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valentina_108 [34]
2 years ago
11

Answer numbers 16-18

Mathematics
1 answer:
lana66690 [7]2 years ago
4 0
Number 16- 216
number 17- 180
number 18- 252
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All the cubes root of <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B3%20%2B%20i%7D%20" id="TexFormula1" title=" \sqrt{3 + i
melisa1 [442]

If you're looking for the cube roots of √(3 + <em>i </em>), you first have to decide what you mean by the square root √(…), since 3 + <em>i</em> is complex and therefore √(3 + <em>i </em>) is multi-valued. There are 2 choices, but I'll stick with 1 of them.

First write 3 + <em>i</em> in polar form:

3 + <em>i</em> = √(3² + 1²) exp(<em>i</em> arctan(1/3)) = √10 exp(<em>i</em> arctan(1/3))

Then the 2 possible square roots are

• √(3 + <em>i</em> ) = ∜10 exp(<em>i</em> arctan(1/3)/2)

• √(3 + <em>i</em> ) = ∜10 exp(<em>i</em> (arctan(1/3)/2 + <em>π</em>))

and I'll take the one with the smaller argument,

√(3 + <em>i</em> ) = ∜10 exp(<em>i</em> arctan(1/3)/2)

Then the 3 cube roots of √(3 + <em>i</em> ) are

• ∛(√(3 + <em>i</em> )) = ¹²√10 exp(<em>i</em> arctan(1/3)/6)

• ∛(√(3 + <em>i</em> )) = ¹²√10 exp(<em>i</em> (arctan(1/3)/6 + <em>π</em>/3))

• ∛(√(3 + <em>i</em> )) = ¹²√10 exp(<em>i</em> (arctan(1/3)/6 + 2<em>π</em>/3))

On the off-chance you meant to ask about the cube roots of 3 + <em>i</em>, and not √(3 + <em>i </em>), then these would be

• ∛(3 + <em>i</em> ) = ⁶√10 exp(<em>i</em> arctan(1/3)/3)

• ∛(3 + <em>i</em> ) = ⁶√10 exp(<em>i</em> (arctan(1/3)/3 + 2<em>π</em>/3))

• ∛(3 + <em>i</em> ) = ⁶√10 exp(<em>i</em> (arctan(1/3)/6 + 4<em>π</em>/3))

3 0
2 years ago
What is 9962 divided by 41
ruslelena [56]
9962 divided by 41 is 242.98.
3 0
2 years ago
Uggh!! help pls last question
RideAnS [48]

Answer:

The answer is 46.

Step-by-step explanation:

You have to substitute the value of a and c into the expression :

a + 9c

Let a = 10,

Let c = 4,

10 + 9(4)

= 10 + 36

= 46

8 0
3 years ago
Read 2 more answers
In Mark's collection of antique bottles, 1 over 2 of of the bottles are dark green. Write three equivalent fractions for 1 over
dalvyx [7]

Answer:

2/4, 3/6, and 4/8

Step-by-step explanation:

Equivalent fractions are made by multiplying the numerator and denominator by the same factor.

For 1/2, you can multiply the top and bottom by 2, 3, or 4 to get 2/4, 3/6, and 4/8 respectively.

3 0
3 years ago
Round off - 126,945 to the nearest hundred thousand nearest ten thousand nearest thousand which of these rounds amount to the cl
VARVARA [1.3K]
100,000 30,000 7,000

the first one i believe
5 0
3 years ago
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