Precalculus Examples

$h (300) = \frac{- 32 x^{2}}{140^{2}} + 300$

Step 1

Replace the variable $x$ with $300$ in the expression.

$h (300) = \frac{- 32 {(300)}^{2}}{140^{2}} + 300$

Step 2

Simplify the result.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Raise $300$ to the power of $2$ .

$h (300) = \frac{- 32 \cdot 90000}{140^{2}} + 300$

Step 2.1.2

Raise $140$ to the power of $2$ .

$h (300) = \frac{- 32 \cdot 90000}{19600} + 300$

Step 2.1.3

Multiply $- 32$ by $90000$ .

$h (300) = \frac{- 2880000}{19600} + 300$

Step 2.1.4

Cancel the common factor of $- 2880000$ and $19600$ .

Tap for more steps...

Step 2.1.4.1

Factor $400$ out of $- 2880000$ .

$h (300) = \frac{400 (- 7200)}{19600} + 300$

Step 2.1.4.2

Cancel the common factors.

Tap for more steps...

Step 2.1.4.2.1

Factor $400$ out of $19600$ .

$h (300) = \frac{400 \cdot - 7200}{400 \cdot 49} + 300$

Step 2.1.4.2.2

Cancel the common factor.

$h (300) = \frac{400 \cdot - 7200}{400 \cdot 49} + 300$

Step 2.1.4.2.3

Rewrite the expression.

$h (300) = \frac{- 7200}{49} + 300$

Step 2.1.5

Move the negative in front of the fraction.

$h (300) = - \frac{7200}{49} + 300$

Step 2.2

To write $300$ as a fraction with a common denominator, multiply by $\frac{49}{49}$ .

$h (300) = - \frac{7200}{49} + 300 \cdot \frac{49}{49}$

Step 2.3

Combine $300$ and $\frac{49}{49}$ .

$h (300) = - \frac{7200}{49} + \frac{300 \cdot 49}{49}$

Step 2.4

Combine the numerators over the common denominator.

$h (300) = \frac{- 7200 + 300 \cdot 49}{49}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $300$ by $49$ .

$h (300) = \frac{- 7200 + 14700}{49}$

Step 2.5.2

Add $- 7200$ and $14700$ .

$h (300) = \frac{7500}{49}$

Step 2.6

The final answer is $\frac{7500}{49}$ .

$\frac{7500}{49}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{7500}{49}$

Decimal Form:

$153.06122448 \dots$

Mixed Number Form:

$153 \frac{3}{49}$

Step 4