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marta [7]
3 years ago
13

In what direction is the line containing the point (5, 4) and (-2, 4) going?

Mathematics
1 answer:
vampirchik [111]3 years ago
7 0
The answer is going be B
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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
X+6-5=8-2 <br> x=? <br> solve the following equation. then place the correct number in the box
Valentin [98]
X
+
6
−
5
=
8
−
2

+
6
−
5
=
8
−
2
Solve
1
Subtract the numbers
x
+
6
−
5
=
8
−
2

+
6
−
5
=
8
−
2
x
+
1
=
8
−
2

+
1
=
8
−
2
2
Subtract the numbers
x
+
1
=
8
−
2

+
1
=
8
−
2
x
+
1
=
6

+
1
=
6
3
Subtract
1
1
from both sides
x
+
1
=
6

+
1
=
6
x
+
1
−
1
=
6
−
1

+
1
−
1
=
6
−
1
4
Simplify
Subtract the numbers
Subtract the numbers
x
=
5

=
5
7 0
2 years ago
Here are 10 numbers. 3 7 2 4 7 5 7 1 8 8 what is the median
klemol [59]

Answer:    7

Step-by-step explanation:

234577788

        ^

the number in the middle is 7

3 0
2 years ago
Helpppp pleaseeeeeeeeeeeeeeeeeeeee it's due at 12:00 odjsoisjsis please see helppp, with explanation pleaseee
Fudgin [204]
1) rate of change is 1
2) rate of change is 2
5 0
3 years ago
15-(37+8)÷3=<br> How do you the work for this problem?
klasskru [66]

Answer:

0

Step-by-step explanation:

P=( )

E=exponents

M/D=multiplication or division

A/S= addition or subtraction

15-(37+8)÷3

first you start out with whats inside the () which is (37+8) which equals (45)

15-(45)÷3

after you want to divide 45 by 3 which is 15

15-15

you get 0

8 0
3 years ago
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