Answer/Step-by-step explanation:
Volume of a sphere = ⁴/3πr³
1. r = ½ of 14.4 = 7.2 in.
Volume = ⁴/3 × π × 7.2³ = 1563.46 ≈ 1563.5 in.³
2. r = 6 yd
Volume = ⁴/3 × π × 6³ = 904.78 ≈ 904.8 yd³
3. r = 8 mm
Volume = ⁴/3 × π × 8³ = 2144.66 ≈ 2144.7 mm³
4. r = ½ of 13.5 = 6.75 cm
Volume = ⁴/3 × π × 6.75³ = 1288.25 ≈ 1288.3 cm³
5. r = 4.7 in.
Volume = ⁴/3 × π × 4.7³ = 434.89 ≈ 434.9 in.³ (nearest tenth)
It depends on the original size.
Answer:
should be C. No, there are no y-values that have more than one x-value
but if i'm wrong let me know!
The local minimum of function is an argument x for which the first derivative of function g(x) is equal to zero, so:
g'(x)=0
g'(x)=(x^4-5x^2+4)'=4x^3-10x=0
x(4x^2-10)=0
x=0 or 4x^2-10=0
4x^2-10=0 /4
x^2-10/4=0
x^2-5/2=0
[x-sqrt(5/2)][x+sqrt(5/2)]=0
Now we have to check wchich argument gives the minimum value from x=0, x=sqrt(5/2) and x=-sqrt(5/2).
g(0)=4
g(sqrt(5/2))=25/4-5*5/2+4=4-25/4=-9/4
g(-sqrt(5/2))=-9/4
The answer is sqrt(5/2) and -sqrt(5/2).