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GaryK [48]
3 years ago
5

Find [4(cos15° + isin15°)]^3 and express it in a + bi form.

Mathematics
1 answer:
arsen [322]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

Using De Moivre's theorem

Given

[ 4(cos15° + isin15° ) ]³, then

= 4³ [ cos(3 × 15°) + isin(3 × 15°) ]

= 64 (cos45° + isin45° )

= 64 (\frac{\sqrt{2} }{2} + \frac{\sqrt{2} }{2} i )

= 64 (\frac{\sqrt{2} }{2} (1 + i) )

= 32\sqrt{2} (1 + i)

= 32\sqrt{2} + 32\sqrt{2} i

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Simplify the expression (-7)2.<br><br><br>-14<br><br>49<br><br>-49<br><br>14<br>OwO
MissTica

Answer:

-14

Step-by-step explanation:

-7*2= -14

8 0
3 years ago
Read 2 more answers
HELP Use either law of sines or law of cosine. Need help on this problem! show work please!​
Marina86 [1]

Answer: x = 15.035677095729 approximately

Round this however you need to.

=================================================

Explanation:

I'm assuming you want to find the value of x, which your diagram is showing to be the length of segment QR.

If so, then we'll need to find the measure of angle Q first. Using the law of sines, we get the following:

sin(Q)/q = sin(R)/r

sin(Q)/PR = sin(R)/PQ

sin(Q)/13 = sin(85)/19

sin(Q) = 13*sin(85)/19

sin(Q) = 0.6816068987

Q = arcsin(0.6816068987) ... or ... Q = 180-arcsin(0.6816068987)

Q = 42.9693397461 ... or ... Q = 137.0306602539

These values are approximate.

----------------

Now if Q = 42.9693397461 approximately, then angle P is

P = 180-Q-R

P = 180-42.9693397461-85

P = 52.0306602539

Similarly, if Q = 137.0306602539 approximately, then,

P = 180-Q-R

P = 180-137.0306602539-85

P = -42.0306602539

A negative angle is not possible, so we'll ignore Q = 137.0306602539

----------------

The only possible value of angle P is approximately P = 52.0306602539

Let's apply the law of sines again to find side p, aka segment QR

sin(P)/p = sin(R)/r

sin(P)/QR = sin(R)/PQ

sin(52.0306602539)/x = sin(85)/19

19*sin(52.0306602539) = x*sin(85)

19*sin(52.0306602539)/sin(85) = x

x = 15.035677095729

This value is approximate.

Round this value however you need to.

4 0
3 years ago
Read 2 more answers
a rectangular sheet is 62cm long and 42cm wide from each of its corners a square of side 6cm is cut out and an open box is made
Alla [95]

Answer:

The volume of rectangular box is 9,000 cubic centimeters

Step-by-step explanation:

Given as :

The length of the rectangular sheet = L = 62 cm

The width of the rectangular sheet = B = 42 cm

Let The volume of rectangular box = v cubic centimeters

From each corner of sheet a square of 6 cm is cut out and an open box made

So, The length of box = L' = (L - 6 - 6)

i.e L' = (62 - 6 - 6)

Or, L' = 50 cm

Or, Length of the box = 50 cm

And The width of the box = B' = (B - 6 - 6)

i.e B' = (42 - 6 - 6)

Or, B' = 30 cm

Or width of the box = 30 cm

And,

The height of the box = H = 6 cm

∴ volume of rectangular box = Length of box × Breadth of box × Height of  box

i.e v = L' × B' × H

Or, v = 50 cm × 30 cm × 6 cm

Or, v = 9,000 cm³

So, The volume of rectangular box = v = 9,000 cm³

Hence, The volume of rectangular box is 9,000 cubic centimeters Answer

4 0
3 years ago
Please help I’m stuck
Nutka1998 [239]

Answer:

96

Step-by-step explanation:

Its a pattern :) BTW can you help with mine please

3 0
2 years ago
Please simplify this ITS URGENT !!
frutty [35]

Answer:

5 {x}^{2}  - 4x -  3

Step-by-step explanation:

(8 {x}^{2}  - 5x + 1) - (3 {x}^{2}  - x + 4) \\  = 8 {x}^{2}  - 5x + 1 -  3{x}^{2}  + x - 4 \\  = 5 {x}^{2}  - 4x - 3

5 0
3 years ago
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