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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suppose that p is invested in a savings account in which interest k, is compounded continuously at 3% per year. What is the exponential growth function in terms of P and 0.03?
b) if $6000 is invested what is the balance after 4 years?
c) when will an investment of $6000 double itself?
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I am going to re-word your question a little.
Suppose that P is invested in a savings account at 3% p.a. interest, compounding annually. (the interest is added at the end of each year)
I am going to call the future value S (in my experience S is the standard letter used for future value.)
I am going to let the number of years invested be n

a) S = P * 1.03 ⁿ

b) S = 6000 * 1.03 ⁴
you can finish this one.

c) 2P = P * 1.03 ⁿ
2 = 1.03 ⁿ
log 2 = log 1.03 ⁿ
log 2 = n*log1.03
n = log2 / log1.03
n = 23.449 years
Since the interest is added at the end of the year it will be doubled in 24 years (It will be a little more than double at this time)

Melody05.12.2013

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what is the solution of
y=8x+4 y=2(x+5)

you have to put

8x + 4 = 2(x + 5)
solve for x
then substitute the x value into one of the original equations and solve for y

Melody05.12.2013

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Dax opens a new box of chocolate. There is a total of 60 pieces inside of 3 types of flavours: white, milk, and dark chocolate. 30% is white, 60% is milk, and 10% is dark. Dax eats 2 chocolates how many pieces of each chocolate are left in the box?

That would depend on which type of chocolates that Dax ate.

Melody05.12.2013

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2+4+6+8+......+200=

This is an arithmetic progression AP for short

a = 2
d=2
n=100
s _n= n/2[a+T ₁₀₀]

sum = 50(2+200) = 50*202 = 10100

Melody05.12.2013

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Solve 12cosx-5sinx=4 for 0<x<90

You have to divide everything by sqrt(12 ²+5 ²) = 13
so
12/13 * cosx - 5/13 * sinx = 4/13

The reason that this is useful is that 5, 12, 13 is a pythagorean triad. (Draw the triangle, it will help you understand)
And I know that

sin(theta)cos(x) - cos(theta)sin(x) = sin(theta - x)
so
If sin(theta)=12/13, then cos(theta) has to equal 5/13 (put theta on your triangle and convince yourself that this is true)

also theta = sin ^-1(12/13) = 67.380 degrees
NOW

12/13 * cosx - 5/13 * sinx = 4/13

sin(67.380)*cosx - cos(67.380)*sinx = 4/13

sin (67.380 - x) = 4/13

sin ^-1(4/13) = 67.380 - x

17.920 = 67.380 - x

x = 67.380 - 17.920

x = 49.46 = 49 degrees (to the nearest degree.)

Melody05.12.2013

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what is the answer and what are the steps
(7+x)/3=8

multiply both sides by 3
then
subtract 7 off both sides.

Melody05.12.2013

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By putin in the angle and then pressing inv tan

Melody05.12.2013

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It is probably more important that you remember why!

Remember

cosine is adjacent / hyptotenuse

sine is opposite over hypotenuse

The hyptoenuse HAS to be the longest side so sine and cosine have to be between 0 and 1 (for first quadrant)
In the other quadrants only the sign changes.

So sine and cos have to be between -1 and 1.

Hope that helps Special.

Melody05.12.2013

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It is probably more important that you remember why!

Remember

cosine is adjacent / hyptotenuse

sine is opposite over hypotenuse

The hyptoenuse HAS to be the longest side so sine and cosine have to be between 0 and 1 (for first quadrant)
In the other quadrants only the sign changes.

So sine and cos have to be between -1 and 1.

Hope that helps Special.

Melody05.12.2013

+118725

0

I've never had a calulator that allows this.
If I wanted to put the exact value of 0.333333.... in I would put in 1/3

A question for Special,
What kind of calculator do you have?
Melody.

Melody05.12.2013