Calculus Examples

$14000 = 2400 \sqrt{25 - {(3)}^{2}} + C$

Step 1

Rewrite the equation as $2400 \sqrt{25 - {(3)}^{2}} + C = 14000$ .

$2400 \sqrt{25 - {(3)}^{2}} + C = 14000$

Step 2

Simplify each term.

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Step 2.1

Raise $3$ to the power of $2$ .

$2400 \sqrt{25 - 1 \cdot 9} + C = 14000$

Step 2.2

Multiply $- 1$ by $9$ .

$2400 \sqrt{25 - 9} + C = 14000$

Step 2.3

Subtract $9$ from $25$ .

$2400 \sqrt{16} + C = 14000$

Step 2.4

Rewrite $16$ as $4^{2}$ .

$2400 \sqrt{4^{2}} + C = 14000$

Step 2.5

Pull terms out from under the radical, assuming positive real numbers.

$2400 \cdot 4 + C = 14000$

Step 2.6

Multiply $2400$ by $4$ .

$9600 + C = 14000$

Step 3

Move all terms not containing $C$ to the right side of the equation.

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Step 3.1

Subtract $9600$ from both sides of the equation.

$C = 14000 - 9600$

Step 3.2

Subtract $9600$ from $14000$ .

$C = 4400$