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1 year ago

What is the perimeter of the rectangle shown below?

Mathematics

1 answer:

lesantik [10]1 year ago

7 0

Answer: D. 26 units

Step-by-step explanation: perimeter is the distance around the figure, or all the sides added together.
With a rectangle it is known that the opposite sides are congruent, or the same, so 8+8+5+5 = 26

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Let F⃗ =2(x+y)i⃗ +8sin(y)j⃗ .

Alik [6]

Answer:

-42

Step-by-step explanation:

The objective is to find the line integral of $F$ around the perimeter of the rectangle with corners (4,0), (4,3), (−3,3), (−3,0), traversed in that order.

We will use <em>the Green's Theorem </em>to evaluate this integral. The rectangle is presented below.

We have that

$F(x,y) = 2(x+y)i + 8j \sin y = \langle 2(x+y), 8\sin y \rangle$

Therefore,

$P(x,y) = 2(x+y) \quad \wedge \quad Q(x,y) = 8\sin y$

Let's calculate the needed partial derivatives.

$P_y = \frac{\partial P}{\partial y} (x,y) = (2(x+y))'_y = 2\\Q_x =\frac{\partial Q}{\partial x} (x,y) = (8\sin y)'_x = 0$

Thus,

$Q_x -P_y = 0 -2 = - 2$

Now, by the Green's theorem, we have

$\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA = \int \limits_{-3}^{4} \int \limits_{0}^{3} (-2)\,dy\, dx \\ \\\phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-2y) \Big|_{0}^{3} \; dx\\ \phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-6)\; dx = -6x \Big|_{-3}^{4} = -42$

4 0

2 years ago

Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2

Sloan [31]

-3x²-2 .................

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3 years ago

A plate moving at a rate of 4 is moving toward a plate that is 10,000 km away. In how many years will the plates collide?

iVinArrow [24]

Answer:

the answer is 250 million years

Step-by-step explanation:

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3 years ago

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The price of pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these sh

olga nikolaevna [1]

The answer to the problem is as follows:

We can convert 4.5% into a decimal form by moving the decimal to the left two places. This becomes: .045

<span>63.20 x .045 = $2.84

</span>I hope my answer has come to your help. God bless and have a nice day ahead!

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2 years ago

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What percent of 40 is 5

horsena [70]

Answer:

12.5%

Step-by-step explanation:

Five divided by 40 is 12.5

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3 years ago