Answer:
1
Step-by-step explanation:
Divide 12 in to 12 separate groups and you get 1 group of 12.
Answer:
h ≈ 7.816 cm
r ≈ 5.527 cm
Step-by-step explanation:
The volume of a cone is:
V = ⅓ π r² h
The lateral surface area of a cone is:
A = π r √(r² + h²)
1/4 of a liter is 250 cm³.
250 = ⅓ π r² h
h = 750 / (π r²)
Square both sides of the area equation:
A² = π² r² (r² + h²)
Substitute for h:
A² = π² r² (r² + (750 / (π r²))²)
A² = π² r² (r² + 750² / (π² r⁴))
A² = π² (r⁴ + 750² / (π² r²))
Take derivative of both sides with respect to r:
2A dA/dr = π² (4r³ − 2 × 750² / (π² r³))
Set dA/dr to 0 and solve for r.
0 = π² (4r³ − 2 × 750² / (π² r³))
0 = 4r³ − 2 × 750² / (π² r³)
4r³ = 2 × 750² / (π² r³)
r⁶ = 750² / (2π²)
r³ = 750 / (π√2)
r³ = 375√2 / π
r = ∛(375√2 / π)
r ≈ 5.527
Now solve for h.
h = 750 / (π r²)
h = 750 / (π (375√2 / π)^⅔)
h = 750 ∛(375√2 / π) / (π (375√2 / π))
h = 2 ∛(375√2 / π) / √2
h = √2 ∛(375√2 / π)
h ≈ 7.816
Notice that at the minimum area, h = r√2.
Answer:
Step-by-step explanation:
X= or
Answer:
Step-by-step explanation:
14=r-9
+9
23=r
Answer:
(x²+x-12)(x²-5x-6)= x².x²+ x².(-5x)+x²(-6)+ x.x²+x.(-5x)+x.(-6)
(-12).x²+(-12)(-5x)+(-12)(-6)
= x⁴-5x³-6x²+x³-5x²-6x-12x²+60x+72
=x⁴-4x³-23x²+54x+72