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 ..

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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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More information is needed

Melody13.11.2013

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How do you evaluate ln(lne^(e)^(100))?

=ln[e^100*lne]

=ln[ (e^100)*1]

=ln e^100

=100 * lne

=100

Melody13.11.2013

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what is sin^-1(sin(4pi/5))

4pi/5 is in the second quadrant and sine is positive there

so sin(4pi/5) = sin (pi/5)

and sin^-1(sin(pi/5)) = pi/5

Melody13.11.2013

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consider the region bounded by f(x)= -x^2+x+6 and the x-axis. partiton into n rectangles of equal width, using their right endpoints to find their height. What is the summation that gives the area of these n rectangles?

I experimented with a much simpler problem to start with.
I let f(x)=2x
and found the area from x=2 to x=7 (above the x axis) using 4 strips
Then I went on to find n strips
then I was ready to tackle your problem

f(x)=-(x-3)(x+2) This is a concave down parabola that crosses the x axis at 3 and -2

The width of each strip is (3--2)/n = 5/n (where n is the the number of rectangles)
The right end point of each rectangle is x= -2 + (5/k) Where k can be any integer from 1 to n
The height
h = -(-2 + (5/k)-3)(-2 + (5/k)+2)
h = -(-5+(5/k))(5/k)
h = 5/k (5-5/k)

Area of each rectangle = 5/n * 5/k (5-5/k)

Area = The sum of k from 1 to n of [ 5/n * 5/k (5-5/k) ]

Area = The sum of k from 1 to n of [ (25/n*k) (5-5/k) ]

I think this is right but you had best check it very carefully.

I haven't actually plugged any numbers in to check that it works but if you divide the area into five rectangles you could see if it works for that quite easily.
If it doesn't work or you get stuck, post again, I should see you post easily enough.

Melody13.11.2013

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do it on a calculator

Melody12.11.2013

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how is the sqrt(2/2)/sqrt(2/2), 1?

Anything divided by itself is 1 (except for 0) you can't divide by 0.

Melody12.11.2013

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If someone deposits $4650 in a bank that gives 3% interest compound annually, how much money will that person have after 8 years?

"Alternate routes" as the right idea.

S = P * (1 + i ) ⁿ

where S is the future value
P is the principle which is the initial value = $4650
i is the interest rate in the compounding period (written as a fracion) = 0.03
n is the number of compounding period = 8

Melody12.11.2013

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What is the cos^-1 29/48

Make sure your calculator is in degrees mode. This is a common mistake

then enter

shift Cos (29 over 48) =

Ans : 52.83110034

press the degrees minutes and seconds button and the answer is 52degrees, 49minutes and 51.96 seconds

Melody12.11.2013

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if $516 yeilds $58 in simple interestover 6 years, what is the annual rate

P=principle=$516
I = Interest = $58
t = time = 6 years
r = rate (as a decimal)

I=Prt
58 = 516 * r * 6
58/(516*6) = r
r = 0.01873385
r = 1.873385 %

Melody12.11.2013

+118724

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First give the unknown a pronumeral. I chose N
Multiply both sides by 12 to get rid of the fraction.
Take all the x terms to one side and the non-x terms on the other side.
Factorise out the x
Divide both sides by what ever was in front of the x (the co-efficent of x)
Now you have x = a fraction with an N on the top and an N on the bottom (along with other stuff)
This can only have a solution if the denominator (bottom) is not equal to 0
forget about the top and put the bottom = 0
solve this new equation
You'll get N= something
That something is what N cannot equal if the original equation is to have a solution.

Melody12.11.2013