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1 year ago

Express( (√3 +i )^60 )in polar form

Mathematics

1 answer:

Zinaida [17]1 year ago

4 0

Observe that

|√3 + i| = √((√3)² + 1²) = √4 = 2

and

arg(√3 + i) = arctan(1/√3) = π/6

so that

√3 + i = 2 exp(i π/6)

By de Moivre's theorem, we get

(√3 + i)⁶⁰ = 2⁶⁰ exp(i π/6 • 60) = 2⁶⁰ exp(i 10π) = 2⁶⁰

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Dolbear's law states the relationship between the rate at which Snowy Tree Crickets chirp and the air temperature of their envi

tia_tia [17]

I assume that if we write the equation in its mathematical form it will appear like this:
T = 50 + (N - 40)/4
Substituting the value of T given,
58 = 50 + (N-40)/4
The value of N from the generated equation above is equal to 72. Therefore, the Snowy Tree Crickets chirp 72 times per minute at a temperature of 58°F.

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2 years ago

Read 2 more answers

Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to

Alex Ar [27]

Answer:

About 376.99 cubic inches

Step-by-step explanation:

Cylinder has a volume of:

$V=\pi r^2h$

Where

V is the volume

r is the radius

h is the height

We need to find the volume of the cylinder, then multiply that answer by 3/4 to get the solution to this problem. First, the full volume of the cylinder.

Given

r = 4

h = 10

So,

$V=\pi r^2h\\V=\pi (4)^2 (10)\\V=502.65$

Now, we multiply by 3/4:

$502.65*\frac{3}{4}=376.99$

Mary should be vase to 376.99 cubic inches

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2 years ago

Original price of a soda: $800 tax 7% selling price: $

Kobotan [32]

Answer:

$856

Step-by-step explanation:

Find 7% of $800 and then add it to $800

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3 years ago

!!!!!! URGENT PLS HELP ME ANSWER !!!!

laila [671]

Answer:

1) A = 547.1136, C = 82.896

2) A = 678.5226, C = 92.316

3) A = 844.5344, C = 102.992

4) A = 1554.49625, C = 139.73

5) A = 1561.4906, C = 140.044

6) A = 994.8776, C = 111.784

Step-by-step explanation:

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{26.4}{2})^2 = 3.14 * 13.2^2 = 547.1136$

$C = \Pi D = 3.14 * 26.4 = 82.896$

$A = \Pi r^2 = 3.14*(14.7)^2 = 678.5226$

$C = 2\Pi r = 14.7*2 * 3.14 = 92.316$

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{32.8}{2})^2 = 3.14 * 16.4^2 = 844.5344$

$C = \Pi D = 3.14 * 32.8 = 102.992$

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{44.5}{2})^2 = 3.14 * 22.25^2 = 1554.49625$

$C = \Pi D = 44.5*3.14 = 139.73$

$A = \Pi r^2 = 3.14*22.3^2 = 1561.4906$

$C = 2\Pi r = 2 * 3.14 * 22.3 = 140.044$

$A = \Pi r^2 = 3.14 * 17.8^2 = 994.8776$

$C = 2\Pi r = 2 * 3.14 * 17.8 = 111.784$

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2 years ago

How do i write 12.009 in a word form?

tia_tia [17]

Your answer will be twelve and nine thousandths because in place value decimals are like tenths, hundredths, thousandths. In place value for regular numbers are ones, tens, hundreds and so on. So, when you have 12.009, you are going to separate the decimals with the numbers. Then, write down the number in words which would be twelve. Now, go to the decimal and write that down, which is 9 thousandths. Finally, combine the both of them to get: twelve and nine thousandths.

Hope this helps :)
and good luck

5 0

2 years ago

Express( (√3 +i )^60 )in polar form​

Express( (√3 +i )^60 )in polar form