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Pachacha [2.7K]
3 years ago
6

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above.

Mathematics
1 answer:
olga55 [171]3 years ago
5 0
 <span>∫c F · dr 
= ∫∫s curl F · dS, by Stokes' Theorem 
= ∫∫ <2, 0, -x> · <-z_x, -z_y, 1> dA 
= ∫∫ <2, 0, -x> · <1, 0, 1> dA, since z = 2 - x 
= ∫∫ (2 - x) dA. 

Since the region of integration is inside x^2 + y^2 = 9, convert to polar coordinates: 
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2 - r cos θ) * (r dθ dr) 
= ∫(r = 0 to 3) (2 * 2π - 0) * r dr 
= 2πr^2 {for r = 0 to 3} 
= 18π. 
</span>
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Usando un sistema de ecuaciones, se encuentra que

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  • Cada pera cuesta $1.

-----------------------

  • Un sistema de ecuaciones soluciona esta pergunta.
  • El custo de una manzana es x.
  • El custo de una pera es y.

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  • <u>Seis manzanas y 8 peras cuestan $26</u>, o sea, 6x + 8y = 26
  • <u>Cada manzana cuesta el triple de cada pera</u>, o sea, x = 3y

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Primero, encontramos el cuesto de una pera, substituyendo la segunda en la primera ecuación.

6x + 8y = 26

6(3y) + 8y = 26

18y + 8y = 26

26y = 26

y = \frac{26}{26}

y = 1

Cada pera cuesta $1.

-----------------------

<u>Cada manzana cuesta el triple de cada pera</u>, o sea, x = 3y = 3(1) = 3.

Cada manzana cuesta $3.

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