In 2003, a remote controlled airplane became the first ever to fly nonstop across the Atlantic ocean

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

Archy [21]

Answer: ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3

Step-by-step explanation:

Given that;

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)

Green's Theorem is given as;

∫c (P(x,y)dx + Q(x,y)dy) = ∫∫ₐ { (-β/βy) P(x,y) + (β/βy) Q(x,y) } dA

Now our P(x,y) = 3y + 7e^(√x) and our Q(x,y) = 8x + 5 cos (y²)

Since we know this, therefore; we substitute

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ { (-β/βy) (3y + 7e^(√x)) + (β/βy) (8x + 5 cos (y²)) } dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ ( 8-3) dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA

from the question, our region is defined by a lower bound: y = x² and an upper bound of y = √x

going from x = 0 to x = 1

Now calculating ∫∫ₐ 5dA by means of the description of the region, we say;

∫∫ₐ 5dA = 5¹∫₀ ₓ²∫^(√x) dydx

∫∫ₐ 5dA = 5¹∫₀ (y)∧(y-√x) ∨(y-x²) dx

∫∫ₐ 5dA = 5¹∫₀ (√x-x²) dx

∫∫ₐ 5dA = 5 [ ((x^(3/2))/(3/2)) - x³/3]¹₀ NOW since ∫[f(x)]ⁿ dx = ([f(x)]ⁿ⁺¹ / n+1) + C

then

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3) - ((0^(3/2))/(3/2)) - 0³ / 3) ]

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3)

∫∫ₐ 5dA = 5/3

Therefore ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA = 5/3

5 0

4 years ago

. Which calculation best matches the expression 3+2?

elena-s [515]

Answer:

3+2=5

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

You are riding along a straight river from east to the west at speed of 160m/m. At a given time, you will see the bearing of a c

yuradex [85]

Using the given information, the width of the river is 505.96 m

<h3>Bearing and Distances</h3>

From the question, we are to determine the width of the river

Consider the given diagram,

Let F be the first position of the biker

S be the second position

and C be the position of the church

First, we will determine the distance covered from F to S

Speed = 160m/min

Time = 4 minutes

Using the formula,

Distance = Speed × Time

Distance covered = 160 × 4

Distance covered = 640 m

That is, /FS/ = 640 m

Now, consider ΔFSC

∠F = 90° - 70° = 20°

∠S = 90° + 56° = 146°

and ∠C = 180° - 20° - 146° = 14°

By the Law of Sines

$\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}$

∴ $\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}$

$/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}$

/FC/ = 1479.33 m

Now,

By SOH CAH TOA

$cos \ 70^\circ = \frac{d}{/FC/}$

NOTE: d is the width of the river

∴ d = /FC/ × cos70°

d = 1479.33 × cos70°

d = 505.96 m

Hence, the width of the river is 505.96 m

Learn more on Bearing and distances here: brainly.com/question/19351991

#SPJ1

7 0

2 years ago

Which graph represents the following system of inequalities? y>(1)/(2)x-1 y<=-x+1 y>-2x-1

raketka [301]

Answer:

? We don't see any graphs to choose from

Step-by-step explanation:

$y>\frac{1}{2}x-1$ Graph a dotted line (to show it's not included) with y-intercept 1 and slope 1/2. Test the origin (0, 0) in the inequality:

$0 > \frac{1}{2}0 - 1 = -1$ This is true, so shade the side of the line that the origin is on (above the line).

Next inequality...

$y \le x+1$ Graph a solid line with y=intercept 1 and slope 1. Test the origin.

$0 \le 0+1=1$ True! Shade the side of the line the origin is on (below the line). See image2, attached.

$y>-2x-1$ Graph a dotted line with y-intercept -1 and slope -2. Test the origin (0, 0).

$0>-2(0)-1=-1$ True, so shade the side the origin is on (above the line).

The solutions are located where all the shadings intersect. See image3. The solutions are above the red line, above the green line and below the blue line.

4 0

3 years ago

Tim wants to build a rectangular fence around his yard. He has feet of fencing. If he wants the length to be twice the width, wh

Citrus2011 [14]

Answer:

how many feet of fencing does he have?

\

Step-by-step explanation:

8 0

3 years ago