Mathematics, 30.08.2019 05:30 probablyacommunist

What to the third power is equal to 729

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If you had absolutely no idea, then you'd have roughly two choices
of how to find it:

#1). Try numbers until you find the right one.

Pick a number.
Cube it.
If you get less than 729, go back and try a bigger number.
If you get more than 729, go back and try a smaller number.
Eventually you find the right one.

Try 1.    1³ = 1 .    Too small.
Try 2.    2³ = 8 .    Still too small.
Try 5.    5³ = 125 .    Still too small.
Try 20. 20³ = 8,000. Ooops. Too big.
Try 10. 10³ = 1,000   Too big.
Try 8. 8³ = 512.     . Too small, but maybe getting close.
Try 8.5. 8.5³ = 614.125   Still too small, but very close.
Try 9.    9³ = 729 . That's it !    yay !

#2). x³ = 729

Take the log of each side: log(x³) = log(729)

   3 log(x) = log(729)

Divide each side by 3 : log (x) = (1/3) log(729)

Look up log(729) :     log(x) = (1/3) (2.86272...)

=    0.95424...
Raise 10 to the power
of each side:    10^log(x) = 10⁰·⁹⁵⁴²⁴···

   x = 8.99994...

   (That's the way it is with logs.
      They never come out even.)

Answer from: Quest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

Answer from: Quest

the answer is c.

for continuous functions, they continue in the same pattern and you have to find that pattern kinda like slope

Ineed on this ! and you . i set this for 45 points!

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