Please help its inequalities 2x

Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

6 0

2 years ago

Georgia kassem installs fencing. she is paid $7.50 per hour for an 8-hour day and time and a half for overtime for any work over

Dominik [7]

Georgia worked overtime on 4 of the 5 days. Her total overtime hours were

... (12-8) +(9 -8) +(10 -8) +(10 -8) = 4 +1 +2 +2 = 9

Then her pay for the week is

... (hours) × (pay per hour)

... = ((7 + 4×8) +1.5×9) × $7.50

... = 52.5 × $7.50

... = $393.75 . . . . Georgia's gross pay for the week

_____

Pay for "time and a half" can be computed by multiplying pay by 1.5 for overtime hours, or multiplying overtime hours by 1.5 and using straight pay. Either way, it is (overtime hours)×(1.5)×(straight pay).

4 0

3 years ago

Read 2 more answers

What is the solution to -2(8x - 4) < 2x + 5?

Svetradugi [14.3K]

Answer:

See image below:)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If you lived in a hobbit house and had a round window that needed? trim, how much trim would be needed to go around a window wit

katen-ka-za [31]

Answer:

To find out how much trim you would need for the window, you would need to calculate the Circumference.

Step-by-step explanation:

<u>Circumference</u> is the length around a circle and is calculated using the following formula.

$C = 2\pi r$

In which C is the circumference and r is the radius. Since we already know the radius all we have to do is plug it into the equation and solve for C.

$C = 2\pi (4.2)$

$C = 26.389 ft$

<u>Answer:</u> The window has a Circumference of 26.389 feet so you would need that amount of trim to fit the area around the window.

Hope my answer would be a great help for you.

If you have more questions feel free to ask here at Brainly.

4 0

3 years ago

A daily lottery is conducted in which three winning numbers are selected out of 100 numbers (without duplicates). how many diff

Black_prince [1.1K]

That is 100 choices for the first number
99 for the 2nd number
98 for the 3rd number

in total, there are 100*99*98 or 970200 possible combos of winning numbers

7 0

2 years ago

Please help its inequalities 2x < 6