Please help! I need an answer fast

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

3 years ago

Pls Help i dont understand ittttttttttt

agasfer [191]

The given scale for the map means that a distance of 1 cm between two locations on the map corresponds to a real distance between them of 600,000 cm = 6 km.

So, if the distance between two places in reality is 87 km, on the map this would be represented by a distance of 14.5 cm, since

87 = 84 + 3

87 = 6 • 14 + 6 • (1/2)

87 = 6 • (14 + 1/2)

3 0

2 years ago

PLS HELP!!! I NEED IT ASAP (FAILING)

RoseWind [281]

Answer:

It is the longest one (20).

Step-by-step explanation:

The hypotenuse is the length opposite the right angle and between the legs. In this case it is the longest one.

4 0

2 years ago

If you answer this i will give you the BRAINLIEST Pls answer Asap

Eva8 [605]

Answer:

You know that negative 3 1/2 is the lowest number so you would put that first. The greatest number would be the coldest in Celsius, and 1/20 would be the last question (the sea level) if calculations are correct, you would get full credit.

5 0

2 years ago

A curve is traced by a point p(x,y) which moves such that its distance from the point a(-1,1) is three times its distance from t

Gre4nikov [31]

Refer to the figure shown below.

The point c, on line segment ab, is in a 3:1 ratio from a.
Therefore,
the x-coordinate of c is -1 +(3/4)*(3) = 5/4 = 1.25.
the y-coordinate of c is 1 - (3/4)*(2) = -1/2 = -0.5.

At point p(x,y), we want d1 = 3d₂, or d₁² = 9d₂².
Therefore
(x + 1)² + (y - 1)² = 9[(x - 2)² + (y + 1)²]
x² + 2x + 1 + y² - 2y + 1 = 9x² - 36x + 36 + 9y² + 18y + 9
8x² - 38x + 8y² + 20y + 43 = 0
x² - 4.75x + y² + 2.5y + 5.375 = 0
(x - 2.375)² - 5.6406 + (y + 1.25)² - 1.5625 + 5.375 = 0
(x - 2.375)² + (y + 1.25)² = 1.828
This is a circle with center at (2.375, -1.25) and radius 1.352.

Answer:
(x - 2.375)² + (y +1.25)² = 1.828

8 0

3 years ago