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uysha [10]
2 years ago
13

Using the Slope-Intercept form, find the equation of a line that has a slope of 3 and y - intercept (2)

Mathematics
1 answer:
RideAnS [48]2 years ago
5 0

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 and c = 2 , then

y = 3x + 2 ← equation of line

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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
Your checking account has grown from 2,675.25 to 3,750.25. what is your growth rate in percentage
zvonat [6]

Answer:

40.2%

Step-by-step explanation:

(New-old)/old

(3750.25-2675.25)/2675.25=0.4018

0.4018×100= 40.2%

6 0
3 years ago
What is the slope intercept form of the linear equation that passes through the point (0, 9) and has a slope of -6?
STALIN [3.7K]

Answer:

y - 9 = -6( x - 0)

y - 9 = -6x + 0

y = -6x + 9

Step-by-step explanation:

7 0
3 years ago
7(2x+5) = 11x-9-x <br><br> Please HELP
mr_godi [17]

Step-by-step explanation:

7(2x+5)=11x-9-x

14x+35=10x-9

4x+35=-9

4x=-44

x=-11

3 0
3 years ago
6×10(6)+7×10(5)+3×10(2)+8×10+2
anastassius [24]

Answer:

852

6×10(6)+7×10(5)+3×10(2)+8×10+2= 852

Step-by-step explanation:

ORDER OF OPERATIONS Will really help you solve this long problem.

Order of operations is PEMDAS.

P-parenthesis

E-exponents

M-multiplication

D-division

A-addition

S-subtraction

6)(10)(6)+(7)(10)(5)+(3)(10)(2)+(8)(10)+2

=(60)(6)+(7)(10)(5)+(3)(10)(2)+(8)(10)+2

=360+(7)(10)(5)+(3)(10)(2)+(8)(10)+2

=360+(70)(5)+(3)(10)(2)+(8)(10)+2

=360+350+(3)(10)(2)+(8)(10)+2

=710+(3)(10)(2)+(8)(10)+2

=710+(30)(2)+(8)(10)+2

=710+60+(8)(10)+2

=770+(8)(10)+2

=770+80+2

=850+2

=852

7 0
3 years ago
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