Archive for category Blogini

Infinite serie of powers

Olkoon seuraava yhtälö:

Miten sen voisi ratkaista?

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How old is what

Those big numbers are bit hard to grasp, so lets make analogy.

Lets say that earth is one day old. I mean that it started to exist about 7AM in the morning and now is 6PM in the evening.

0700 and 1800 respectively. It makes 11 hours, or 11*60=660 minutes, 11*60*60=39600 seconds.

Perfect. Google implies that 4.543 billion years old. 4.543 billion is 4.543*10^9 years. That is 4 543 000 000 years.

Ok. Now we have relation 39600 seconds=4 543 000 000 years. Let X=39600/4543000000 s/y

Lets see when universe started to exist. Google implies that universe is 13.799*10^9

So – universe*x=120627.01s, thus universe started to exist 120000 seconds ago, this is about 1.4 days ago, or even better 33 hours ago, assuming now is 18:00 – that is about 09:00 on a previous day.

Let us see when dinosaurs became extinct. Google implies 65 million years ago. That is 65000000 years. Or in our analogy – less then 10 minutes ago.

When did life appeared on earth? Google implies 3.5*10^9 years ago.. That is less than 9 hours ago, or on our scale – somewhere in between of 11:00-12:00

How long human existed?  Let us take oldest number – 450 000 years. That is less than 4 seconds ago.vert

Let us draw those things

 

Pyramidi 10, Lukio integraalilaskenta, 241

a)
b)
c)

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Pyramidi 10, Lukio integraalilaskenta, 240

a)
b)
c)

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Pyramidi 10, Lukio integraalilaskenta, 238

a)
b)
c)

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Implisiittinen derivointi

Olkoon yhtälö .

Määritä arvoa vastavien pisteiden , ja kautta kulkevien ratkaisukäyrien tangenttien kulmakertoimet.

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Ratkaise yhtälo (Suomi24)

 

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Ratkaise yhtälö (Suomi24)

Ratkaise yhtälö

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Ratkaise x kaikilla klla (Suomi24)

Ratkaise yhtälö vakion kaikilla arvoilla.

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Lukion matematiikka ratkaisuja

Pulmatehtävä? Ota yhteyttä, yritä kertoa tehtävästä selkeästi tai ota kuva tehtävän paperista.

Olen hyvin varma että osan auttaa (lukio, pitkä/lyhyt)matematiikan kanssa.

Voi toki kysyä kemiasta tai fyysikasta, mutta ratkaisun saaminen on vähemmän todennäköistä.

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