PLZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!1

Please answer as well?

dimulka [17.4K]

Answer:

I think it is the 3rd one

Step-by-step explanation:

I hope it is. Sorry if not, I tried.

8 0

3 years ago

Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

3 years ago

Please help me with 19 and 20 please

lesya [120]

9514 1404 393

Answer:

19. B -- continued, but modest ...

Step-by-step explanation:

19. There is no decline or decrease indicated on this graph. If growth were exponential, the graph would be concave upward, which it is not. There is continued growth indicated.

__

20. The percentage change from 2005 to 2010 is ...

(60 -20)/20 × 100% = 2 × 100% = 200%

One might compute an average rate of change per year of ...

200%/(5 yr) = 40%/yr

_____

<em>Additional comment</em>

As with any statement of percentage, you need to be very clear about what the base is.

Here, 100% is the number of farms in 2005, so an increase of 40% per year is an increase by 40% of the number in 2005. That is very different from 40% of the number in the previous year, which is how an annual percentage increase is usually interpreted. (The average annual rate of change is closer to 24% with respect to the previous year's number.)

3 0

3 years ago

F(1) = -3<br> f(n) = 2 · f(n − 1) +1<br> f(2)=

raketka [301]

Answer:

-5

Step-by-step explanation:

f(2) = 2 * f(1) + 1

f(2) = 2 * -3 + 1

f(2) = -6 + 1

f(2) = -5

6 0

3 years ago

a rectangular plot of land 8m long and 6m wide.there is a flower bed in the form of a circle of radius 3m.find 1.area of land. 2

mixer [17]

Answer:

1)Area of the Land is 48 square meters

2) Area of flower bed is 28.26 square meter

3)Area of land excluding flower bed is 19.74 square meters

4)cost of planting grass in land excluding flower bed is Rs 118.44

Step-by-step explanation:

Given:

Length of the Rectangular plot = 8m

Width of the rectangular plot = 6m

Radius of the circular flower bed = 3m

1)Area of the Land

Area of the Rectangular plot = Area of the Land

Area of the Land = length x width

Area of the Land = 8*6

Area of the Land = 48 square meters-----------------------------(1)

2. Area of flower bed

Area of flower bed = 4 x area of one quadrant

Area of flower bed = area of the circle

Area of flower bed = $\pi r^2$

where r is the radius

Now , substituting the values

Area of flower bed = $\pi (3)(3)$

Area of flower bed = 28.26 square meters-----------------------------(2)

3)Area of land excluding flower bed

Area of land excluding flower bed = Area of the rectangular land - area of flower beds

Area of land excluding flower bed = 48 - 28.26

Area of land excluding flower bed = 19.74 square meters

4)cost of planting grass in land

Cost of planting grass per square meter = 6

Excluding the flower bed we have 19.74 square meters. to plant grass for this 19. 74 square meters, the cost will be

= $19. 74 \times 6$

= Rs 118.44

6 0

3 years ago