Calculus Examples

$R (52) = 18 (52) - \frac{1}{4} {(52)}^{2}$

Step 1

Simplify.

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Step 1.1

Multiply $18$ by $52$ .

$R (52) = 936 - \frac{1}{4} \cdot 52^{2}$

Step 1.2

Raise $52$ to the power of $2$ .

$R (52) = 936 - \frac{1}{4} \cdot 2704$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$R (52) = 936 + \frac{- 1}{4} \cdot 2704$

Step 1.3.2

Factor $4$ out of $2704$ .

$R (52) = 936 + \frac{- 1}{4} \cdot (4 (676))$

Step 1.3.3

Cancel the common factor.

$R (52) = 936 + \frac{- 1}{4} \cdot (4 \cdot 676)$

Step 1.3.4

Rewrite the expression.

$R (52) = 936 - 1 \cdot 676$

Step 1.4

Multiply $- 1$ by $676$ .

$R (52) = 936 - 676$

Step 1.5

Subtract $676$ from $936$ .

$R (52) = 260$

Step 2

Divide each term in $R (52) = 260$ by $52$ and simplify.

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Step 2.1

Divide each term in $R (52) = 260$ by $52$ .

$\frac{R (52)}{52} = \frac{260}{52}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $52$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{R \cdot 52}{52} = \frac{260}{52}$

Step 2.2.1.2

Divide $R$ by $1$ .

$R = \frac{260}{52}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $260$ by $52$ .

$R = 5$