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3 years ago

Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours have they worked?

1 answer:

7 0

The common denominator of these fractions will be 12. So Ann worked 306/12 hours, Mary worked 244/12 hours, and John worked 123 hours, meaning they have worked 673/12 hours together.

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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

3 years ago

Help pls ;) 9 points :0

zavuch27 [327]

I believe it’s b- it might not be correct I believe

6 0

3 years ago

Which of the following IS the graph of y = -(x-2)/3 -5?

stepladder [879]

.............................Answer:

3 0

3 years ago

Use the equation below to find y, if m=2, x=8, and b=3.

Blizzard [7]

Answer:

y = 19

Step-by-step explanation:

Plug in the values

y = 2*8 + 3

y= 16+3

y= 19

5 0

2 years ago

Read 2 more answers

Find the slope of the line that contains (−7,−1) and (−7,9).

Nitella [24]

Answer:

undefined

Step-by-step explanation:

Slope = y - y / x - x

9 - (-1) / -7 - (-7)

= 9 + 1 / -7 + 7

= 10 / 0, undefined.

Cannot divide by zero.

7 0

3 years ago

Read 2 more answers