Write in normal form 2.8 x 10⁶ ?

Mathematics

2 answers:

Genrish500 [490]3 years ago

6 0

Answer

The answer is2600000

Aliun [14]3 years ago

3 0

It would be 2,800,000

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Zadanie optymalizacyjne z matematyki. Proszę o rozwiązanie i wyjaśnienie

Yakvenalex [24]

Volume of the pyramid:

$V=\dfrac{s^2h}3$

Perimeter of the cross-section:

$40=\sqrt2\,s+2\sqrt{\dfrac{s^2}2+h^2}=\sqrt2\left(s+\sqrt{s^2+2h^2}\right)$

$\implies h=\sqrt{\dfrac{(20\sqrt2-s)^2-s^2}2}=\sqrt{400-20\sqrt2\,s}$

Area of the cross-section:

$P=\dfrac12(\sqrt2\,s)h=\dfrac{sh}{\sqrt2}$

$\implies P=\dfrac{s\sqrt{400-20\sqrt2\,s}}{\sqrt2}=s\sqrt{200-10\sqrt2\,s}$

First derivative test:

$\dfrac{\mathrm dP}{\mathrm ds}=\dfrac{20\sqrt2-3s}{\sqrt{4-\dfrac{\sqrt2}5s}}=0\implies s=\dfrac{20\sqrt2}3$

Then the height of the cross-section/pyramid is

$h=\sqrt{400-20\sqrt2\,s}=\dfrac{20}{\sqrt3}$

The volume of the pyramid that maximizes the cross-sectional area $P$ is

$V=\dfrac{\left(\frac{20\sqrt2}3\right)^2\frac{20}{\sqrt3}}3=\dfrac{16000}{27\sqrt3}$

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3 years ago

A married couple together earns 110,000 a year. The wife earns 16,000 less than twice what her husband earns.what does the husba

Alex17521 [72]

If we place what the husband earns as h and what the wife earns as w, we can begin...
w + h = 110000

but w = 2h - 16000

We can turn it into..

2h - 16000 + h = 110000

Which we can then combine into..

3h - 16000 = 110000

Add 16000 and..

3h = 126000

Divide by three...

h = 42000

(nice)

The husband earns 42,000$ a year

Bonus: The wife then earns 68,000$

42,000 (or h) + 68,000 (or w) = 110,000

Because this is the original equation, we are correct.

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What is the least common denominator (LCD)

Romashka [77]

The least common denominator is 15. The equivalent fractions would be 10/15 and 12/15.

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