An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The area requiring mulch is given by m ( x ) = π x 2 − 2 2 x 2 .
The cost per square foot of mulch is 1.50 , so t h ecos t f u n c t i o ni s g(m) = 1.50m$.
To find the cost of the mulch based on the radius, substitute m ( x ) into g ( m ) to get g ( m ( x )) = 1.50 ( π x 2 − 2 2 x 2 ) .
The expression representing the cost of the mulch based on the radius of the circle is 1.50 ( π x 2 − 2 2 x 2 ) .
Explanation
Understanding the Functions We are given two functions:
$m(x) =
\pi x^2 - 2\sqrt{2} x^2$
, which represents the area requiring mulch, and
g ( m ) = 1.50 m
, which represents the cost of the mulch based on the area. We want to find an expression that represents the cost of the mulch based on the radius of the circle, which means we need to find g ( m ( x )) .
Composition of Functions To find the expression for the cost of the mulch based on the radius of the circle, we need to substitute the expression for m ( x ) into the function g ( m ) . This means we need to evaluate g ( m ( x )) .
Since g ( m ) = 1.50 m , we have
g ( m ( x )) = 1.50 \tims m ( x )
Substitution Now, substitute $m(x) =
\pi x^2 - 2\sqrt{2} x^2$
into the expression for g ( m ( x )) :
$g(m(x)) = 1.50 (
\pi x^2 - 2\sqrt{2} x^2
)$
Final Expression So the expression representing the cost of the mulch based on the radius of the circle is:
1.50 ( π x 2 − 2 2 x 2 )
Examples
Imagine you're designing a garden with a circular flower bed and a unique octagonal fountain in the center. You need to calculate the cost of the soil required to fill the area around the fountain. By using the formula we derived, you can easily determine the amount of soil needed based on the radius of the flower bed. This helps in budgeting and planning your gardening project effectively, ensuring you don't overspend on materials. For instance, if the radius of the flower bed is 5 feet, the area requiring soil is calculated using the formula, and then multiplied by the cost per square foot to get the total expense.
To calculate the number of electrons flowing through an electric device delivering a current of 15.0 A for 30 seconds, we first determine the total charge, which is 450 coulombs. We then convert this charge into the number of electrons, which equals approximately 2.81 x 10^21 electrons. Thus, about 2.81 trillion trillion electrons flow through the device during this time.
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