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LenaWriter [7]
3 years ago
10

Geometry question,. Someone please help me!!

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
3 0

Answer:

I think its 23o

Step-by-step explanation:

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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
The radius of a circle with an area of 60 square centimeters is represented by the expression √60/π centimeters. What is another
monitta

Answer:

r= 2 √(15/π)

Step-by-step explanation:

Given that :

Area of circle =60sq cm

radius=√60/π

Area=\pi r^2\\60=\pi r^2\\\\\sqrt{\frac{60}{\pi}}=r\\\\\sqrt{\frac{15\times 4}{\pi}}=r\\2\sqrt{\frac{15}{\pi}}=r

Hence the radius can be written as 2 √(15/π)

3 0
3 years ago
Which quadratic function has a wider graph than y=2x^2?
ioda

so all those quadratics have their parent y = x², which has the graph of a "bowl".

and depending on the coefficient, the bowl is wider or not.

the larger the coefficient, the narrower the bowl, the smaller the coefficient, the wider the bowl.

well, 1/2 is smaller then 2, thus y = (1/2)x² is wider than y = 2x².

7 0
3 years ago
What is the product?<br> (38b* )-822
sergey [27]

Answer:

\boxed{\sf D)\:-24a^3b^7}

Step-by-step explanation:

\sf (3a^2b^4)(-8ab^3)

We'll use rule of exponents to simplify expression.

\sf 3^1a^2b^4(-8)^1a^1b^3

Now, use the commutative property of multiplication.

\sf 3^1(-8)^1a^2a^2b^4b^4

In order to multiply power of the same base, we add their exponents.

\sf 3^2(-8)^1a^{2+1}b^{4+3}

→ Add exponents:

\sf 3^1(-8)^1a^3b^7

→ Multiply 3* -8

\sf -24a^3b^7

__________________________________________

8 0
2 years ago
Liz wants to buy her favorite musical group's new CD. The CD costs $15.24, including tax. Liz gives the store clerk a twenty-dol
RSB [31]
$20-15.24-Your answer
8 0
2 years ago
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