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kkurt [141]
2 years ago
9

Express( (√3 +i )^60 )in polar form​

Mathematics
1 answer:
Zinaida [17]2 years 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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12 wrestlers compete in a competition. If each wrestler wrestles one match with each
malfutka [58]

Answer: 24

Step-by-step explanation: quick brain math

6 0
2 years ago
What is the volume of the cylinder? Express the answer in terms of Pi. A cylinder with a diameter of 8 centimeters and height of
zepelin [54]

Answer:

288π

Step-by-step explanation:

The equation for the volume of a cylinder is V=πr²h

So, To do this you would plug in the values that are given.

The radius would be 4 because it is half the diameter.

And the height is 18

So V=π(4)²(18)

So you just multiply the numbers and not the pi to get 288π

6 0
3 years ago
Plot and connect the points A(1,-5), B(-4,-3), C(3,-3), and find the area of the triangle it forms.
Dovator [93]

Answer:

  7 square units

Step-by-step explanation:

Two of the points are on the horizontal line y = -3, so it is convenient to call that the "base" of the triangle. The length of the base is the difference in the x-coordinates of its end points:

  b = 3 -(-4) = 7

The height is measured perpendicular to the base, so is the vertical distance from the line y=-3 to the third point. That distance is the difference between -3 and the y-coordinate of point A:

  -3 -(-5) = 2

The triangle has a base of length 7 and a height of 2. Its area is ...

  A = 1/2bh

  A = 1/2(7)(2) = 7 . . . . square units

6 0
2 years ago
(I may give brainliest) The roof of a lean-to-garden shed has a gradient of 0.35.find the height?
UkoKoshka [18]

Answer: 2.325 meters

Step-by-step explanation:

The roof of a lean-to-garden shed has a gradient of 0.35.find the height....they have given the base as 1.5m and a shorter height 1.8m its like a house

-------

It sounds like you have a right triangle with base = 1.5,

----

Use a proportion to get:

(height of that triangle)/1.5 = 35/100

height of that triangle = 1.5*0.35 = 0.5250

-----

greater height of the lean-to = 1.8 + 0.5250 = 2.325 meters

3 0
3 years ago
Read 2 more answers
Eddie walks 450.25 feet in 2.5 minutes. Which value is closest to the number of yards Eddie walks in 1 minute?
Anna71 [15]

Eddie walks 60.03 yards in 1 minute using proportion.

What is proportion?

The term proportionality refers to any relationship that has the same ratio every time. The proportional relationship between the two supplied ratios is defined by an equation. In other terms, the proportion declares that the two fractions or ratios are equal. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.

Here let us take time and distance as proportional values,

=> \frac{distance}{Time}

=> 450.25/2.5 = x/1

=> x = 180.1 feet.

To convert feet to yards divide the length by 3. then

=> 180.1/3=60.03 yards,

Therefore Eddie Walks 60.03 yards in 1 minute.

To learn more about proportion refer the below link

brainly.com/question/19994681

#SPJ1

7 0
1 year ago
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