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4 years ago

Help pleasesolve for x: -3x+3<6a. x>-1b. x<-1c. x<-3d. x>-3

Mathematics

1 answer:

Angelina_Jolie [31]4 years ago

7 0

The answer is A.

I hope that helped let me know if i am correct!

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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

You and a friend are playing a best-of-three series (first to win 2 games wins the series). You are a stronger player and have a

mariarad [96]

Answer and Step-by-step explanation:

Given that probability of you winning each game = 0.68

And probability of you winning next game = 0.81

Your friend's chance of winning/you losing would be = 1-0.68= 0.32

also his chance of winning next game = 0.73

To find probability that you would win the series given that you need to win two games to win the series

= probability that you win first game and second game+ probability that you win first game, lose second game and win third game + probability that you lose first game, win second game and win third game

= 0.68*0.81+0.68*0.32*0.68+0.32*0.68*0.81

=0.8750

Therefore probability that you would win the series = 0.8750

Note: here we found the probability of winning by adding(or) up the three possible combinations that would result in a win

6 0

3 years ago

A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean y

zhannawk [14.2K]

Answer:

A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean yield is 24 liters. He buys another cow that he is told will produce 28 liters of milk a week. Work out the effect this will have on the mean milk yield of his cows.

Step-by-step explanation:

Hope it helps<3

8 0

2 years ago

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Please help me with questions 3 and 4!!! It's really past due and I haven't been the best so far. Send help!!! (This is middle s

e-lub [12.9K]

Answer:

3.) 4

4.) 4j=44

4j/4=44/4

j=11

Pls mark Brainliest :)

Step-by-step explanation:

3 0

3 years ago

50 POINTS !!<br><br><br> PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

lesya692 [45]

Answer:

90 cm

Step-by-step explanation:

82²+35²=hypotenuse

√8281=√hyp²

90=hyp

7 0

3 years ago

Read 2 more answers