Given the force field F, find the work required to move an object on the given oriented curve. F = (y, - x) on the path consisting of the line segment from (1, 5) to (0, 0) followed by the line segment from (0, 0) to (0, 9) The amount of work required is ____ (Simplify your answer.)

Answers

Answer 1
Answer:

Answer:

0

Step-by-step explanation:

We want to compute the curve integral (or line integral)

\bf \int_(C)F

where the force field F is defined by

F(x,y) = (y, -x)

and C is the path consisting of the line segment from (1, 5) to (0, 0) followed by the line segment from (0, 0) to (0, 9).

We can write  

C = \bf C_1+C_2

where  

\bf C_1 =  line segment from (1, 5) to (0, 0)  

\bf C_2 = line segment from (0, 0) to (0, 9)

so,

\bf \int_(C)F=\int_(C_1)F+\int_(C_2)F

Given 2 points P, Q in the plane, we can parameterize the line segment joining P and Q with

r(t) = tQ + (1-t)P for 0 ≤ t ≤ 1

Hence \bf C_1 can be parameterized as

\bf r_1(t) = (1-t, 5-5t) for 0 ≤ t ≤ 1

and \bf C_2 can be parameterized as

\bf r_2(t) = (0, 9t) for 0 ≤ t ≤ 1

The derivatives are

\bf r_1'(t) = (-1, -5)

\bf r_2'(t) = (0, 9)

and

\bf \int_(C_1)F=\int_(0)^(1)F(r_1(t))\circ r_1'(t)dt=\int_(0)^(1)(5-5t,t-1)\circ (-1,-5)dt=0

\bf \int_(C_2)F=\int_(0)^(1)F(r_2(t))\circ r_2'(t)dt=\int_(0)^(1)(9t,0)\circ (0,-9)dt=0

In consequence,

\bf \int_(C)F=0

Answer 2
Answer:

Final answer:

The work done by the force field F = (y, -x) along the given path is -5 Joules. This was calculated by breaking the path into two segments and calculating the work done for each segment.

Explanation:

To calculate the work done by the force field F = (y, -x) when moving an object along a specific path, we utilize the concept of the line integral or the dot product of the force and the displacement vector. We can break down the given path into two line segments and solve each separately.

The first segment is from (1, 5) to (0, 0). Only the x component of the displacement is non-zero here, the force is F = (5, -1). Thus the work done on this segment is given by W = F.d = Fd cos θ = -(5 N)(1 m)(cos(180)) = -5 J, where J stands for Joules, the unit of work or energy.

The second segment is from (0, 0) to (0, 9). The force and displacement are perpendicular so the work done is 0.

By adding the work done on these two segments, we arrive at the total work done: W_total = -5 J + 0 J = -5 J

Learn more about Work done by a force field here:

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1. Trapezoid BEAR has a height of 8.5 centimeters and parallel bases that measure 6.5 centimeters and 11.5 centimeters. To the nearest square centimeter, find the area of the trapezoid.Area of trapezoid BEAR = ___________ square centimeters

2. Regular pentagon PENTA has side lengths that are 9 meters long. To the nearest square meter, find the area of the pentagon.

Area of pentagon PENTA = _____square centimeter

Answers

Given

1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.

2) Regular pentagon PENTA with side lengths 9 m

Find

The area of each figure, rounded to the nearest integer

Solution

1) The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

Answer:139 cm squared

The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

Stephanie claims that 26540is greater than 50. Do you agree or disagree? Explain.

Answers

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4(4x - 2) = x + 4
asnwerplsssssssss

Answers

Answer:

4(4x - 2) = x + 4

16x - 8 = x + 4

15x = 12

x = 12/15 = 4/5

Answer:

x = 0.8

Step-by-step explanation:

4(4x - 2) = x + 4

16x - 8 = x + 4

16x - x = 4 + 8

15x = 12

x = 0.8

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Answers

Answer:

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Step-by-step explanation:

Probability of 4 = 1/6

Probability tail = 1/2

Multiply them

Answer:

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Step-by-step explanation:

Probability of 4 = 1/6

Probability tail = 1/2

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Answers

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