PLZ HELP

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

Y=-4x+6<br> Find an equation for the inverse relation

kherson [118]

Answer:

Step-by-step explanation:

y = -4x + 6.....switch x and y and solve for y

x = -4y + 6 ....subtract 6 from both sides

x - 6 = -4y....divide by -4 on both sides

(x - 6) / -4 = y or y = -1/4x + 3/2 <====

3 0

2 years ago

What two square roots are used to estimate the square root of 67

Georgia [21]

It would be 8.185 since there aren't 2 numbers that evenly go into 67

7 0

3 years ago

Read 2 more answers

Help with these problems please, DUE T O D A Y !!!! I’ll try to make you guys brainlist who ever answers first

Makovka662 [10]

Answer:

19) n = -14

20) x = 4

21) b= -14

22) x = 2

23) x = -1

24) x = -9

Step-by-step explanation:

19) Use the distributive property to get rid of the parentheses. You will get: 20-4n = 76. So, n = -14.

20) Multiply both sides of the equation by 2 to get: -8 + x = -4. So, x = 4

21) Add 3 to both sides to get: $\frac{b}{14}$ = -1. So, b = -14

22) Use the distributive property to get rid of the parentheses. You will get: -40 - 5x = -50. Then, add 40 to both sides to get: -5x = -10. So, x = 2.

23) Use the distributive property to get rid of the parentheses. You will get: -72 = -64 + 8x. Then, add 64 to both sides to get: -8 = 8x. So, x = -1

24) Add 2 to both sides to get: $\frac{x}{3}$ = -3. So, x = -9

Hope this helps :)

4 0

2 years ago

Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug. How much will be left after 12

hammer [34]

The amount of drugs that will be left after 12 hours is 17.42 mg provided Sarah takes 550 mg of an antibiotic every hour.

<h3>What is exponential decay?</h3>

Exponential decay can be described as a reduced amount of an original substance by a definite percentage over a period of time. It can be determined by using the formula:

$\mathbf{y = a(1 - r)^t}$

where;

y = total amount,
a = initial amount = 550 mg
r = the growth rate = 0.25
t = number of growth periods = 12 hours

$\mathbf{y = 550(1 - 0.25)^{12}}$

y = 17.42 mg

Therefore, we can conclude that the amount of drugs that will be left after 12 hours is 17.42 mg.

Learn more about the exponential decay model here:

brainly.com/question/12940982

7 0

2 years ago