член: Melody

921 Questions
34315 Answers

1739

+118723

Mathigon website

I just discovered a site called mathigon

https://mathigon.org/dashboard
прочитайте больше ..

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Melody 2 апр. 2022 г.

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604

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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. прочитайте больше ..

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Melody 16 мар. 2022 г.

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1435

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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 прочитайте больше ..

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Melody 15 мар. 2022 г.

-3

868

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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

прочитайте больше ..

Не по теме

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Melody 13 мар. 2022 г.

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WELCOME BACK CPHILL !

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Melody 11 февр. 2022 г.

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715

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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. прочитайте больше ..

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Melody 1 февр. 2022 г.

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884

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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 прочитайте больше ..

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Melody 9 янв. 2022 г.

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992

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HAPPY BIRTHDAY CHRIS!

прочитайте больше ..

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Melody 20 дек. 2021 г.

5527

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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 прочитайте больше ..

Не по теме

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Melody 4 нояб. 2021 г.

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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

Не по теме

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Melody 29 окт. 2021 г.

+118723

More information is needed

Melody13 нояб. 2013 г.

+118723

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

=ln[e^100*lne]

=ln[ (e^100)*1]

=ln e^100

=100 * lne

=100

Melody13 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

do it on a calculator

Melody12 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

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 нояб. 2013 г.

+118723

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 нояб. 2013 г.

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