To determine the effect of changing the diameter of a sphere to its volume, we would need to know the formula for the volume of a sphere which is V = 4πr³/3 where r is half of the diameter. As you can see, there is a direct relationship.
r1 = d1/2
r2 = d2/2 = 2d1/2 = d1
V2/V1 = (4πd1³/3) / (4π(d1/2)³/3)
V2/V1 = 8
Therefore, the volume of the sphere would be 8 times the original volume.
Answer:
4:16 or 1:4
Step-by-step explanation:
1/5 of 20 = 4
there are 4 red marbles
there are 16 blue marbles
4:16 or 1:4
Answer:
200 Years
Step-by-step explanation:
0.5% X 10 = 5% Increase. So after 10 years 5% Increase
0.5% X 100 = 50% increase. So after 100 years 50% Increase
0.5 X 200 = 100% Increase. So after 200 years it will double.
Answer:
Two functions f(x) and g(x) are inverses if and only if:
f( g(x) ) = x
and
g( f(x) ) = x
In this case, we have:
f(x) = 1*x - 6
g(x) = 6*x + 1
Let's check if the functions are inverses.
f( g(x) ) = 1*g(x) - 6 = 1*(6x + 1) - 6 = 6x + 1 - 6 = 6x - 5
and
g( f(x) ) = 6*f(x) + 1 = 6*(1x - 6) + 1 = 6x - 36 + 1 = 6x - 35
So we can see that:
f( g(x) ) ≠ x
g( f(x) ) ≠ x
Thus, f(x) and g(x) are not inverses.
Particularly, the two compositions are:
f( g(x) ) = 6x - 5
g( f(x) ) = 6x - 35
Both of these are linear functions, thus the domain in both cases is the set of all real numbers, that can be written as:
domain = (-∞, ∞)
What shape do <em>linear <u /></em><u />equations make? To picture the solution visually, you can imagine two of those shapes meeting on a graph at one (and only one) point, (-4,5).
