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Maksim231197 [3]
2 years ago
9

The weight of 10 identical samples of a substance is 0.01 pound. what is the weight of 10000 samples?

Mathematics
1 answer:
Licemer1 [7]2 years ago
3 0
The answer is 10 pounds.

I set up a proportion of 10 / 0.01 = 10000 / x. 

Cross-multiply to get 10x = 10000(0.01). Simplify to get 10x = 100. Divide by 10 to isolate the variable. 

x = 10. 10000 samples would weigh 10 pounds. 

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motikmotik

Given:

There are given that the cos function:

cos210^{\circ}=-\frac{\sqrt{3}}{2}

Explanation:

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

So,

From the half-angle formula:

cos(\frac{\theta}{2})=\pm\sqrt{\frac{1+cos\theta}{2}}

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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7 0
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