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3 years ago

How many feet of fencing would a farmer need if she wanted

Mathematics

1 answer:

Sauron [17]3 years ago

7 0

Answer:

Well, it's the perimeter, so...40.

You just calculate the perimeter of a rectangle with the lenght of 12 and width of 8, by the formula

$P = 2L+2W$

or you can factor it out.

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Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

2 years ago

GIVING BRAINLIEST Use the inequality 186< -3 (4x - 2).

a_sh-v [17]

Answer:

x < -15

Step-by-step explanation:

I solved the inequality but i don't know if that was what you were asking for lol, if not sorry.

3 0

2 years ago

What’s the degree of

Leno4ka [110]

The degree would be 3

7 0

3 years ago

Los cuadrilateros paralelismo

kkurt [141]

Answer:

¿Qué quieres que te responda?

Step-by-step explanation:

El paralelismo cuadrilátero es cuando las líneas paralelas se mantienen separadas a la misma distancia y nunca se cruzan (cruzan). Las líneas verdes marcan los lados de igual (la misma) longitud y las flechas azules marcan los lados que son líneas paralelas. Los cuadriláteros con líneas perpendiculares tienen lados que se encuentran en un ángulo recto (90 °).

3 0

3 years ago

Read 2 more answers

Select the correct answer.

emmasim [6.3K]

Answer:

the answer is 45/8 very direct

4 0

3 years ago

Read 2 more answers