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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You will have to use trig to solve this:
The side you have is adjacent to the known angle
The side you are looking for is opposite the known angle
^^^This means you need to use tan:
tan(24) =
.445222 =
^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x
5.3 ≈ x
Hope this helped!
Answer:
cubic units
Step-by-step explanation:
Volume of the square pyramid is given as ⅓*area of base*height of pyramid.
Where,
Area of base = 6*6 = 36
Height of pyramid = altitude = units
Plug the values into the formula to find volume.
cubic units