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Valentin [98]
3 years ago
14

Multiple-Choice Integration, Picture Included, Please Include Work

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
4 0
\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx

Recall that a circle of radius 2 centered at the origin has equation

x^2+y^2=4\implies y=\pm\sqrt{4-x^2}

where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius r is \pi r^2, it follows that the area of a quarter-circle would be \dfrac{\pi r^2}4.

You have r=2, so the definite integral is equal to \dfrac{2^2\pi}4=\pi.

Another way to verify this is to actually compute the integral. Let x=2\sin u, so that \mathrm dx=2\cos u\,\mathrm du. Now

\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx=\int_0^{\pi/2}\sqrt{4-(2\sin u)^2}(2\cos u)\,\mathrm du=4\int_0^{\pi/2}\cos^2u\,\mathrm du

Recall the half-angle identity for cosine:

\cos^2u=\dfrac{1+\cos2u}2

This means the integral is equivalent to

\displaystyle2\int_0^{\pi/2}(1+\cos 2u)\,\mathrm du=2u+\sin2u\bigg|_{u=0}^{u=\pi/2}=\pi
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What is the irrational number in This set: 12.89, square root of 12 and 12/144 ?
kifflom [539]
Good night, 

<span>Irrational numbers are those that can't be expressed as a fraction:

12.89 can be expressed as: </span>\frac{1289}{100}

\frac{12}{144}= \frac{1}{12}

<span>The above numbers can be expressed as a fraction, then the logical answer is: </span>\sqrt{12}

But we will check the answer: 

\sqrt{12}= \sqrt{2^{2}*3 }  =2* \sqrt{3} =3.4641016...

As you can see we can't express that number as a fraction, so that is te correct answer.

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3 years ago
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2 years ago
Solve the system of equations below by elimination.<br> (Show your work)<br> 2x+3y=1<br> 5x+7y=3
nikdorinn [45]

Answer:

-2x+2y+3z=0

-2x-y+z=-3

2x+3y+3z=5

---------------

-2x+2y+3z=0

-2x-y+z=-3

---------------- Subtract

3y + 2z = 3 Eqn A

=========================

-2x-y+z=-3

 

2x+3y+3z=5

---------------- Add

2y + 4z = 2

6y + 4z = 6 Eqn A times 2

------------------------------------ Subtract

-4y = -4

y = 1

-----------------

z = 0

-------------------

x = 1

8 0
3 years ago
18. A glasscutter needs to cut rectangular pieces of
ololo11 [35]

For the cut glass pieces to be rectangular in shape, the glass cutter should ensure:

  1. All four interior angles = 90° each.
  2. Opposite sides are parallel and equal to each other.
  3. Diagonals should be of the same length and should bisect each other.

<h3>Properties of a Rectangle</h3>
  • All four angles of a rectangle are 90° each.
  • There are two pairs of parallel sides that are equal in length.
  • The diagonals bisect each other and are of equal length.

Thus, to ensure the cut glass pieces are rectangular in shape, he should ensure the following:

  1. Make the four interior angles 90° each.
  2. The opposite sides should be parallel and equal to each other.
  3. The diagonals should be of the same length and should bisect each other.

Learn more about properties of rectangle on:

brainly.com/question/2835318

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2 years ago
V(t) = 1 + 2sin(t^2/2) solve for t
Crank

Answer:

omg i'm so sorry thats the wronge answer i ment this to go to a diffrent question

Step-by-step explanation:


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