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levacccp [35]
2 years ago
9

Last week Fred had

Mathematics
2 answers:
Flura [38]2 years ago
7 0
3 dollars is the answer.
Elden [556K]2 years ago
6 0

Answer: He made 3 more dollars.

Step-by-step explanation: 50-47=3.

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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
What is the solution got the graphed system of equations ? <br><br> Help please :(
Anvisha [2.4K]

Answer:

It's where they meet! I can't really see the coordinate clearly, but if I could I would tell you already.

8 0
3 years ago
There are 15 books on a shelf. 9 of these books are new. The rest of them are used. what is the ratio of all books​
Andrew [12]

Answer:

a)15:6 b)2:3

Step-by-step explanation:

No. of used books=15-9=6

a) 15:6

b)

6:9

2:3

6 0
3 years ago
What fractions are in between -1/3 any -2/3
UNO [17]

To find a fraction between two fractions, all we need to do is make the sum of the numerators be the new numerator, and the sum of the denominators be the new denominator.(x) So, for example, a fraction between 7/13 and 6/11 is (7 + 6)/(13+ 11) =13/24.(x)

7/13 = .5384615(x)

6/11 = .545454(x)

13/24 = .541666�

 

Given that a/b < c/d, why is it true that a/b < (a+c)/(b+d)< c/d?

6 0
3 years ago
_ABC is a right triangle where m_B = 90Á. The coordinates of A and B are (5, 0) and (2, 5), respectively. If the x-coordinate of
Leokris [45]
Since the triangle is a right triangle at point B, then line AB is perpendicular to line BC.
For perpendicular lines, the product of their slopes is -1.
Slope of AB = (5 - 0)/(2 - 5) = 5/-3 = -5/3
Slope of BC = (y - 5)/(7 - 2) = (y - 5)/5

-5/3(y - 5)/5 = -1
-5(y - 5)/15 = -1
-5(y - 5) = -15
y - 5 = 3
y = 3 + 5 = 8

Therefore, the y-coordinate of point C is 8.
4 0
3 years ago
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