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2 years ago

Which of the following is an example of an ultra-processed food?.

1 answer:

7 0

<em> Chicken nuggets, chips, chocolate, candy, ice-cream, sweetened breakfast cereal and soft drinks </em>are example of an ultra-processed food

<h3>Ultra-processed foods</h3>

Ultra-processed foods are foods made from substances used in food preparation, but not consumed as foods. These foods go through multiple processes in which many ingredients are added.

Examples are<em> Chicken nuggets, chips, chocolate, candy, ice-cream, sweetened breakfast cereal and soft drinks</em>.

Find out more on Ultra-processed foods at: brainly.com/question/15203562

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3 years ago

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strojnjashka [21]

Given that y = cos(x) makes up part of the boundary of C, I suspect you mean the given points to be (-π/2, 0) and (π/2, 0).

I also assume the given vector field is

$\vec F(x,y) = \left\langle e^{-x} + y^2, e^{-y} + x^2 \right\rangle$

Since $\vec F$ has no singularities on C or in its interior, Green's theorem applies:

$\displaystyle \int_C \vec F(x,y) \cdot d\vec r = \iiint_D \frac{\partial(e^{-y}+x^2)}{\partial x} - \frac{\partial(e^{-x}+y^2)}{\partial y} \, dA = 2 \iiint_D (x + y) \, dA$

where D is the interior of C, the region

$D = \left\{ (x, y) : -\dfrac\pi2 \le x \le \dfrac\pi2 \text{ and } 0 \le y \le \cos(x) \right\}$

The integral then reduces to

$\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \int_0^{\cos(x)} (x + y) \, dy \, dx$

$\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac12 \cos^2(x) \right) \, dx$

$\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac{1 + \cos(2x)}4 \right) \, dx$

$\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 4x\cos(x) + 1 + \cos(2x) \right) \, dx$

Since 4x cos(x) is an odd function over the symmetric interval [-π/2, π/2], its contribution to the integral is 0, and the remaining integral is trivial.

$\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 1 + \cos(2x) \right) \, dx = \boxed{\frac\pi2}$

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2 years ago