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Mathematics

1 answer:

ivanzaharov [21]3 years ago

5 0

Answer:

1/5

because reach section is equal, you have a 1 out of 5 chance of hitting 5.

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Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise.The circulation line

tino4ka555 [31]

The line integral you need to compute is

$\displaystyle\int_C\langle2xy^2,4x^3+y\rangle\cdot\mathrm d\vec r$

By Green's theorem, this is equivalent to the double integral,

$\displaystyle\iint_D\left(\frac{\partial(4x^3+y)}{\partial x}-\frac{\partial(2xy^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_D(12x^2-4xy)\,\mathrm dx\,\mathrm dy$

where $D$ is the region with boundary $C$ . This integral is equal to

$\displaystyle\int_0^\pi\int_0^{\sin x}(12x^2-4xy)\,\mathrm dy\,\mathrm dx=\int_0^\pi(12x^2\sin x-2x\sin^2x)\,\mathrm dx=\boxed{\frac{23\pi^2}2-48}$

6 0

3 years ago

There is enough fencing to surround the dog's play yard. The yard must have a perimeter of n more than 38 feet. The length of th

Ierofanga [76]

Answer:

Step-by-step explanation:

Let y = length of side parallel to the side with no fence

x = length of each of the other two sides

Then, y+2x = 64. So, y = 64-2x

Area = A = xy = x(64-2x)

The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).

By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.

So, the area is maximized when x = 16 ft

y = 64 - 2x = 32 ft

Maximum area = xy = (16)(32) = 512 ft2

To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.

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Long N. answered • 10/06/16

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For the fixed given perimeter, the maximum area which can be obtained is a square.

So for 3 sides= 64 feet

one side = 64/3

The maximum area is 64/3*64/3 square feet