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2 years ago

What is the area of the parallelogram? Explain your reasoning.

Mathematics

1 answer:

AVprozaik [17]2 years ago

3 0

Answer:

multiply the base of the perpendicular by its height

Step-by-step explanation:

It should be noted that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base.

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Convert the integral below to polar coordinates and evaluate the integral.

Lelechka [254]

Answer:

$\int\limits_{0}^{4/\sqrt{2}}\int\limits_{y}^{\sqrt{16-y^2}} xy \, dxdy = \int\limits_{0}^{\pi/4} \, \int\limits_{0}^{4} r^3 cos(\theta)\sin(\theta) \,\, drd\theta = 16$

Step-by-step explanation:

We are trying to evaluate this integral.

$\int\limits_{0}^{4/\sqrt{2}}\,\,\int\limits_{y}^{\sqrt{16-y^2}} xy \,\,dxdy$

The first thing that we have to do is understand this region in the plane.

$\{ (x,y) \in \mathbb{R} : 0\leq y \leq \frac{4}{\sqrt{2}} \,\, , y \leq x \leq \, \sqrt{16-y^2} \}$

If you graph it looks something like the photo I join.

Now we need to describe that same region in polar coordinates.

That same region in polar coordinates would be

$\{ (r,\theta) : \,\, 0 \leq \theta \leq \frac{\pi}{4} \,\,\, 0\leq r \leq 4 \}$

Now remember that when we do the polar transformation we use the following formula

$\int\limits_{a}^{b} \, \int\limits_{c}^{d} f(x,y) \,dxdy = \int\limits_{\theta_1}^{\theta_2} \, \int\limits_{r_1}^{r_2} r* f(rcos(\theta),rsin(\theta)) \,drd\theta$

Then our integral would be

$\int\limits_{0}^{4/\sqrt{2}}\int\limits_{y}^{\sqrt{16-y^2}} xy \, dxdy = \int\limits_{0}^{\pi/4} \, \int\limits_{0}^{4} r^3 cos(\theta)\sin(\theta) \,\, drd\theta = 16$

6 0

3 years ago

For x= 2, what is the value of the expression in the box? The expression is 3.6 divided by x A. 1.6 B.18 C.0.18 D.1.8

Ostrovityanka [42]

Answer:

please give me brainiest

Step-by-step explanation:

algebraic Expressions Calculator. An online algebra calculator simplifies expression for the input you given in the input box. If you feel difficulty in solving some tough algebraic expression, this page will help you to solve the equation in a second.

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3 years ago

What is the least common multiple of 4 and 6? * 1. 24 2. 12 3. 4 4. 6

azamat

Answer:

Step-by-step explanation:

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3 years ago

The screen of Breonna‘s new phone is 2.85 centimeters long. What mixed number represents the length of the phone screen?

tatyana61 [14]

19/20 centimeters long

6 0

3 years ago

Four siblings are to share in an inheritance. They are to receive money in the money in the amount of $88,000 in the ratio of 5:

11111nata11111 [884]

The answer is 44,000 dollars. due to 5+3+2+1=10, you divide 88,000 by 10 and you then multiply that by the largest number to get 44,000

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3 years ago