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Assoli18 [71]
2 years ago
11

ula1" title="(\frac{8a^{-5}b^{4} }{12a^{-6}b^{-2} })" alt="(\frac{8a^{-5}b^{4} }{12a^{-6}b^{-2} })" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Kobotan [32]2 years ago
6 0

Step-by-step explanation:

→ \frac{8 {a}^{( - 5) } {b}^{(4)}  }{12 {a}^{( - 6)} {b}^{( -  2)}  }  =  \frac{2 {a}^{(6 - 5)}{b}^{(4 + 2)} }{3}   =  \boxed{ \frac{2}{3}a {b}^{6} }✓ \\

  • <u>(2/3)ab⁶</u> is the right answer.
Dima020 [189]2 years ago
4 0
2ab6/3 is the awnser for this one
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How to simplify 4(2a)+7(-4b)+(3×c×5)
maw [93]
→ Solutions

⇒ Simplify <span><span><span>4<span>(<span>2a</span>)</span></span>+<span>7<span>(<span>−<span>4b</span></span>)</span></span></span>+<span><span>3c</span><span>(5)</span></span></span><span>⇒ </span><span><span><span><span><span>8a</span>+</span>−<span>28b</span></span>+<span>15<span>c

Answer
 </span></span></span></span><span>⇒ </span><span>8a−28b</span><span>+</span><span>15c</span>
5 0
2 years ago
Read 2 more answers
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
Answer these plssssss
blondinia [14]

Answer:

1. 8/24

2. 9/27

3. 5/15

4. 10/30

5. 2/6

6.1/3

Step-by-step explanation:

Start with 1/3 then multiply that by the number that is given.

6 0
2 years ago
Two less than 3/2 of a number (x) is more than 5 1/2
djverab [1.8K]
<h2>Answer:   (3/2)x - 2</h2>

Step-by-step explanation:

Let the number be x.

"Two less than 3/2 of a number (x)"   means    (3/2)x - 2

"is no more than"  means     "≤"

  5 1/2

* Hopefully this helps:) Mark me the brainliest:)!!!

4 0
3 years ago
What type of transformation is shown?
Blizzard [7]
Translation is shown.
3 0
3 years ago
Read 2 more answers
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