You have been assigned a 9-digit identification number. How many identification numbers are possible?

1 answer:

3 0

Permutations are all possible variations, in which a set of numbers or characters can be ordered. The number of permutations on a set of n elements is given by n!. In our case we have 9 digits, which means 9 elements.
There are 9!=9*8*7*6*5*4*3*2*1=362880 possible variations, or 362880 possible identification numbers.

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Answer:

Step-by-step :

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Given that the volume of the aquarium is 20m^3.

Volume = Area of Base x height

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Area of the four side faces of the aquarium is 4 times the length of the base times the height = $4\times\sqrt{ \frac{20}{h} }\times h=\sqrt{16\left(\frac{20}{h}\right)h^2}=\sqrt{320h}$

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Cost of the entire metal frame = $7\left(\sqrt{\frac{1,280}{h}}+4h\right)= \sqrt{49\left(\frac{1,280}{h}\right)}+7(4h) = \sqrt{\frac{62,720}{h}}+28h$

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