the hypotenuse and 1 on the adjacent side. Now you have sec theta = 4
use pythagoras to get the other side as square root 15.
tan theta = opp/adj=root15/1 but it is in the 4th quad so it is negative
tan theta = -root15

Melody06.11.2013

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cubed root of [(x^3+3x^2-8)-x-1]=0
A cubed root is a power of 1/3

[(x^3+3x^2-8)-x-1] ^1/3 = 0

Raise both sides to the power of 3

{[(x^3+3x^2-8)-x-1] ^1/3} ³ = 0 ³

(x^3+3x^2-8)-x-1= 0

x^3+3x^2-8-x-1= 0

x^3+3x^2-x-9= 0

I can't do this, I think one of the digits is wrong. Are you sure you copied the question correctly?

Melody06.11.2013

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Now it is your turn Rosey,

John saved for a car.
He bought a car and borrowed 72% of its total value from a bank.
He borrowed $3600
He used all of his own savings for the balance. (The rest of the cost)
How much had he saved?
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Ahora es tu turno Rosey,

John guardado para un coche.
Compró un auto y pidió prestado el 72% de su valor total de un banco.
Pidió un préstamo de $3600
Él utilizó todos sus ahorros para el equilibrio. (El resto del coste)
¿Cuánto había salvado?

Melody06.11.2013

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Hi Rosey,

It is nice to hear from you again!

I think you mean something like this.
The CEO of a company owns 1800 shares and this is 60% of the whole company.
He wants to buy the rest of the shares. How many shares does he want to buy?

Well he wants to buy 40% but how much is that?
If 60% is 1800shares
then
60/60% must be 1800/60 shares (I divided them both by 60 to find 1% )
1% must be 1800/60 shares
1*40% must be 1800/60 *40 shares
40% must be 1200 shares.
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Hola Rosey,

Es lindo volver a oír de usted!

Creo que te refieres a algo como esto.
El CEO de una empresa posee acciones de 1800 y éste es el 60% de toda la empresa.
Quiere comprar el resto de las acciones. ¿Cuántas acciones quiere comprar?

Bueno que quiere comprar el 40%, pero ¿cuánto es?
Si el 60% es 1800shares
Entonces
60/60% deben ser acciones de 1800/60 (Dividí las dos por 60 a encontrar 1%)
1% debe ser 1800/60 acciones
1 * 40% deben ser 1800/60 * 40 acciones
40% debe ser 1200 acciones.

Melody06.11.2013

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Hi mimi,
I assume you mean Given f(x) = x + 2 and g(x) = x ², what is the value of f(g(x))

It is just f(g(x)) = x ² +2

You simply replace the x in the f(x) function with the value of g(x).

Melody05.11.2013

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I asssume lg2 means log base 2 that is log ₂

http://en.wikipedia.org/wiki/List_of_logarithmic_identities

lg2(x+3)-lg2(x-6)=1+lg2(x-2)-lg2(x-4)

lg2(x+3)-lg2(x-6)-lg2(x-2)+lg2(x-4) =1

lg ₂ { [(x+3)(x-4)] / [(x-6)(x-2)] } = lg ₂(2)

[(x+3)(x-4)] / [(x-6)(x-2)] = 2

etc

Melody05.11.2013

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A die is rolled 8 times. Find the probability of rolling no more than 4 sixes?

For each roll, P(6)=1/6 P(not a 6)=5/6

P of rolling r sixes in 8 rolls = 8Cr (1/6)^r * (5/6)^(8-r)

You want the probability of rolling, 0,1,2,3 or 4 sixes. Work them out seperately and add them together.

Melody05.11.2013

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Maria spent half of her weekly allowance on clothes. To earn more money her parents let her mow the lawn for $8. What is her weekly allowance if she ended with $18? Please show all the steps,

Let maria's weekly allowance be x dollars.
She spent half of it so she is left with x/2 dollars.

She earned another $8
so now she has x/2+8 dollars and we are told that this equals $18.

You can do it now I think.

Melody05.11.2013

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Š(x^3+3x^2-8)-x-1=0

What is S?

Melody05.11.2013

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Hi sws,
If there are 2 unknowns, then you need 2 equations.

Melody05.11.2013