All categories

2 years ago

PLEASE HELP ME! Find the cube roots of 125(cos 288° + i sin 288°).

1 answer:

6 0

◆ COMPLEX NUMBERS ◆

125 ( cos 288 + i sin 288 ) can be written as -

125.e^i( 288)
125.e^i( 288 +360 )
125.e^i( 288+ 720)

[ As , multiples of 360 can be added to an angle without changing any trigonometric functions or sign ]

To find the cube root , take the cube root of above 3 expressions ,

We get -
5 e^( i 96 )
5 e^( i 216 )
5 e^( i 336 )

Now using Euler's formula , We rewrite above as -

5 ( cos 96 + i sin 96 )
5(c os 216 + i sin 216 )
5 ( cos 336 + i sin 336 ) Ans.

You might be interested in

Counting from 1 to 46, how many 4s will you encounter? 8 10 11 12 14

Ray Of Light [21]

Answer:

Step-by-step explanation:

4=1

14=2

24=3

34=4

40=5

41=6

42=7

43=8

44=9

45=10

46=11

You will encounter 11 4s.

5 0

2 years ago

Bernardo and Ogechi were asked to find an explicit formula for the sequence 1\,,\,8\,,\,64\,,\,512,...1,8,64,512,...1, comma, 8,

MatroZZZ [7]

Answer:

$h_{n}=1.(8)^{n-1}$ will be the correct formula for the given sequence.

Step-by-step explanation:

The given sequence is 1, 8, 64, 512...........

The given sequence is a geometric sequence having a common ratio (r) of

r = $\frac{\text{Second term}}{\text{First term}}$

r = $\frac{8}{1}=8$

Since explicit formula of a geometric sequence is given by

$T_{n}=a(r)^{n-1}$

where $T_{n}$ = nth term of the sequence

a = first term of the sequence

r = common ratio of the successive term to the previous term

Now we plug values of a and r in the formula to get the explicit formula for the given sequence.

$T_{n}=1.(8)^{n-1}$

Therefore, if Bernardo is saying that the formula of the sequence is

h(n) = $1.(8)^{n-1}$ then he is correct.

7 0

2 years ago

Read 2 more answers

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin

djyliett [7]

Answer:

A) (7.6, 8.8)

which are the coordinates of the treasure.

Missing Problem Statement:

Given Options:

A) (11.4, 14.2)

B) (7.6, 8.8)

C) (5.7, 7.5)

D) (10.2, 12.6)

I have added the picture showing the traced map onto a coordinate plane to find exact location of treasure.

The coordinates of Tree are (16,21)

Coordinates of rock are (3,2)

Step-by-step explanation:

Let,

Coordinates of treasure be (a,b)

$d_{1}$ = distance from tree to treasure

$d_{2}$ =distance from rock to treasure

$d_{1}=\sqrt{(16-x)^2 + (21-y)^2}$

$d_{2}=\sqrt{x\2 + (y-2)^2}$

Given ratio between rock and tree, $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55_______(Equation.1)

which will be used to locate the treasure.

Now we just need to cross check by putting the coordinates given in the options one by one to find out value of $d_{1}$ , $d_{2}$ and checking if it satisfies the Equation 1.

Check (A) (11.4, 14.2)

$d_{2}$ = 14.8, $d_{1}$ = 8.2,

$\frac{d_{2}}{ d_{1}}$ = 1.8