Please help! 20 pts.

Mathematics

2 answers:

Daniel [21]3 years ago

5 0

Your answer would be the last option, 80 cm.

As this is a right triangle, you can use Pythagoras's Theorem, a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the legs, to find the missing side.

This gives us:

48² + 64² = 2,304 + 4,096 = 6,400
√6,400 = 80

So 80 is your answer.

I hope this helps!

Gnesinka [82]3 years ago

5 0

the answer would be 80. i think.

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Which of the following is a solution of z^5 = 1 + √3 i?

nordsb [41]

Answer:

Option 2 is right

Step-by-step explanation:

Given that

$z^5=1+\sqrt{3} i$

We can write this in polar form with modulus and radius

$|z^5|= \sqrt{1+3} =2\\tan of Angle t =\sqrt{3} \\$

Hence angle = 60 degrees and

$|z^5|= 2(cos60+isin60)$

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360

Using Demoivre theorem we get 5th root would be

5th root of 2 multiplied by 1/5 th of 60, 420, 780,....

$z= \sqrt[5]{2} (cos12+isin12)\\z=\sqrt[5]{2} (cos84+isin84)\\\\z=\sqrt[5]{2} (cos156+isin156)\\\\z=\sqrt[5]{2} (cos228+isin228)\\\\z=\sqrt[5]{2} (cos300+isin300)\\$