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Nuetrik [128]
3 years ago
9

I WILL GIVE BRAINLIEST!!

Mathematics
2 answers:
vlabodo [156]3 years ago
7 0

The answer is the square root of 4.

2 * 2 = 4

2 is a rational number; therefore, the square root of 4 is a rational number.

arlik [135]3 years ago
6 0

Answer:

Square root of 4

Step-by-step explanation:

First we need to find the square root of each of these numbers

Square root of 2: 1.41421356 and so on

Square root of 3: 1.73205080 and so on

Square root of 4: 2----- this is the only rational number

Square root of 5: 2.2360679 and so on




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Find the area of the region that lies inside the first curve and outside the second curve.
marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = \dfrac{1}{2}

\theta = -\dfrac{\pi}{3}, \ \  \dfrac{\pi}{3}

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \  \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \  5^2 d \theta

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \  \theta  d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \   d \theta

A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  \dfrac{cos \ 2 \theta +1}{2}  \end {pmatrix} \ \ d \theta - \dfrac{25}{2}  \begin {bmatrix} \theta   \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}

A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  {cos \ 2 \theta +1}  \end {pmatrix} \ \    d \theta - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}}    \ \ - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{2 \pi}{3} \end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3})  \end {bmatrix} - \dfrac{25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} +   \dfrac{\pi}{3}  \end {bmatrix}- \dfrac{ 25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3}   \end {bmatrix}- \dfrac{ 25 \pi}{3}

A =    \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx
7 0
3 years ago
A recipe requires 3/4 of a cup of flour.
nalin [4]

Answer:

<h2>168.75 g</h2>

Step-by-step explanation:

the required mass of flour = (3÷4)×225 = 168.75

8 0
4 years ago
The cost of a bagel and a cup of coffee is $1.45. The cost of 3 bagels and a cup of coffee is $2.95. What is the cost of a cup o
seropon [69]

<em> </em><em>The</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>0</em><em>.</em><em>7</em><em>5</em><em>.</em><em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>.</em>

8 0
3 years ago
Bob plays a game at the school fair. He starts with 0 points. He gets 25 throws
kolbaska11 [484]
Whats the question exactly??

8 0
3 years ago
According to the graph, how far did the object move between the second and third seconds?
Setler79 [48]

Answer:

Your answer would be B

Step-by-step explanation:

This is because in between the 2nd and 3rd seconds, there is a 2 unit space so that is how far the object moved in between these seconds,

Hope this helps you out!! Have a good day:))

7 0
3 years ago
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