A baker sells a dozen for &3.99 the cost of to make three donuts is $0.45 how much is the total profit on 5 dozen donuts?

Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

3 years ago

The difference of the same side angles of two parallel lines is 35°. Find all angles

Pavel [41]

<h3>Answer:</h3>

All acute angles are 72.5°; all obtuse angles are 107.5°.

<h3>Explanation:</h3>

Angles on the same side of a transversal cutting parallel lines have measures that total 180°. If o and a represent the measures of the obtuse and acute angles, respectively, then we have ...

... o + a = 180

... o - a = 35

Adding these two equations gives ...

... 2o = 215

... 215/2 = o = 107.5 . . . . degrees

Then the other angle is ...

... a = 107.5 - 35 = 72.5 . . . . degrees

_____

All corresponding angles have the same measures. All vertical angles have the same measures. So the 8 angles that arise from the intersection of the transversal with these two parallel lines will have one or the other of these two measures.

3 0

3 years ago

3. Given Q = (-1,4) and P = (-2,-2), find QP.

astra-53 [7]

Step-by-step explanation:

QP=P-Q

QP=(-2,-2)-(-1,4)

QP=(-1,-6)

5 0

2 years ago

Which of the following expressions are equivalent to the expression below?

photoshop1234 [79]

A: 2-3x

First distribute 8-3(x+2) to get
8-3x-6.

Combine like terms to simplify the equation: 8-6=2

And now the answer is 2-3x

3 0

2 years ago

Suppose you add or subtract two quadratic trinomials that use the same variable. What are the possible classifications for the s

Leno4ka [110]

Answer:

quadratic monomial, quadratic trinomial, constant monomial, linear monomial, quadratic binomial, linear binomial.

Step-by-step explanation:

two quadratic trinomials each have a degree-2, degree-1, and degree-0 term. It is possible that the coefficients of all or some of the terms cancel each other while adding or subtracting the polynomials.

3 0

3 years ago