Question

A rocket ship is travelling at an average speed of 1.75 × 104 miles per hour. How many miles will the rocket ship travel in 1.2 × 102 hours?1. Write the expression:       (1.75 × 104)(1.2 × 102)
2. Rearrange the expression:     (1.75 × 1.2)(104 × 102)

3. Multiply the coefficients:      (2.1)(104 × 102)

4. Apply the product of powers:    2.1 × 10y

The rocket ship will travel 2.1 × 10y miles. What is the value of y in the solution?

Answer 1

Answer:

The distance covered is $2.1\times 10^{6}$  

The value of y is 6.          

Step-by-step explanation:

Given : A rocket ship is travelling at an average speed of $1.75 \times 10^4$ miles per hour.

To find : How many miles will the rocket ship travel in $1.2 \times 10^2$  hours and find the value of y in the solution expression?

Solution :

The speed is  $1.75 \times 10^4$ miles per hour.

The time taken is  $1.2 \times 10^2$  hours

The distance covered is $d=s\times t$

$d=(1.75 \times 10^4)(1.2 \times 10^2)$

Step 1 -  Write the expression:

$(1.75 \times 10^4)(1.2 \times 10^2)$

Step 2 - Rearrange the expression :

$(1.75 \times 1.2)(10^4 \times 10^2)$

Step 3 - Multiply the coefficients :

$(2.1)(10^4 \times 10^2)$

Step 4 - Apply the product of powers :

$2.1\times 10^{4+2}$

$2.1\times 10^{6}$  

The distance covered is $2.1\times 10^{6}$  

On comparing with $2.1\times 10^{y}$  

The value of y is 6 in the solution.

Answer 2

y = 4 + 2 = 6 ( the sum of the exponents)