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Mamont248 [21]
3 years ago
8

nelson got a pack of 12 pencils he took 3 pencils to pit in his desk at school and 2 pencils to put in his locker at school. wha

t is the fraction of total pencils that nelson took to school
Mathematics
2 answers:
g100num [7]3 years ago
6 0
 the fraction of pencils he took to school is 
5/12
sattari [20]3 years ago
4 0
Nelson took a total of 5 pencils to school and he bought 12 so the fraction would be 5 over 12
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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.

Formula:

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.

3 0
3 years ago
What is the length of side AB with endpoints<br> A(–5, 3) and B(4, 3)? units
padilas [110]

Answer:

9 units

Step-by-step explanation:

7 0
3 years ago
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Ethan forgot the four-digit code to the lock on his briefcase. However, he did remember that the first digit is 9 and the last d
gogolik [260]
We've got the first number, so now we need the others.
There is 1 possibilty for the first digit, 10 for the middle ones, and 2 for the last one.
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Does anybody know the graph ?
navik [9.2K]
Y= 1/2x is the answer
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4 years ago
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Please help if i don't pass I'm done
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5 x 10 x 15 =750
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