Trigonometry Examples

$\frac{1000 (\frac{1}{2}) t}{28} = 30$

Step 1

Cancel the common factor of $1000$ and $28$ .

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Step 1.1

Factor $4$ out of $1000 (\frac{1}{2}) \cdot t$ .

$\frac{4 (250 (\frac{1}{2}) \cdot t)}{28} = 30$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $28$ .

$\frac{4 (250 (\frac{1}{2}) \cdot t)}{4 (7)} = 30$

Step 1.2.2

Cancel the common factor.

$\frac{4 (250 (\frac{1}{2}) \cdot t)}{4 \cdot 7} = 30$

Step 1.2.3

Rewrite the expression.

$\frac{250 (\frac{1}{2}) \cdot t}{7} = 30$

Step 2

Multiply both sides by $7$ .

$\frac{250 (\frac{1}{2}) \cdot t}{7} \cdot 7 = 30 \cdot 7$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{250 (\frac{1}{2}) \cdot t}{7} \cdot 7$ .

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Step 3.1.1.1

Simplify the numerator.

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Step 3.1.1.1.1

Combine $250$ and $\frac{1}{2}$ .

$\frac{\frac{250}{2} t}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.1.2

Combine $\frac{250}{2}$ and $t$ .

$\frac{\frac{250 t}{2}}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.2

Reduce the expression by cancelling the common factors.

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Step 3.1.1.2.1

Reduce the expression $\frac{250 t}{2}$ by cancelling the common factors.

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Step 3.1.1.2.1.1

Factor $2$ out of $250 t$ .

$\frac{\frac{2 (125 t)}{2}}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.2.1.2

Factor $2$ out of $2$ .

$\frac{\frac{2 (125 t)}{2 (1)}}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.2.1.3

Cancel the common factor.

$\frac{\frac{2 (125 t)}{2 \cdot 1}}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.2.1.4

Rewrite the expression.

$\frac{\frac{125 t}{1}}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.2.2

Divide $125 t$ by $1$ .

$\frac{125 t}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.3

Cancel the common factor of $7$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{125 t}{7} \cdot 7 = 30 \cdot 7$

Step 3.1.1.3.2

Rewrite the expression.

$125 t = 30 \cdot 7$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $30$ by $7$ .

$125 t = 210$

Step 4

Divide each term in $125 t = 210$ by $125$ and simplify.

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Step 4.1

Divide each term in $125 t = 210$ by $125$ .

$\frac{125 t}{125} = \frac{210}{125}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $125$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{125 t}{125} = \frac{210}{125}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{210}{125}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $210$ and $125$ .

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Step 4.3.1.1

Factor $5$ out of $210$ .

$t = \frac{5 (42)}{125}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $5$ out of $125$ .

$t = \frac{5 \cdot 42}{5 \cdot 25}$

Step 4.3.1.2.2

Cancel the common factor.

$t = \frac{5 \cdot 42}{5 \cdot 25}$

Step 4.3.1.2.3

Rewrite the expression.

$t = \frac{42}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{42}{25}$

Decimal Form:

$t = 1.68$

Mixed Number Form:

$t = 1 \frac{17}{25}$