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1. ### Proving |A U B| Given Disjoint A & B

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2. ### Proving |A U B| Given Disjoint A & B

Hi everyone, Could someone please show me how to prove this? Homework Statement Determine |A U B| in terms of |A| and |B| assuming that A and B are disjoint Homework Equations The Attempt at a Solution I know that A U B must be finite because A and B are disjoint, but...
3. ### Gravitational field of the moon

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4. ### A net gravitational problem

Well, in the problem it states that the two objects are separated by .420 m. Is that what you mean? Thus, the 41.0 object is at .420 m, right? Thank you
5. ### Resultant gravitational force

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6. ### Gravitational field of the moon

[SOLVED] gravitational field Homework Statement How much work is done by the Moon's gravitational field as a 1100kg meteor comes in from outer space and impacts on the Moon's surface? Homework Equations W=GMm/r The Attempt at a Solution W=6.67 X 10^-11(6 X 10^22)(1100kg)/1.5 X...
7. ### Resultant gravitational force

Thank you I just need it in terms of i and j. So, wouldn't that be correct the way it is? F32 is negative and F13 is positive, right? Thank you
8. ### Resultant gravitational force

Thank you The triangle is placed in the second quadrent, where m3 is at (0,0) m2 is at (-4,0)m and m1 is at (0,3) Does this look correct? F32=-6.67X10^-11Nm^2/kg(5.5kg)(4kg)/4^2= -9.2 X 10^-11i F13= -6.67X10^-11Nm^2/kg^2(4)(2)/3^2= 5.9X10^-11j Thank you
9. ### A net gravitational problem

It's in the middle. Is that what you mean? So, wouldn't you just take 6.67 X 10^-11(145)(41/2)/.42^2? 6.67 X 10^-11(445kg)(41.0kg)/2/(.42)^2? Thank you
10. ### Resultant gravitational force

Hi everyone, Could someone please help me with this problem? Homework Statement Three uniform spheres of mass m1=2.00kg, 4.00kg, and m2=5.50 kg are placed at the corners of a right triangle. Calculate the resultant gravitational force on the 4.00 kg object, assuming the spheres are...
11. ### A net gravitational problem

Thank you very much For part a., would I just take 4.7 X 10^-6 and divide it by 2? Thank you
12. ### A net gravitational problem

Thank you very much Could you please tell me if a. looks correct? For part b., would you just take the first one plus the middle one plus the third one and set it equal to the total force and solve for the middle one? Thank you
13. ### Harmonic oscillator problem

Yes, that was correct Thank you very much Regards
14. ### Harmonic oscillator problem

Thank you very much Isn't 11.5 just the time or is that also the period? Thank you
15. ### A net gravitational problem

Hello everyone, Could someone please help me with this problem? Homework Statement A 145kg object and a 445kg object are separated by .420m. a. Find the net gravitational force exerted by these objects on a 41.0kg object placed midway between them. b. At what position can the 41.0kg...
16. ### Harmonic oscillator problem

Thank you very much Could you please explain to me how to find one of these? Once I can find one, I can find the others. It seems like there isn't enough information given, because the 11.5 s is not used in any of the equations, right? Thank you
17. ### Harmonic oscillator problem

Hi everyone, Could someone please help me with this problem? Homework Statement A simple harmonic oscillator takes 11.5s to undergo four complete vibrations. a. Find the period of its motion b. Find the frequency in Hertz c. Find the angular frequency in radians per second...
18. ### Harmonic motion problem

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19. ### Determine the gravitational force that you exert on another person

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20. ### Harmonic motion problem

Hi everyone, Could someone please help me with this problem? Homework Statement In an engine, a piston oscilates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds. x=5.00cmcos(3t+pi/5) a. At...
21. ### Determine the gravitational force that you exert on another person

Hi everyone, Could someone please help me with this problem? Homework Statement Determine the gravitational foce that you exert on another persona 1.00 m away. Assume that you and the other person are point masses of 73.0 kg each. Homework Equations F=Gm1(m2)/r^2 The Attempt...
22. ### Particle Problem: Work Done on Raindrop by Grav & Air Resistance

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23. ### Average force of a steel ball

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24. ### Find Mass & Center of Mass for a Rod of Length 38.5 cm

Homework Statement A rod of length 38.5 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end. λ=50.0g/m+16.5g/m^2 a. What is its mass in g? b. How far from the x=0 end is its center of mass in m? Homework Equations The...
25. ### Average force of a steel ball

Does this look right? Favg(.200s)=3.0kg(9.0) Favg=-135N Thank you
26. ### Average force of a steel ball

Edit: Does this look right? integral 3.00(9.8)dt from 0 to .200= 3.00kg(9.8m/s^2)x= 3.00(9.8)(.200)= 5.88 Thank you very much
27. ### Impulse problem

Thank you very much Does this look right? integral from 1.25 to .800 (.110kg)(9.8m/s^2)dt =.8624-1.35 =-.4876 Thank you very much
28. ### Average force of a steel ball

Thank you very much Does this look right? integral from 1.25 to .800 (.110kg)(9.8m/s^2)dt =.8624-1.35 =-.4876 Thank you
29. ### Impulse problem

Homework Statement A ball of mass .110 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of .800 m. What impulse was given to the ball by the floor? Homework Equations I=ΣFΔt Δp=I The Attempt at a Solution Could someone please tell...
30. ### Average force of a steel ball

Homework Statement A 3.00 kg stell ball strikes a wall with a speed of 9.0m/s at an angle of 60° with the surface. It bounces off with the same speed and angle. If the ball is in contact with the wall for .200 s, what is the average force exerted by the wall on the ball? Homework...
31. ### Solving the 'Work' Problem

Would it be like this? Integral (2xi+5yj)(idx)|0 to 4.96= integral 0 to 4.96(2x)dx= 2xx|0 to 4.56= 2x^2|0 to 4.56= 41.6 Work done in the y direction=0 Total work=41.6J Thank you
32. ### Solving Motorist's 7min Trip Vectors & Speeds

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33. ### Particle Problem: Work Done on Raindrop by Grav & Air Resistance

Thank you very much Could you tell me if this is correct? a. As it falls 50m, what is the work done on the raindrop by the gravitational force? Wouldn't this be 0J? Because when it is perpendicular the work is 0, right? b. What is the work done on the raindrop by air resistance...
34. ### Solving Motorist's 7min Trip Vectors & Speeds

Homework Statement A motorist drives south at 24.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 3.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 7.00 min trip, find the following values. a. Total vector displacement displacement b. Average speed c...
35. ### Finding the Dot Product of Vector A & B

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36. ### Particle Problem: Work Done on Raindrop by Grav & Air Resistance

Could you please give me a hint? Is what I did so far correct? Thank you
37. ### Relations and partitions

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38. ### Partition on R^3

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39. ### Particle Problem: Work Done on Raindrop by Grav & Air Resistance

Homework Statement A raindrop of mass 3.07 X 10^-5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. a. As it falls 50m, what is the work done on the raindrop by the gravitational force? b. What is the work done on the...
40. ### Solving the 'Work' Problem

"work" problem Homework Statement A force F(2xi+5yi)N acts on an object as it moves in the x direction from the origin to x=4.96m. Find the work W=integral vector F(dr) done by the force on the object Homework Equations The Attempt at a Solution integral 0 to 4.96...
41. ### Finding the Dot Product of Vector A & B

Homework Statement Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 49° with each other. Find (vector A)(vector B) Homework Equations The Attempt at a Solution (5i+0j)(0i+9j)= (5N)(0m)+(0N)(9m)= square root...
42. ### Prove -|x|</x</|x|

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43. ### Triangle inequality proof

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44. ### Triangle inequality proof

Homework Statement Prove that |x+y|</|x|+|y| Homework Equations The Attempt at a Solution Assume that x and y are real numbers. |5+2|</|5|+|7| 7</7 |-5-2|</|-5|+|-2| 7</7 I know that it is true by testing different numbers, but I'm not sure how to prove it. Could someone...
45. ### Partition math help

Thank you So, it would be 3n and not 3n+1? Thank you
46. ### Partition on R^3

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47. ### Relations and partitions

Thank you I'm looking for the partition. Could you please tell me how you would find that? Thank you
48. ### Partition math help

Thank you very much Would this work? {{3}, {6}, {9}, {12}, {15}, {3n+3}} Thank you
49. ### Describing partition

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50. ### Prove -|x|</x</|x|

Thank you very much In order to prove that |x|</a if and only if -a</x</a where a>/0, would I do the same thing as in the previous problem? Thank you