Ask question

Ask question

All categories

Mekhanik [1.2K]

3 years ago

14

Write each complex number in rectangular form.

1 answer:

hram777 [196]3 years ago

4 0

Hello,

A)
cos 135°=- cos 45°=-√2/2
sin 135°=sin45°=√2/2
2(cos 135°+i sin 135°)=-√2 + i*√2

B)
cos 120°=-cos 30°=-√3 /2
sin 120°=sin 30°=1/2

3(cos 120° + i sin 120)=-3/2*√3 +i*3/2

C)
cos (5π/4)=-cos (π/4)=-√2 /2
sin (5π/4)= -sin(π/4)=-√2 /2
5(cos (5π/4)+i sin (5π/4))=-5/2*√2 +i *5/2*√2

D)
cos(5π/3)=cos(π/3)=√3 /2
sin (5π/3)=-sin(π/3)=-1/2

4(cos(5pi/3)+i sin (5pi/3))
=2√3- 2*i

You might be interested in

The triangle below is equilateral. Find the length of side x in simplest radical form

Molodets [167]

Answer:

4sqrt(3)

Step-by-step explanation:

If the triangle is equilateral, the hypotenuse is 2x

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (2x)^2

x^2 + 144 = 4x^2

144 = 4x^2 -x^2

144 = 3x^2

48 = x^2

Taking the square root of each side

sqrt(48) = sqrt(x^2)

sqrt(16*3) = x

4 sqrt(3) =x

6 0

3 years ago

If events A and B are mutually exclusive, P(A or B) = 0.5, and P(B) = 0.3; then what is P(A)?

11Alexandr11 [23.1K]

Answer:

$P(A) = 0.2$

Step-by-step explanation:

We have that:

$P(A) = P(a) + P(A \cap B)$

In which P(a) is the probability of a but not b and $P(A \cap B)$ is the probability of both A and B.

By the same logic, we have that:

$P(B) = P(b) + P(A \cap B)$

Also

P(A or B) is

$P(A \cup B) = P(a) + P(b) + P(A \cap B)$

Events A and B are mutually exclusive

This means that $P(A \cap B) = 0$

$P(B) = 0.3 = P(b)$

$P(A \cup B) = P(a) + P(b) + P(A \cap B)$

$0.5 = P(a) + 0.3$

$P(a) = 0.2$

$P(A) = P(a) + P(A \cap B) = 0.2 + 0 = 0.2$

4 0

4 years ago

A cylinder has a height of 13 millimeters and a radius of 17 millimeters what is is volume?

Rus_ich [418]

Answer:

11802.96

explanation:

5 0

2 years ago

Translate the sentence and solve: "2 less than a number is 25"

Salsk061 [2.6K]

(the number) - 2 = 25

(the number) = 25 + 2
(the number) = 27

3 0

3 years ago

Read 2 more answers

Lulu is taking a road trip to visit family. Her car has a 20-gallon gas tank and the car uses 12 gallons to travel 216 miles.

Diano4ka-milaya [45]

Answer:

<u>The answer is G = 20 - m/18, but none of the answers given is correct.</u>

Step-by-step explanation:

1. Let's review the information given to us to help Lulu to answer the question correctly:

Capacity of the gas tank of Lulu's car = 20 gallons

Lulu can travel 216 miles using 12 gallons

2. Which linear equation represents the number of gallons of gas, G, left in the tank after driving m miles?

G = number of gallons left in Lulu's car

m = Miles driven by Lulu

miles per gallon = 216/12 = 18 miles per gallon

Now, we can write the linear equation, this way:

G = Capacity of the gas tank of Lulu's car - miles driven/miles per gallon

Replacing with the values we know:

<u>G = 20 - m/18</u>

Let's assume Lulu drives 180 miles, using our linear equation, we have:

G = 20 - 180/18

G = 20 - 10 = 10 gallons left

Let's assume Lulu drives 54 miles, using our linear equation, we have

G = 20 - 54/18

G = 20 - 3 = 17 gallons left

8 0

3 years ago