Answer:
See the attached figure.
Step-by-step explanation:
The given function is called piecewise function which is the function that can be in pieces, i.e: defined by multiple sub-functions.
So, need to graph 2x in the interval [3,∞)
And graph -(1/3) x + 7 in the interval (-∞,3]
We will find that f(3) at the function 2x will be equal f(3) at the function -(1/3) x + 7
Which mean the function is continuous.
The attached figure represents the graph of function, it was graphed using the tables on the graph.
Answer:
Option A. The volume of the sphere is multiplied by 1/343.
Step-by-step explanation:
The volume of a sphere can be obtained by the following formula:
V = 4/3πr^3
Let the initial volume (V1) of the sphere be:
V1 = 4/3πr^3 = (4πr^3)/3
Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:
V2 = 4/3 x π x (1/7r)^3
V2 = 4/3 x π x 1/343r^3
V2 = (4πr^3)/1029
Now we determine the ratio of V2 : V1 as shown below:
V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3
V2/V1 = (4πr^3)/1029 × 3/(4πr^3)
V2/V1 = 3/1029
V2/V1 = 1/343
V2 = 1/343 x V1
Therefore, the volume of the sphere is multiplied by 1/343.
