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IRINA_888 [86]
3 years ago
15

Please help me on this question thank u

Mathematics
1 answer:
mafiozo [28]3 years ago
5 0
System of equations:
w=(3/2)*h          (1)
w*h=54      area (2)

w=54/h substitute into (1)
54/h=3h/2
3h²=54*2
h²= 36  (we take only positive solution)
h = √36=6
h=6 in.
w=(3/2)*h=(3/2)*6= 9
w=9 in.
correct answer is D
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Answer:

1,800 ft

Step-by-step explanation:

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The equation that describes the internal angle of a regular polygon is:

A = \frac{(n-2)*180}{n}

For A = 160 degrees:

160n=(n-2)*180\\(180-160)n=360\\n=18\ sides

If each side is 100 ft long, the total distance that Rebecca has walked is:

d = 18*100\\d=1,800\ ft

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Answer:

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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.
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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
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