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Yanka [14]
3 years ago
12

Which statement is correct? A) 13/ 3 < 4.25 < 43 /10 B) 43 /10 < 13 /3 < 4.25 C) 4.25 < 13 /3 < 43/ 10 D) 4.25

< 43 /10 < 13 /3
I NEED A CORRECT ANSWER!
Mathematics
2 answers:
gulaghasi [49]3 years ago
5 0

we will check each options

option-A:

\frac{13}{3}

we can write in decimal form

4.3333

4.333 is always greater than 4.25

this is FALSE

option-B:

\frac{43}{10}

we can write in decimal form

4.3

this is FALSE

option-C:

4.25

we can change it into decimal form

4.25

we know that

4.333>4.3

so, this is FALSE

option-D:

4.25

we can write in decimal form

and we get

4.25

so, this is TRUE

Ivan3 years ago
4 0
D. 4.25 < 43/10 < 13/3 
     
4.25   = 4.25
43/10 = 4.3
13/3   = 4.33

4.25 < 4.3 < 4.33
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Use the formula for the cosine of the difference of two angles to find the exact value of the following expression.
Zolol [24]

Answer:

Exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

Step-by-step explanation:

Given:

Cos(45° - 60°)

We have to apply the formula of cosine for difference of the two angles.

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cos(a-b)=cos(a)\ cos(b)+sin(a)\ sin(b)

Plugging the values.

⇒ cos(45-60)=cos(45)\ cos(60) + sin(45)\ sin(60)

We know that the values :

sin(45) =cos(45) = \frac{1}{\sqrt{2} }

sin(60)=\frac{\sqrt{3} }{2}  and  cos(60)=\frac{1}{2}

So,

⇒ cos(45-60)=(\frac{1}{\sqrt{2} } \times \frac{1}{2} ) + (\frac{1}{\sqrt{2} } \times \frac{\sqrt{3} }{2})

⇒ cos(45-60)=(\frac{1}{2\sqrt{2} }  + \frac{\sqrt{3} }{2\sqrt{2} })

⇒ cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )

⇒ cos(45-60)=(\frac{1+\sqrt{3} }{2\sqrt{2} } )\times \frac{2\sqrt{2} }{2\sqrt{2} }  ...<em>rationalizing </em>

⇒ cos(45-60)=\frac{2\sqrt{2} +2\sqrt{6} }{ 8}

⇒ cos(45-60)=\frac{2(\sqrt{2}+\sqrt{6})}{8}       ...<em>taking 2 as a common factor</em>

<em>⇒ </em>cos(45-60)=\frac{(\sqrt{2}+\sqrt{6})}{4}

To find the exact values we have to put the values of sq-rt .

As<em>, </em>\sqrt{2}=1.41     and   \sqrt{6} =2.44

Then

<em>⇒ </em>cos(45-60)=\frac{( 1.41+2.44)}{4}<em />

<em>⇒ </em>cos(45-60)=\frac{( 3.85)}{4}<em />

⇒ cos(45-60)=0.96

So the exact value of Cos(45° - 60°) is 0.96 using difference of two angles.

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3 years ago
8,397 divided by 27 equals ?
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