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Andreyy89
2 years ago
5

HELP HELP HELP PLEASE

Mathematics
1 answer:
Kay [80]2 years ago
8 0

Answer:

iuncheck uछन् UFC cho idol bro ici u cry

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Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b
trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) \cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}

( 2 ) \sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}

These two identities makes sin(π / 10) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and cos(π / 10) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}.

Therefore cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}. Substitute,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right]

And now simplify this expression to receive our answer,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right] = -\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i,

-\frac{3\sqrt{5+\sqrt{5}}}{4} = -2.01749\dots and \:\frac{3\sqrt{3-\sqrt{5}}}{4} = 0.65552\dots

= -2.01749+0.65552i

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}, cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}

We know that 6\sqrt{5+\sqrt{5}} = 16.13996\dots and -\:6\sqrt{3-\sqrt{5}} = -5.24419\dots . Therefore,

Solution : 16.13996 - 5.24419i

Which rounds to about option b.

7 0
3 years ago
Tickets to a baseball game are 20 dollars for an adult and 15 dollars far a student. A school bus tickets for 45 adu6and 600 stu
yulyashka [42]

Answer:The total amount of money that the school will spend for tickets is $9900

Step-by-step explanation:

Tickets to a baseball game are 20 dollars for an adult and 15 dollars for a student. A school bus tickets for 45 adults and 600 students. This means that the total amount spent by the school on adult tickets is 20 × 45 = $900

The total amount spent by the school on students tickets is 15 × 600 = $9000

The total amount of money that the school will spend for tickets will be the sum of the amount spent on adult tickets and student tickets. It becomes

900 + 9000 = $9900

4 0
3 years ago
4 diff salds 7 kinds of pizza and 6 desserts how many options
babymother [125]
I would say 168 is the answer.
8 0
3 years ago
An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die
Dahasolnce [82]

Answer:

Kindly check attached picture and explanation

Step-by-step explanation:

A.) The tree diagram is attached in the picture below.

B.) Number less than 3 :

Event A:

A = {1HH, 1HT, 1TT, 1TH, 2H, 2T}

C.)

Event B:

B = {1TT, 3TT, 5TT}

D.)

Event C:

C = {1HT, 1TH, 3HT,3TH,5HT, 5TH}

E.)  

A' = Elements not in A = number ≥ 3

A' = {3HH,3HT, 3TT, 3TH, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

Question f and G are not well formatted ;

h. Check attached picture

I) i. Are A and B mutually exclusive? Are A and C mutually exclusive? Are B and C mutually exclusive?

A and B are mutually exclusive if AnB = ∅

Check :

AnB = {1TT}

Hence, A and B are not mutually exclusive

A and C

AnC = {1HT, 1TH}

A and C are not mutually exclusive.

B and C

BnC = ∅

B and C are mutually exclusive

4 0
2 years ago
How many ten thousands in 2,689,456
pav-90 [236]
There are eight, if I'm understanding the question correctly. 8 is in the ten thousands place, at least
6 0
2 years ago
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