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svet-max [94.6K]
3 years ago
5

In a bag full of smallballs 1/4 of these balls are green 1/8 are blue, 1/2 are yellow and the remaining 26 white. How many balls

are blue?
Mathematics
1 answer:
kirill [66]3 years ago
4 0

Step-by-step explanation:

Green: 1/4 = 2/8

Blue: 1/8

Yellow: 1/2 = 4/8

= 7/8

White: 1/8 = 26

Blue: 1/8 = 26

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motikmotik

Given:

There are given that the cos function:

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Explanation:

To find the value, first, we need to use the half-angle formula:

So,

From the half-angle formula:

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Then,

Since 105 degrees is the 2nd quadrant so cosine is negative

Then,

By the formula:

\begin{gathered} cos(105^{\circ})=cos(\frac{210^{\circ}}{2}) \\ =-\sqrt{\frac{1+cos(210)}{2}} \end{gathered}

Then,

Put the value of cos210 degrees into the above function:

So,

\begin{gathered} cos(105^{\circ})=-\sqrt{\frac{1+cos(210)}{2}} \\ cos(105^{\operatorname{\circ}})=-\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}} \\ cos(105^{\circ})=-\sqrt{\frac{2-\sqrt{3}}{4}} \\ cos(105^{\circ})=-\frac{\sqrt{2-\sqrt{3}}}{2} \end{gathered}

Final answer:

Hence, the value of the cos(105) is shown below:

cos(105^{\operatorname{\circ}})=-\frac{\sqrt{2-\sqrt{3}}}{2}

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