A blacksmith has been studying vector calculus and wants to calculate the total mass of a curved metal fitting. Given that the m
etal fitting has a helix shape parameterized by C:[0,π] → IR3 C(t) = (cos (t), sin(t), t) And the density of the metal material is given by the function:f(x,y,z) = 22 How can the black smith calculate the total mass of the fitting and what is this mass?
1 answer:
Answer:
4483.1
Step-by-step explanation:
Helix shape of the metal fitting parameterized :
C(t) = (cos(t), sin(t), t )
This shows that: x = cos(t), y = sin(t), z = t
density of the metal can be represented as
f (x(t), y(t), z(t) = 2z = 2t
To calculate the mass of the fitting an integral is generated below ( attached below is remaining part of the solution )
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Answer:
Kindly check attached picture
Step-by-step explanation:
A standard dice has 6 faces numbered {1,2,3,4,5,6}
For 2 dice, n = 2 ; sample space = n² = 6² = 36
The sum of the 2 upward facing dots:
{(1,1) (1,2) (1,3) (1,4) (1,5) (1,6);
(2,1 ) (2,2),(2,3),(2,4),(2,5),(2,6) ;
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6);
(4,1)(4,2)(4,3) (4,4)(4,5)(4,6);
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6);
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}
