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Free_Kalibri [48]
3 years ago
14

If the second question is asking us to shade

Mathematics
1 answer:
Alika [10]3 years ago
6 0

Answer:

We should shade 37 out of 100 boxes

Step-by-step explanation:

37%

Percent means out of 100

37/100

We should shade 37 out of 100 boxes

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What are the real and complex solutions of the polynomial equation? x^3-8=0. with imaginary numbers
seraphim [82]

Answer:

Solutions are 2,  -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

or 2,  -1 +  1.58 i  and -1 - 1.58i

(where the last 2 are equal to nearest hundredth).


Step-by-step explanation:

The real solution is x = 2:-

x^3 - 8 = 0

x^3 = 8

x = cube root of 8 = 2

Note that a cubic equation must have  a total of 3 roots ( real and complex in this case).  We can find the 2 complex roots by using the following identity:-

a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Here  a = x and b = 2 so we have

(x - 2)(x^2 + 2x + 4) = 0

To find the complex roots we solve x^2 + 2x + 4 = 0:-

Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2

= -1 +/- (sqrt( -10)) / 2

= -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

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cestrela7 [59]
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Write 4 1/5 as a improper fraction
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21/5

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