#1**+2 **

a) For the last pair, here's an example and explanation.

Imagine someone is putting air in a spherical balloon. The radius of the balloon is increasing as time passes. Let's say we have a function that can tell us the radius at any point in time....

the radius of the balloon = g(x) , where x is the time in some units, let's say seconds.

So if someone asked, "What is the radius of the balloon when the time is 7 seconds?"

It would just be g(7) .

We also have a function that tells us the volume, if we know what the radius is....

the volume of the balloon = h(x) , where x is its radius in inches.

So if someone asked, "What is the volume of the balloon when the radius is 3 inches?"

It would just be h(3) .

Now what if someone asked, "What is the volume of the balloon when the time is 7 seconds?"

We know the radius at any given time: When the time is 7 , the radius is g(7) .

We know the volume at any given radius: When the radius is g(7) , the volume is h( g(7) ).

So when the time is 7 seconds, the volume is h( g(7) )

So....

h( g(x) ) = the volume as a function of time.

hectictar Dec 30, 2017

#2**+2 **

6)

Let k(t) = distance between lighthouse and the ship....where t is in hours

Let d(t) = distance the ship had traveled since 11AM = 35t [this is the answer to (b) ]

Expressing k as a function of d we have that

k = sqrt [ 10^2 + (d(t))^2 ] [ this is the answer to (a) ]

(c) ( k _{°} d) = k (d(t)) = sqrt [ 10^2 + (35t)^2 ]

k actually represents the hypotenuse length of a right triangle where 10 km is one leg and 35t km the other leg

CPhill Dec 31, 2017