Q54. - Algebra 2

Question

FIREWORKS 

Suppose you are about a mile from a firework display. You count 5 seconds between seeing the light and hearing the sound of the firework display. You estimate the viewing angle is about $4°$. Using the information at the left, estimate the width of the firework display.

Information at the left

To estimate the width $w$ in feet of a firework burst, use the formula $w=20At$. In this formula, $A$ is the estimated viewing angle of the firework display and $t$ is the time in seconds from the instant you see the light until you hear the sound.

Step-by-Step Solution

Answer

The width of the firework display is 400 feet

Step 1 - Substitute given values

Substitute $4°$ for A and 5 for t in given equation

$\begin{array}{l}w=20At\\ w=20\times 4\times 5\end{array}$

Step 2 - Order of simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 3 - Simplify w = 20 × 4 × 5

Follow order of simplification

Multiply numbers from left and right

 $\begin{array}{c}w=20\times 4\times 5\\ =80\times 5\\ =400\end{array}$

Thus, width of the firework display is 400 feet