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3 years ago

Subtract 4 from n then multiply by 6

Mathematics

1 answer:

geniusboy [140]3 years ago

3 0

Answer:

multiply 4 and 6 and the answer should be n-24

Step-by-step explanation:

n-4*6

n-24

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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

Select all ratios equivalent to 30:6

Korolek [52]

Answer:

60 : 12

90 : 18

120 : 24

150 : 30

3 0

3 years ago

Kate swam 18 laps at practice This is three fourths The number Of laps that paco swam at practice write an equation that can be

Lunna [17]

18÷4=5×3=15 laps that paco swam

5 0

3 years ago

Yuson used her calculator to solve the equation 4/5x - 8 = 3. She entered the following on her screen and got an incorrect answe

Firlakuza [10]

Answer:

55/4

Explanation:

Let's solve your equation step-by-step.

4 /5x−8=3

Step 1: Add 8 to both sides.

4 /5x−8+8=3+8

4 /5 x = 11

Step 2: Multiply both sides by 5/4.

( 5 /4 )*( 4 /5 x)=( 5 /4 )*(11)

x= 55/4

Answer:

55 /4

Hope that helps :)

4 0

3 years ago

Read 2 more answers

PLZZZZZZZZZZZZZZZZ HELP ME i begging YOUUUUU !!!!!!!!!!!!!!!!!!!!!!!!!!!

pantera1 [17]

Answer:

-11/20

Step-by-step explanation:

2 8 1

(0-— ÷ (0-—))+—

3 9 5

Simplify —

8/9

2 8 1

(0 - — ÷ (0 - —)) + —

3 9 5

Simplify —

2/3

2 -8 1

(0 - — ÷ ——) + —

3 9 5

2 -8

Divide — by ——

3 9

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

2 -8 2 9

— ÷ —— = — • ——

3 9 3 -8

(0--3/4)+1/5

Least Common Multiple:

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = 4

3 • 5 + 4 -11

————————— = ———

20 20

-11/20

3 0

3 years ago

Read 2 more answers