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

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

Answer 2

The distance covered is
`2.1* 10^(6)`

The value of y is 6.

Explanation:

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

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

Solution :

The speed is
`1.75 * 10^4` miles per hour.

The time taken is
`1.2 * 10^2` hours

The distance covered is
`d=s* t`

`d=(1.75 * 10^4)(1.2 * 10^2)`

Step 1 - Write the expression:

`(1.75 * 10^4)(1.2 * 10^2)`

Step 2 - Rearrange the expression :

`(1.75 * 1.2)(10^4 * 10^2)`

Step 3 - Multiply the coefficients :

`(2.1)(10^4 * 10^2)`

Step 4 - Apply the product of powers :

`2.1* 10^(4+2)`

`2.1* 10^(6)`

The distance covered is
`2.1* 10^(6)`

On comparing with
`2.1* 10^(y)`

The value of y is 6 in the solution.