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frosja888 [35]
2 years ago
9

Riley rakes 1/6 of a lawn in 2/3 hour. How many lawns can Riley rake per hour?

Mathematics
1 answer:
sergey [27]2 years ago
4 0
3/6 or 3/3 maybe I’m not sure
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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
Which number completes this number sentence? [ ? ] &gt; -6<br> A.-8<br> B.-7<br> C.-6<br> D.0
Xelga [282]

Answer:

It is 0

Step-by-step explanation:

Unlike the positive side of the number line which increases its value as it goes up in numbers, the negative side of a number line increases its value as it goes goes down in numbers as the more closer a negative number is to the positive side of infinity, the greater value it has. In this instance, zero is the greater number than -6 and all other negative numbers.

8 0
3 years ago
I need help with this question
Rama09 [41]

Answer:

G

Step-by-step explanation:

An integer is a whole number. Round each of your answers to the nearest tenth (for the 5's, you round up), and you see that choice G, 5.5, can be divided by 1.1 to equal 5.

6 0
3 years ago
Read 2 more answers
Can someone please help
Sonja [21]

Answer:

i have no idea lol make it more clearer

6 0
3 years ago
A bank loaned out $21,500 , part of it at the rate of 11% annual interest, and the rest at 10% annual interest. The total intere
Luda [366]

Answer:

The loaned amount at 11 % is $ 19,000

The loaned amount at 10 % is $ 2,500

Step-by-step explanation:

Given as :

The total loan amount = $21,500

The total interest earn = $2,340.00

The rate of interest are 11 %  and 10 %

Let The loan amount at 11 % rate = $P

and The loan amount at 10 % rate = $21,500 - $P

Let The loan took for 1 year

Now,<u> From Simple Interest method </u>

Simple Interest = \dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}

SI_1 = \dfrac{P_1\times R_1\times \textrm Time}{100}

Or, SI_1 = \dfrac{P\times 11\times \textrm 1}{100}

Similarly

SI_2 = \dfrac{21,500 - P\times 10\times \textrm 1}{100}

∵  SI_1 +  SI_2 =  $2,340

Or, \dfrac{P\times 11\times \textrm 1}{100} + \dfrac{21,500 - P\times 10\times \textrm 1}{100} = $2,340

Or, 11 P - 10 P + 215000 = 234000

Or, P = 234000 - 215000

∴ P = $ 19,000

And $21,500 - $ 19,000 = $ 2,500

Hence The loaned amount at 11 % is $ 19,000

And     The loaned amount at 10 % is $ 2,500    Answer

8 0
3 years ago
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