Question

Welcome, Cynthia! Logout A weather satellite has a lifespan of 4 43 years. A communications satellite's higher orbit gives it a 1 5 times 6 as long a lifespan than the weather satellite. A stronger solar battery adds another 21 years to the communications satellite's lifespan. How many years will the communication satellite operate? 4 The communications satellite will operate for years. DONE

Answer 1

Given:

Lifespan of weather satellite = 4½ years

Lifespan communication satellite adds = 1⅚ times of the weather satellite

Solar battery adds 2¼ years to the communication's satellite lifespan

Let's find how long the communications satellite will operate for.

To find the number of years the communication satellite will operate, we have the equation:

`Y=4(1)/(2)\ast1(5)/(6)+2(1)/(4)`

Where Y represents the number of years the communication satellite will operate.

To evaluate, convert the mixed fractions to improper fractions:

`\begin{gathered} Y=((9)/(2)\ast(11)/(6))+(9)/(4) \\ \\ Y=(99)/(12)+(9)/(4) \\ \\ Y=(1(99)+3(9))/(12) \end{gathered}`

Solving further:

`\begin{gathered} Y=(99+27)/(12) \\ \\ Y=(126)/(12) \\ \\ Y=(21)/(2) \\ \\ Y=10(1)/(2) \end{gathered}`

Therefore, the communication satellite will operate for 10½ years

ANSWER:

`10(1)/(2)\text{ years}`