What is the answer for Y=-1(x)+3

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

Given the function f(x) = 4(x + 3) -5, solve for the inverse function when x=3

daser333 [38]

Answer: Your answer would be -120

Step-by-step explanation: Remove Parentheses (3 + 3) add them together and make it 6 and plug in the 6 into the equation. -4 x 6 x 5. Then, you multiply the numbers together and get -120. There is no inverse for -120 since both sides aren't equal.

I hope this helps you!!

6 0

3 years ago

Plz Help meee!!!<br><br>Factor the Trinomial<br><br>x^2+12x+27

mojhsa [17]

Answer:

(x + 9)(x + 3)

Step-by-step explanation:

Factor 27 so that the factors, when combined, will equal 12:

x² + 12x + 27

x 9

x 3

(x + 9)(x + 3) is your answer.

Check: Use the FOIL method. Multiply the first two terms, the outside terms, the inside terms, and then the last two terms. Combine like terms:

(x + 9)(x + 3) = x² + 3x + 9x + 27 = x² + 12x + 27 (√)

~

5 0

3 years ago

Read 2 more answers

Which statement is true about the prime polynomial 2x2 + 3x + 3?

dedylja [7]

Answer:

It cannot be modeled with a rectangle.

Step-by-step explanation:

The given expression 2x^2 + 3x +3 cannot be factored.

That means that it cannot be modeled with a rectangle.

So your answer is, It cannot be modeled with a rectangle.

6 0

3 years ago

Read 2 more answers

Please help. i will kiss u

kenny6666 [7]

Answer:

The area of the figure is 7.5 $units^2$ .

Step-by-step explanation:

In order to make the calculation process easier, you can cut the shape into a trapezoid and a triangle. The triangle's base has a length of 3 units and a height of 2 units, so its area is 3 $units^2$ . The top base of the trapezoid has a length of 1 unit, the bottom base of the trapezoid has a length of 2 units, and the trapezoid has a height of 3 units, so the area of the trapezoid is 4.5 units. To find the area of the shape, add the areas of the trapezoid and the triangle together, which is 3 + 4 .5 = 7.5

4 0

3 years ago

What is the answer for Y=-1(x)+3​

What is the answer for Y=-1(x)+3