# juanpro

Popular questions and responses by juanpro
1. ## probability

Alice and Bob each choose at random a real number between zero and one. We assume that the pair of numbers is chosen according to the uniform probability law on the unit square, so that the probability of an event is equal to its area. We define the

2. ## physics

This problem explores the difference between solving a circuit using the KCL/KVL method and the node method. The circuit shown below has five elements: three resistors, a current source and a voltage source. The resistance of the resistors and the

3. ## probability

Let X and Y be independent random variables, each uniformly distributed on the interval [0,1]. Let Z=max{X,Y}. Find the PDF of Z. Express your answer in terms of z using standard notation. For 0

4. ## electromagnetism

Consider a coaxial cable with a central conducting wire (r=1mm) surrounded by an outer coaxial conducting sheath (rinner=3mm,router=3.2mm) as shown. A current i=300mA flows down the center wire (into the page) and back through the conducting sheath (out of

5. ## probability

PROBLEM 7: SAMPLING FAMILIES (3 points possible) We are given the following statistics about the number of children in the families of a small village. There are 100 families: 10 families have no children, 40 families have 1 child each, 30 families have 2

6. ## physics

A yoyo of mass 2 kg and moment of inertia 0.04 kg m consists of two solid disks of radius 0.2 m, connected by a central spindle of radius 0.15 m and negligible mass. A light string is coiled around the central spindle. The yoyo is placed upright on a flat

7. ## electromagnetism

A rectangular wire loop with current i=200mA, width W=20cm and length L=50cm is placed in a uniform magnetic field B=7T as shown. The normal to the loop, represented by the dashed line, is θ=20degrees from the magnetic field direction. #3A (6 points

8. ## probability

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/2. Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. You may want to refer to the

9. ## mechanics

You drop a block from rest. The block lands on the spring (spring constant = 160Nm) and compresses it .5 m before the block and spring momentarilty come to rest. (The spring then pushes the block upward.) What is the mass of the block? If needed, g=10ms2.

10. ## probability

Fred is giving away samples of dog food. He makes visits door to door, but he gives a sample away (one can of dog food) only on those visits for which the door is answered and a dog is in residence. On any visit, the probability of the door being answered

11. ## probability

In this problem, you are given descriptions in words of certain events (e.g., "at least one of the events A,B,C occurs"). For each one of these descriptions, identify the correct symbolic description in terms of A,B,C from Events E1-E7 below. Also identify

12. ## mit

A small circular block of mass M traveling with a speed v on a frictionless table collides and sticks to the end of a thin rod of with length D and mass M. The picture shows a top down view of the block and rod on the frictionless table. What is the rod's

13. ## mit

A small circular block of mass M traveling with a speed v on a frictionless table collides and sticks to the end of a thin rod of with length D and mass M. The picture shows a top down view of the block and rod on the frictionless table. What is the rod's

14. ## calculus

A person is jumping straight up and down on a trampoline. The height of the center of mass of the person is measured every tenth of a second. It takes just over one second to complete one full bounce. (If you want to see the data, look at the video above.)

15. ## calculus

You are given that f(x) =1+ax+ax2 f′(x) =−(x+2)ax3 f′′(x) =(2x+6)ax4 and the constant a>0. Write down all intervals on which the function is increasing, decreasing, concave up or concave down. (Enter using notation (a, b). Use a comma to separate

16. ## electromagnetism

Consider a coaxial cable with a central conducting wire (r=1mm) surrounded by an outer coaxial conducting sheath (rinner=3mm,router=3.2mm) as shown. A current i=300mA flows down the center wire (into the page) and back through the conducting sheath (out of

17. ## masterin quantum

Consider the left shift operator on the space of infinite sequences of complex numbers: L(z1,z2,…)=(z2,z3,…). Is L injective? Yes Yes - incorrect No Is L surjective? Yes Yes - correct No Find the eigenvalues and eigenvectors of L. Then complete the

18. ## mechanics

A 2kg box starts from rest and slides down an incline as shown in the picture above. If the block loses 24 Joules of energy due to friction as it slides down the ramp, what is the speed of the box as it reaches the bottom of the ramp? If needed, g=10ms2

19. ## probability

In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and 'mu' for μ. Follow standard notation. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly one o'clock, two o'clock,

20. ## probability

For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there are seats available

21. ## probability

Let X be a continuous random variable. We know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h. We will use 1.5 as a conservative value

22. ## probability

For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let Ui=X1+X2+⋯+Xii,i=1,2,…. What value does the

23. ## probability

A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first Heads (note that K is a random variable). For k=0,1,2,…,K, let Xk be a continuous random variable that is uniform over the

24. ## classical mechanic

A small cube of mass m1= 1.0 kg slides down a circular and frictionless track of radius R= 0.4 m cut into a large block of mass m2= 4.0 kg as shown in the figure below. The large block rests on a horizontal and frictionless table. The cube and the block

25. ## physics

A gunman standing on a sloping ground fires up the slope. The initial speed of the bullet is v0= 390 m/s. The slope has an angle α= 19 degrees from the horizontal, and the gun points at an angle θ from the horizontal. The gravitational acceleration is

26. ## biology

Mutant C: Suppose an A/T base pair was inserted in between the two G/C base pairs at positions 18 and 19, marked by the letters above and below the strands. What would the amino acid sequence of the resulting protein be? Be sure to enter the sequence N- to

27. ## biology

Mutant C: Suppose an A/T base pair was inserted in between the two G/C base pairs at positions 18 and 19, marked by the letters above and below the strands. What would the amino acid sequence of the resulting protein be? Be sure to enter the sequence N- to

28. ## mathj

a box contains ten `pairs of shoes if four shoes are retired there are numeration (1 I) (2 I) (10 I) X is the set formed by 20 numbers Find the triplet Calculate probability P(Ai)

29. ## mit

Quiz 12, Problem 4 (2 points possible) A uniform rod of length d is initially at rest on a flat, frictionless table. The rod is pivoted about a point a distance d/3 from one of its ends, and is free to rotate on the table about this pivot. A small glob of

30. ## mit

Two circular pucks, each of mass M and radius R, slide toward each other and are about to collide on frictionless ice. The pucks have glue on their edges and when they collide the pucks will stick together. Before the collision, the rightward-travelling

31. ## mit

1 point possible) A uniform disc of radius R and mass m1 is rotating with an angular speed ωi about an axis passing through its center and perpendicular to the disc's plane. A small box of mass m2, initially at the center of the disc, moves away from the

32. ## mit

A square shaped block of mass travels to the right with velocity on a frctionless table surface. The block has side-length . The block hits a very small, immovable obstacle on the edge of the table and starts to tip. The block has moment of inertia about

33. ## calculus

This problem requires a calculator. Enter answers as decimals. Grass clippings are placed in a bin, where they decompose. The amount of grass clippings measured in kilograms is modeled by A(t)=7.0(0.95)t, where t is measured in days. (a) Find the average

34. ## calculus

F. (12) (1 punto posible) You are at a point x=x(t) along a horizontal line, representing the ground. You are flying a kite which maintains a constant height of 40 meters. Assume also that the kite string is a straight line. The kite is above the point

35. ## calculus

F. (11) (2 puntos posibles) Consider a circular cone with base of radius a and a height of a. Find the vertical cylinder of largest volume inside this cone. In terms of a, what is the radius of this largest cylinder? (Enter ∗ for multiplication: type 2*x

36. ## calculus

(a) Give the linear approximation for the function e−x1+x near x=0. (Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12.) - sin responder (b) Give the quadratic approximation for the function ln(cosx) near x=0. (Enter

37. ## calculus

F. (7) (2 puntos posibles) Let f(x)={tanxax+bπ/4

38. ## calculus

Evaluate these limits. (Enter answer as a decimal. Enter INF if the limit is +∞; -INF if the limit is −∞; and DNE if the limit is neither ±∞ and does not exist.) (a) limx→04+x−−−−−√−2x= - sin responder (b) limx→0tan(2x)sec(3x)x

39. ## calculus

Draw the graph of the function (qualitatively accurate). y=x+1−−−−−√/(x−b),1

40. ## calculus

Find the tangent line to the curve xy3+2y−2x=1 through the point (x,y)=(1,1). (Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12.) Tangent Line y=

41. ## calculus

F.(0) (10 puntos posibles) C1 What is limh→0cos(π6+h)−cos(π6)h? (Enter the answer as a decimal. If the limit does not exist, enter DNE.) sin responder Loading C2 At which of the five points on the graph are dydx and d2ydx2 both negative? Click all

42. ## electromagnetism

A series RLC circuit is made with a C=100pF capacitor, an L=100μH inductor, and an R=30Ω resistor. The circuit is driven at 5×106rad/s with a 1V amplitude. #12A (4 points possible) What is the current oscillation amplitude in A? What is the current

43. ## electromagnetism

A series RLC circuit is connected to a a DC battery via a switch. #11A (3 points possible) A long time after the switch is closed, what is the current in the circuit? A long time after the switch is closed, what is the current in the circuit? - unanswered

44. ## electromagnetism

#10 (5 points possible) At what frequency in Hz will this circuit have the same current with the switches open and with the switches closed? - unanswered

45. ## electromagnetism

Two identical bar magnets A and B are held at rest as shown and released to fall simultaneously. Magnet A as it falls passes through the center of a copper ring, magnet B does not. #9 (4 points possible) Which of the following statements is true? -

46. ## electromagnetism

An infinitely long wire carries a current I=100A. Below the wire a rod of length L=10cm is forced to move at a constant speed v=5m/s along horizontal conducting rails. The rod and rails form a conducting loop. The rod has resistance of R=0.4Ω. The rails

47. ## electromagnetism

A rectangular wire loop has a R=10Ω resistor on the back as it moves into a region of uniform B=3T field at v=10m/s. The rectangle is w=5cm wide by l=20cm long. #7A (2 points possible) As the loop enters the field, which way will the induced current flow?

48. ## electromagnetism

#6 (6 points possible) The demonstration in LS6.U5 uses a Helmholtz coil, which is a pair of wire coils along a common axis that creates a somewhat uniform magnetic field at the center. To achieve a uniform field, the coil separation is equal to the coil

49. ## electromagnetism

#5 (5 points possible) Two identical solenoids are merged as shown in the figure. Which plot best represents the y-component of the magnetic field as it varies along the x-axis? Treat them as ideal solenoids.

50. ## electromagnetism

Three long, thin, co-planar wires are separated by 10cm and arranged as shown. The top wire carries 1A, the middle wire carries 2A, and the bottom wire carries 3A. 2A (6 points possible) What is the magnitude of the force per unit length on the TOP wire in

51. ## electromagnetism

the middle wire carries 2A, and the bottom wire carries 3A. 2A (6 points possible) What is the magnitude of the force per unit length on the TOP wire in N/m? 1000 - incorrect 1000 What is the direction of the force on the TOP wire? left right up up -

52. ## mastering quantum mechanics

Problem 4: Variational principle and bounds (3 parts, 30 points) PART A (15 points possible) Consider a particle of mass m in a box of size L so the wave function vanishes at x=±L/2. Find an upper bound E∗ on the ground state energy Egs using a simple

53. ## mastering quantum mechanics

Problem 3: Rotating a spin state (3 parts , 15 point) PART A (6 points possible) Consider the |+⟩ state of a spin one-half particle (as usual |±⟩=|z;±⟩) and apply to it the rotation operator R that rotates states by an angle θ around the y axis.

54. ## mastering quantum mechanics

PART B (10 points possible) Consider the operator S on an n-dimensional complex vector space so that S(z1,z2,…,zn)=(0,z1,z2,…zn−1). Assume the inner product is the standard one: ⟨(x1,…,xn),(y1,…,yn)⟩=x∗1y1+…+x∗nyn. Calculate

55. ## mechanics

Two pool balls, each of mass 0.2kg, collide as shown in the figure above. Before the collision, the black ball’s velocity makes an angle of 30∘ with the horizontal line. After the collision, the white ball’s velocity makes an angle of 60∘ with the

56. ## mechanics

Dylan hangs a calendar on a refrigerator with a magnetic hook. Unfortunately, the magnet is too weak, so the magnet and calendar slide down the side of the refrigerator to the floor with an acceleration of magnitude 3ms2. If the coefficient of sliding

57. ## mechanics

Jayden holds a 3kg block pressed up against a spring on a horizontal and frictionless surface. The spring has a spring constant of 300Nm. The spring is fixed in place, but the block is free to move. The spring is initially compressed by .5 m and the block

58. ## mechanics

Regarding the figure above, there are three strings tied together suspending a block at rest. Determine the tension in the horizontal string if the mass of the block is 7.5kg. If needed, g=10ms2.

59. ## mechanics

You release a ball from rest attached to a string as shown in Figure A. The ball swings freely, and at the bottom of its circular path it strikes a stationary block. The block slides to the left with a speed of 4ms, and the ball bounces back to the right.

60. ## mechanics

A skydiver is falling straight downward (prior to having deployed his parachute) when he strikes a woman in a hang glider flying horizontally to the east. The skydiver lands on the glider and grabs hold of it. Just prior to this collision, the glider had a

61. ## mechanics

A 2kg box sits at rest on a level floor. Two children push on the box at the same time. Eli pushes horizontally to the right on the box with a force of 4N. Jamie pushes straight downward on the box with a force of 3N. The box does not move (there is

62. ## mechanics

Michah (mass 40kg) is rollerskating east at 6ms when he collides with Joey (mass 60kg) who is rollerskating west at 5ms. As they collide, they quickly push off each other in such a way that Michah travels west at 3ms. What is Joey’s speed once they push

63. ## mechanics

Samuel drops a 2kg ball from some height above the surface of a table. The ball starts from rest and loses 36 Joules of gravitational potential energy before reaching the table’s surface. What is the speed of the ball just before it hits the table? If

64. ## physics

Karen and Bill are rearranging furniture in their house, but they don’t always agree on where all the items should go. At one instant, Karen pushes a large chest of drawers (mass of 20kg) horizontally to the right with a force of 35N, while Bill pushes

65. ## astronomy

You are a pulsar astronomer, and you have been measuring the pulses from a particular milli-second pulsar for several hundred days. You find that they do not arrive at regular intervals - sometimes they arrive a little early and sometimes a little late.

66. ## probability

lengths of the different pieces are independent, and the length of each piece is distributed according to the same PDF fX(x). Let R be the length of the piece that includes the dot. Determine the expected value of R in each of the following cases. In each

67. ## probability

Consider a Poisson process with rate λ. Let N be the number of arrivals in (0,t] and M be the number of arrivals in (0,t+s], where t>0,s≥0. In each part below, your answers will be algebraic expressions in terms of λ,t,s,m and/or n. Enter 'lambda' for

68. ## probability

All ships travel at the same speed through a wide canal. Each ship takes t days to traverse the length of the canal. Eastbound ships (i.e., ships traveling east) arrive as a Poisson process with an arrival rate of λE ships per day. Westbound ships (i.e.,

69. ## probability

Suppose that you have two laptops, both of which you begin using at time 0. Each laptop will eventually fail, and we model each one's lifetime as exponentially distributed with the same parameter λ. The lifetimes of the two laptops are independent. One of

70. ## probability

Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance s, and the random

71. ## gr

Before Dark Energy could be discovered, several preconditions needed to be in place. Tick all the factors below which were necessary for the discovery of dark energy. Radio interferometers, Large telescopes such as Keck, Knowledge of the correlation

72. ## unsolved mysteries astrophysics

Q3.2 COLLAPSE TIMESCALE (5 points possible) Imagine that you live in a distant galaxy far far away. This galaxy is in a different universe, and so may have different cosmology. It seems that in this distant universe, all galaxies have the same luminosity,

73. ## aeronautic

A small wind tunnel is being built for studying insect flight. The first test section built has a uniform height h=0.1m and length ℓ=1m. During operation its walls are found to have boundary layers which effectively start at the inlet at x=0 (the BL

74. ## aeronautic

A dragonfly wing airfoil is essentially a thin plate, whose upper and lower surface velocities can be closely approximated by ue(x)V∞ = (xc)−b(upper surface) (E1.22) ue(x)V∞ = (xc)+b(lower surface) (E1.23) Use the following case-sensitive typed names

75. ## aeronautic

Consider a hill and a ridge as illustrated in the figure below. Both the hill and ridge have a semi-circular xz cross-section of radius R, and the wind is blowing in the x direction with speed V∞. To allow sustained flight with no thermals present, a

76. ## logic and math

Write the reciprocal and the anti-reciprocal of: That a quadrilateral has 4 equal sides, is a necessary condition for that it is a square. That a triangle has 2 equal sides, is a necessary condition for that it is isosceles. Only if f is integrable in an I

77. ## logic and math

Calculate the truth value (f or V) a. Is it true that if (the Papaya is a fruit from the Caricaseas or the Pitahaya is the fruit of a plat from the Cactaseas) then (el Cohombro is a fruit of a plant from the family of the Cucurbitaceas or the Nisper is a

78. ## probability

Consider the random variables X, Y and Z, which are given to be pairwise uncorrelated (i.e., X and Y are uncorrelated, X and Z are uncorrelated, and Y and Z are uncorrelated). Suppose that E[X]=E[Y]=E[Z]=0, E[X2]=E[Y2]=E[Z2]=1, E[X3]=E[Y3]=E[Z3]=0,

79. ## probability

Consider n independent rolls of a k-sided fair die with k≥2: the sides of the die are labelled 1,2,…,k and each side has probability 1/k of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up.

80. ## probability

t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants a, b, c, and d that appear

81. ## global warming science

1a (5 points possible) A schematic of a two layer model of the Earth-atmosphere energy balance is shown in the image below. The atmosphere is assumed to be transparent to solar radiation, and the total solar radiation absorbed by the surface is written in

82. ## logic-math

Calculate the truth value (f or V) a. Is it true that if (the Papaya is a fruit from the Caricaseas or the Pitahaya is the fruit of a plat from the Cactaseas) then (el Cohombro is a fruit of a plant from the family of the Cucurbitaceas or the Nisper is a

83. ## logic-math

Write the reciprocal and the anti-reciprocal of: That a quadrilateral has 4 equal sides, is a necessary condition for that it is a square. That a triangle has 2 equal sides, is a necessary condition for that it is isosceles. Only if f is integrable in an I

84. ## probability

Random variables X and Y are distributed according to the joint PDF fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise. 1 Find the constant a. a= 2 Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y). For

85. ## probability

Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 4 decimal places. 1 P(X>0.75)= 2 P(X≤−1.25)= 3 Let

86. ## Classical mechanics

A boat leaves point P on one side of a river bank and travels with constant velocity V in a direction towars point Q on the other side of the river directly oposite P and distance D from it If r is the instantaneous distance from Q to the boat, θ is the

87. ## p

Alice and Bob each choose at random a real number between zero and one. We assume that the pair of numbers is chosen according to the uniform probability law on the unit square, so that the probability of an event is equal to its area. We define the

88. ## probability

PROBLEM 4: PARKING LOT PROBLEM (3 points possible) Mary and Tom park their cars in an empty parking lot with n≥2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). Mary and Tom pick parking spaces at random. (All

89. ## probability

You flip a fair coin (i.e., the probability of obtaining Heads is 1/2) three times. Assume that all sequences of coin flip results, of length 3, are equally likely. Determine the probability of each of the following events. {HHH}: 3 Heads incorrect {HTH}:

90. ## probability

PROBLEM 2: SET OPERATIONS AND PROBABILITIES (3 points possible) Find the value of P(A∪(Bc∪Cc)c) for each of the following cases: The events A, B, C are disjoint events and P(A)=2/5. P(A∪(Bc∪Cc)c)= incorrect The events A and C are disjoint, and

91. ## classical mechanics

Gliding mass stopped by spring and friction (12 points possible) A small block of mass m=1 kg glides down (without friction) a circular track of radius R=2 m, starting from rest at height R. At the bottom of the track it hits a massless relaxed spring with

92. ## Classical mechanics

A pendulum of mass m= 0.9 kg and length l=1 m is hanging from the ceiling. The massless string of the pendulum is attached at point P. The bob of the pendulum is a uniform shell (very thin hollow sphere) of radius r=0.4 m, and the length l of the pendulum

93. ## Classical mechanics

In the lecture, we discussed the case of an isothermal atmosphere where the temperature is assumed to be constant. In reality, however, the temperature in the Earth's atmosphere is not uniform and can vary strongly and in a non-linear way, especially at

94. ## physics

A spherical non-rotating planet (with no atmosphere) has mass 4 kg and radius 9000 km. A projectile of mass is fired from the surface of the planet at a point with a speed at an angle with respect to the radial direction. In its subsequent trajectory the

95. ## physics

A ruler stands vertically against a wall. It is given a tiny impulse at such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is very small so that . The ruler has mass 250 g and length 30 cm.

96. ## physic

A source of sound emits waves at a frequency 650 Hz. An observer is located at a distance 190 m from the source. Use m/s for the speed of sound. (a) Assume completely still air. How many wavefronts (full waves) are there between the source and the

97. ## physic

Consider a rocket in space that ejects burned fuel at a speed of 1.5 km/s with respect to the rocket. The rocket burns 9 % of its mass in 310 s (assume the burn rate is constant). (a) What is the speed of the rocket after a burn time of 155.0 s? (suppose

98. ## mit physics

A spherical non-rotating planet (with no atmosphere) has mass m 1= 6 ×10 24 kg and radius r 1= 9000 km. A projectile of mass m 2≪ m 1 is fired from the surface of the planet at a point A with a speed v A at an angle α=30 ∘ with respect to the radial

99. ## mit physsics

A merry-go-round (pictured) is sitting in a playground. It is free to rotate, but is currently stationary. You can model it as a uniform disk of mass 200 kg and radius 110 cm (consider the metal poles to have a negligible mass compared to the