27 3/10 - 12 5/9 write in old style math
2 answers:
Answer:
<em>- 15 </em>
Step-by-step explanation:
- We need to make
and
have the same denominator, or bottom half, before we can subtract them.
- In order to do this, we need to find a number that both 10 and 9 (the bottom numbers) both go into. (Hint! Multiplying them together usually helps!)
- This number is 90. (See? 10 • 9 = 90!)
- Since we multiplied 10 by 9 to get 90, we need to multiply the top (3) by 9 too, to get us
.
- We multiply
.
- Now we can subtract 27
- 27 - 12 = 15 (big numbers)
- 27 - 50 = -23 (fractions)
- Now we have - 15
If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
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Answer:
See below for all the cube roots
Step-by-step explanation:
<u>DeMoivre's Theorem</u>
Let be a complex number in polar form, where
is an integer and
. If
, then
.
<u>Nth Root of a Complex Number</u>
If is any positive integer, the nth roots of
are given by
where the nth roots are found with the formulas:
for degrees (the one applicable to this problem)
for radians
for
<u>Calculation</u>
<u />
<u>First cube root where k=2</u>
<u />
<u>Second cube root where k=1</u>
<u>Third cube root where k=0</u>
<u />
The volume as a function of the location of that vertex is
... v(x, y, z) = x·y·z = x·y·(100-x²-y²)
This function is symmetrical in x and y, so will be a maximum when x=y. That is, you wish to maximize the function
... v(x) = x²(100 -2x²) = 2x²(50-x²)
This is a quadratic in x² that has zeros at x²=0 and x²=50. It will have a maximum halfway between those zeros, at x²=25. That maximum volume is
... v(5) = 2·25·(50-25) = 1250
The maximum volume of the box is 1250 cubic units.
