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4 years ago

What is (-i)5? A -1 B 1 C -I D i

Mathematics

1 answer:

dezoksy [38]4 years ago

8 0

Answer:

-i^5=-i

Step-by-step explanation:

rewrite the equation ;

i^4=1

I^4 *-i = 1*-i=-i

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Find the distance between<br> -2-3i<br> and<br> 3+9i

kow [346]

Answer:

Step-by-step explanation:

We can consider the complex number $x+iy$ as point with coordinates $(x,y),$ where $x$ is real part of the complex number and $y$ is an imaginary part of the complex number.

The distance between two complex numbers is exactly tha distance between two points corresponding to each number.

$z_1=-2-3i\Rightarrow A(-2,-3)\\ \\z_2=3+9i\Rightarrow B(3,9)$

Now find the distance between A and B:

$AB=\sqrt{(-2-3)^2+(-3-9)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13\ units$

5 0

3 years ago

A fair coin is tossed three times and the events A, B, and C are defined as follows: A: \{ At least one head is observed \} B: \

Yanka [14]

Answer:

a) $P(A)=0.875$

b) $\text{P(A or B)}=0.875$

c) $\text{P((not A) or B or (not C))}=0.625$

Step-by-step explanation:

Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.

To find : The following probabilities by summing the probabilities of the appropriate sample points ?

Solution :

The sample space is

S={HHH,HHT,HTT,HTH,TTT,TTH,THH,THT}

n(S)=8

A: At least one head is observed

i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

n(A)=7

B: At least two heads are observed

i.e. B={HHH,HTT,TTH,THT}

n(B)=4

C: The number of heads observed is odd.

i.e. C={HHH,HTT,THT,TTH}

n(c)=4

a) Probability of A, P(A)

$P(A)=\frac{n(A)}{n(S)}$

$P(A)=\frac{7}{8}$

$P(A)=0.875$

b) P(A or B)

Using formula,

$\text{P(A or B)}=P(A)+P(B)-\text{P(A and B)}$

$\text{P(A or B)}=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{\text{n(A and B)}}{n(S)}$

$\text{P(A or B)}=\frac{7}{8}+\frac{4}{8}-\frac{4}{8}$

$\text{P(A or B)}=\frac{7}{8}$

$\text{P(A or B)}=0.875$

(c) P((not A) or B or (not C))

A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

not A = {TTT} = 1

B={HHH,HTT,TTH,THT}

C={HHH,HTT,THT,TTH}

not C = {HHT,HTH,THH,TTT} = 4

So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5

$\text{P((not A) or B or (not C))}=\frac{5}{8}$

$\text{P((not A) or B or (not C))}=0.625$

4 0

3 years ago

EMERGENCY A speeding ticket costs $80 plus $10 for each mile per hour over the speed limit the violator was traveling. How much

Basile [38]

Answer:

$200

Step-by-step explanation:

Fine calculated per mile = $10

Fine calculated for 'm' mile = 10 * m = 10m

Cost paid by violator = 80 + 10m

m = 12 miles

Cost paid by the violator = 80 + 10*12

= 80 + 120

= $ 200

3 0

3 years ago

8. Graph the following equation: y = x2 + 4x - 5

Dennis_Churaev [7]

Answer:

Given: y = x2 + 4x – 5

Find the following

y-intercept

x-intercepts or the zeros of the functions or roots

graph of the function, given vertex is at (-2, -9)

Solve the system of linear equations – x + 6y = 8 2x + 5y = 3

Write the names of curves, given their equations:

x2/16 + y2/9 = 1

3y = 2x + 5

(x - 5)2 + (y + 6)2 = 25

x2/16 – y2/25 = 1

y = 2x2 + 10x + 25

Write down the first five terms of the arithmetic progression with the first term 8 and common difference 7, then find the 17th

Write down the first five terms of the geometric progression with the first term 3 and common ratio 2, then find the 17th

6 0

3 years ago

The histogram represents a survey from 390 families about the number of children in each family. How many families from the surv

Mama L [17]

Answer:

There are 4 dots in categories 0 and 1; 9 dots in categories 2 and 3; and 2 dots in categories 4 and 5. The histogram with bar lengths 4, 9, and 2 is the appropriate choice.

3 0

4 years ago