Answer:
k = - 6.6667
Step-by-step explanation:
this is quite very simple to begin. I would encourage you take other practice questions similar to help with understanding it.
let us begin.
Given that ;
dT/dt = k ( Tm - T) where Tm is the temp of the medium
dT/dt = 5 degrees Celsius per minute when T = 70
so we have that, 5 = k ( 25 - 70)
remember to convert 5 degree celsius per minute to seconds
we have that;
5*60(sec) = k ( 25 - 70)
k = 5*60 / ( 25 - 70)
k = - 6.6667
note K is negative because we consider it for cooling process (temp decreasing).
cheers i hope this helps!!!
The correct order would be 0.45, (1/2), 2
Hope I helped :)
Answer:
x = -4
Step-by-step explanation:
8x = 8 + 2(x-10) + 3x
simplify
8x = 8 + 2x - 20 + 3x
simplify again
8x = 5x - 12
subtract 5x from both sides
3x = -12
divide both sides by 4
x = -4
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.
