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melisa1 [442]
3 years ago
8

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?

Mathematics
1 answer:
AlekseyPX3 years ago
7 0

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:

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Step-by-step explanation:

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L^2-2L-35=0

Solving the quadratic equation for 'L' ;

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L^2+5L-7L-35=0

Taking common from the equation :

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OR

L-7=0\\\\L=7

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3 years ago
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3 years ago
(1/2 + 3/2)² + (2/3 x 1/2)³
docker41 [41]

The result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

<h3>How to calculate mathematical expressions?</h3>

According to this question, the following expression is given to solve: (1/2 + 3/2)² + (2/3 x 1/2)³

First, we solve the both parts as follows:

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Therefore, the result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

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