Chemistry Examples

$F_{1} \cdot \cos (30) = 250$

Step 1

Divide each term in $F_{1} \cdot \cos (30) = 250$ by $\cos (30)$ .

$\frac{F_{1} \cdot \cos (30)}{\cos (30)} = \frac{250}{\cos (30)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\cos (30)$ .

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Step 2.1.1

Cancel the common factor.

$\frac{F_{1} \cdot \cos (30)}{\cos (30)} = \frac{250}{\cos (30)}$

Step 2.1.2

Divide $F_{1}$ by $1$ .

$F_{1} = \frac{250}{\cos (30)}$

Step 3

Simplify the right side.

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Step 3.1

Separate fractions.

$F_{1} = \frac{250}{1} \cdot \frac{1}{\cos (30)}$

Step 3.2

Convert from $\frac{1}{\cos (30)}$ to $\sec (30)$ .

$F_{1} = \frac{250}{1} \sec (30)$

Step 3.3

Divide $250$ by $1$ .

$F_{1} = 250 \sec (30)$

Step 3.4

The exact value of $\sec (30)$ is $\frac{2}{\sqrt{3}}$ .

$F_{1} = 250 \frac{2}{\sqrt{3}}$

Step 3.5

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$F_{1} = 250 (\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 3.6

Combine and simplify the denominator.

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Step 3.6.1

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 3.6.2

Raise $\sqrt{3}$ to the power of $1$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 3.6.3

Raise $\sqrt{3}$ to the power of $1$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 3.6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$F_{1} = 250 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 3.6.5

Add $1$ and $1$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 3.6.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 3.6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 3.6.6.3

Combine $\frac{1}{2}$ and $2$ .

$F_{1} = 250 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.6.6.4

Cancel the common factor of $2$ .

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Step 3.6.6.4.1

Cancel the common factor.

$F_{1} = 250 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.6.6.4.2

Rewrite the expression.

$F_{1} = 250 \frac{2 \sqrt{3}}{3^{1}}$

Step 3.6.6.5

Evaluate the exponent.

$F_{1} = 250 \frac{2 \sqrt{3}}{3}$

Step 3.7

Multiply $250 \frac{2 \sqrt{3}}{3}$ .

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Step 3.7.1

Combine $250$ and $\frac{2 \sqrt{3}}{3}$ .

$F_{1} = \frac{250 (2 \sqrt{3})}{3}$

Step 3.7.2

Multiply $2$ by $250$ .

$F_{1} = \frac{500 \sqrt{3}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$F_{1} = \frac{500 \sqrt{3}}{3}$

Decimal Form:

$F_{1} = 288.67513459 \dots$