Answer:
r≥0
V(r) ≥0
Step-by-step explanation:
V(r) = 4/3 * Pi* r^3
The domain is the input values for r
The radius cannot be less than 0 but can be any number bigger than 0
What is the domain of the function in this situation?
r≥0
The range is the output values for the function or the volume
The volume must be greater than or equal to zero
V(r) ≥0
"31-inch piece of steel is cut into three pieces"
Call the pieces a,b,c
a + b + c = 31
"second piece is twice as long as the first piece"
b = 2a
"third piece is one inch more than seven times the length of the first piece"
c = 1 + 7a
Ok, we have our equations, let's substitute the second and third into the first.
a + 2a + 1 + 7a = 31
10a + 1 = 31
10a = 30
a = 30/10 = 3
b = 2a = 6
c = 1 + 7a = 22
Check: 3 + 6 + 22 = 31, good
Answer: 3 inches, 6 inches, 22 inches
Answer:
(x+3)( 3x^2 +5)
Step-by-step explanation:
3x^3+9x^2+5x+15
Split into two groups
3x^3+9x^2 +5x+15
Factor 3x^2 out of the first group and 5 out of the second group
3x^2 ( x+3) + 5(x+3)
Factor out x+3
(x+3)( 3x^2 +5)
Given: f(x)=(2x-2)/4
find f^-1(3)?
we need to find the inverse of f(x), so
x=(2y-2)/4
2y-2=4x
y-1=2x
y=2x+1
so, then f^-1(x)=2x+1
f^-1(3)=2(3)+1
=6+1
=7
so, the answer is 7
