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2 years ago

Find the standard form of the complex number 6(cos(30degree) +i sin (30 degree))

Mathematics

1 answer:

Marat540 [252]2 years ago

6 0

Answer:

= 3√3 + 3i

Step-by-step explanation:

Cos 30° = √3/2

Sin 30° = 1/2

Therefore;

z = 6 (cos 30° + i6 sin 30°)

= 6 (√3/2) + i 6 (1/2)

= 3√3 + 3i

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Each basketball comes in a cubic box with side lengths of 1 foot. The locker is 3 feet long, 2 feet wide, and 5 feet high. How m

LuckyWell [14K]

Answer:

30 basketballs

Step-by-step explanation:

one layer would be 3 x 2 = 6

to find how much you would need to cover the bottom of the locker, you would use the numbers 3 and 2, then multiply them and you get 6. You would need 6 basketballs to cover the bottom of the locker. That would be your first layer

5 layers would be 6 x 5 = 30

So the bottom would be filled with 6 basketballs. Now since the locker is 5 feet high multiply 6 x 5 and that would get you your total of basketballs

4 0

2 years ago

Which equation has the solutions x = -3 ± √3i/2 ?

Maurinko [17]

Answer:Answer is option C : [ $x^{2}$ + 3x + 3 ] =0

Note: None of options matches with given question.

instead of "-3" , there should be "- $\frac{3}{2}$ ".

Step-by-step explanation:

Note: None of options matches with given question.

instead of "-3" , there should be " $\frac{3}{2}$ ".

Here, First thing you have to observe the nature of roots.

∴ x = - $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i and x = - $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$

∴ [ x+( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) ][ x+( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + x( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i)+ x( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + $\frac{3}{2}$ x + $\frac{\sqrt{3}}{2}$ ix + $\frac{3}{2}$ x - $\frac{\sqrt{3}}{2}$ ix + (3- $\frac{\sqrt{3}}{2}$ i)(3+ $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{\sqrt{3}}{2}$ i)( $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{3}{4}$ ) $i^{2}$ ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ + ( $\frac{3}{4}$ ) ] =0

∴ [ $x^{2}$ + 3x + $\frac{12}{4}$ ] =0

∴ [ $x^{2}$ + 3x + 3 ] =0

Thus, Answer is option C : <em>[ $x^{2}$ + 3x + 3 ] =0 </em>

6 0

3 years ago

Steve can run 1 2/9 miles in 10 minutes. How many miles can he run in 30 minutes?

mariarad [96]

Answer:

3 2/3

Step-by-step explanation:

remember to give me brainliest cause I helped you

4 0

2 years ago

Which value of x makes the equation true?

Gnesinka [82]

Answer:

C. x=8.5

Step-by-step explanation:

-18+3x+x=-2(2x-25)

-18+4x=-4x+50

+4x +4x

-18+8x=50

+18 +18

8x=68

8 8

x=8.5

5 0

2 years ago

Point A is at (3, 2.7) and point B is at (3, 1.4) on a coordinate grid. The distance between the two points is ____. Input numbe

lisov135 [29]

The points have the same x-coordinate, so they lie on a horizontal line. The distance between them is the difference between their y-coordinates.

$2.7-1.4=1.3$

The distance between the two points is 1.3.

4 0

3 years ago

Read 2 more answers