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cricket20 [7]
3 years ago
9

2. El cociente de 15 y un número.

Mathematics
1 answer:
GuDViN [60]3 years ago
8 0

Answer:y

Step-by-step explanation:

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Which expression is a cube root of -1+i√3?
Tpy6a [65]

Answer:

<em>The correct option is C.</em>

Step-by-step explanation:

<u>Root Of Complex Numbers</u>

If a complex number is expressed in polar form as

Z=(r,\theta)

Then the cubic roots of Z are

\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)

\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)

\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)

We are given the complex number in rectangular components

Z=-1+i\sqrt{3}

Converting to polar form

r=\sqrt{(-1)^2+(\sqrt{3})^2}=2

\displaystyle tan\theta=\frac{\sqrt{3}}{-1}=-\sqrt{3}

It's located in the second quadrant, so

\theta=120^o

The number if polar form is

Z=(2,120^o)

Its cubic roots are

\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)

\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)

\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)

Converting the first solution to rectangular coordinates

z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)

The correct option is C.

8 0
4 years ago
In a city school of 900 students, 38% of the students are on the honor roll
Vera_Pavlovna [14]

Answer:

if the question is what number of 38 percent, then the answer is 342

7 0
3 years ago
Can you represent the data with an equation? If so write the equation.
dlinn [17]

• Use slope to graph linear equations in two variables. • Find the slope of a line given two points on the line. • Write linear equations in two variables. • Use slope to identify parallel and perpendicular lines. • Use slope and linear equations in two variables to model and solve real-life problems. 2

6 0
4 years ago
HALP I GiVE BRAINLIST
Dmitry [639]

Answer:

8 ÷ 3

Step-by-step explanation:

2\frac{2}{3} = \frac{8}{3}

 \frac{8}{3} = 8 ÷ 3

 

5 0
3 years ago
Read 2 more answers
A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some ty
Sophie [7]

Answer:

The  interval is  0.7187  < p < 2.421

Step-by-step explanation:

From the question we are told that

      The  sample size is  n  = 100

       The  population  proportion is p  =  0.81

       The  confidence level is  C =  98%

The level of significance is mathematically evaluated as

     \alpha  =  100 -98

    \alpha  =  2%%

    \alpha  =  0.02

Here this level of significance represented the left and the right tail

The degree of  freedom is evaluated as

     df =  n-1

substituting value  

    df =  100 - 1

     df = 99

Since we require the critical value of one tail in order to evaluate the  98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The  critical value of  \frac{\alpha}{2} and the evaluated degree of freedom is  

      t_{df , \alpha } =  t_{99 , \frac{0.02}{2}  }  = 2.33

this is obtained from the critical value table  

The standard error is mathematically evaluated as

             SE =  \sqrt{\frac{p(1-p )}{n} }  

substituting value  

           SE =  \sqrt{\frac{0.81(1-0.81 )}{100} }  

           SE = 0.0392  

The 98%  confidence interval is evaluated as

      p  - t_{df ,  \frac{\alpha }{2} } *  SE  < p <  p  + t_{df ,  \frac{\alpha }{2} }

substituting value  

     0.81  - 2.33  *  0.0392  < p <  0.81  +2.33 *  0.0392

      0.7187  < p < 2.421

     

4 0
3 years ago
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