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Questions (62)

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
1. 4 answers
2. 811 views
This problem requires a calculator. Enter answers as decimals.Grass clippings are placed in a bin, where they decompose. The
1. 2 answers
2. 598 views
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
1. 2 answers
2. 571 views
F. (11) (2 puntos posibles)Consider a circular cone with base of radius a and a height of a. Find the vertical cylinder of
1. 2 answers
2. 581 views
You are given thatf(x) =1+ax+ax2 f′(x) =−(x+2)ax3 f′′(x) =(2x+6)ax4 and the constant a>0. Write down all intervals on
1. 2 answers
2. 617 views
(a) Give the linear approximation for the function e−x1+x near x=0.(Enter ∗ for multiplication: type 2*x for 2x. Enter / for
1. 1 answer
2. 435 views
F. (7) (2 puntos posibles)Let f(x)={tanxax+bπ/4<x<π/2x≤π/4 Find a and b such that the function f(x) is differentiable at
1. 1 answer
2. 482 views
Evaluate these limits.(Enter answer as a decimal. Enter INF if the limit is +∞; -INF if the limit is −∞; and DNE if the
1. 1 answer
2. 673 views
Draw the graph of the function (qualitatively accurate).y=x+1−−−−−√/(x−b),1<b<2
1. 1 answer
2. 439 views
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.
1. 3 answers
2. 474 views
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
1. 2 answers
2. 858 views
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
1. 2 answers
2. 544 views
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
1. 2 answers
2. 612 views
#10 (5 points possible)At what frequency in Hz will this circuit have the same current with the switches open and with the
1. 1 answer
2. 451 views
Two identical bar magnets A and B are held at rest as shown and released to fall simultaneously. Magnet A as it falls passes
1. 3 answers
2. 843 views
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
1. 1 answer
2. 646 views
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
1. 1 answer
2. 519 views
#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
1. 3 answers
2. 810 views
#5 (5 points possible)Two identical solenoids are merged as shown in the figure. Which plot best represents the y-component of
1. 1 answer
2. 497 views
Consider a coaxial cable with a central conducting wire (r=1mm) surrounded by an outer coaxial conducting sheath
1. 1 answer
2. 858 views
Consider a coaxial cable with a central conducting wire (r=1mm) surrounded by an outer coaxial conducting sheath
1. 4 answers
2. 855 views
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
1. 3 answers
2. 840 views
Three long, thin, co-planar wires are separated by 10cm and arranged as shown. The top wire carries 1A, the middle wire carries
1. 1 answer
2. 556 views
the middle wire carries 2A, and the bottom wire carries 3A.2A (6 points possible) What is the magnitude of the force per unit
1. 1 answer
2. 450 views
Problem 4: Variational principle and bounds (3 parts, 30 points)PART A (15 points possible) Consider a particle of mass m in a
1. 1 answer
2. 555 views
Problem 3: Rotating a spin state (3 parts , 15 point)PART A (6 points possible) Consider the |+⟩ state of a spin one-half
1. 1 answer
2. 426 views
PART B (10 points possible)Consider the operator S on an n-dimensional complex vector space so that
1. 1 answer
2. 469 views
Consider the left shift operator on the space of infinite sequences of complex numbers:L(z1,z2,…)=(z2,z3,…). Is L injective?
1. 1 answer
2. 521 views
PROBLEM 7: SAMPLING FAMILIES (3 points possible)We are given the following statistics about the number of children in the
1. 4 answers
2. 2,319 views
lengths of the different pieces are independent, and the length of each piece is distributed according to the same PDF fX(x).
1. 2 answers
2. 746 views
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],
1. 4 answers
2. 2,256 views
- unanswered
1. 2 answers
2. 2,601 views
In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and 'mu' for μ. Follow
1. 4 answers
2. 1,183 views
Suppose that you have two laptops, both of which you begin using at time 0. Each laptop will eventually fail, and we model each
1. 2 answers
2. 832 views
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
1. 2 answers
2. 1,056 views
Before Dark Energy could be discovered, several preconditions needed to be in place. Tick all the factors below which were
1. 1 answer
2. 516 views
Q3.2 COLLAPSE TIMESCALE (5 points possible)Imagine that you live in a distant galaxy far far away. This galaxy is in a different
1. 1 answer
2. 796 views
A small wind tunnel is being built for studying insect flight. The first test section built has a uniform height h=0.1m and
1. 1 answer
2. 505 views
A dragonfly wing airfoil is essentially a thin plate, whose upper and lower surface velocities can be closely approximated byue(
1. 2 answers
2. 578 views
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
1. 2 answers
2. 542 views
Write the reciprocal and the anti-reciprocal of:That a quadrilateral has 4 equal sides, is a necessary condition for that it is
1. 1 answer
2. 464 views
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
1. 0 answers
2. 534 views
A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first
1. 4 answers
2. 3,759 views
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
1. 3 answers
2. 5,187 views
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
1. 5 answers
2. 7,704 views
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
1. 7 answers
2. 6,693 views
Let Z=max{3X,Y}. Find the PDF of Z. Express your answer in terms of z using standard notation.For 0<z<1, fZ(z)= - unanswered For
1. 2 answers
2. 10,970 views
1a(5 points possible) A schematic of a two layer model of the Earth-atmosphere energy balance is shown in the image below. The
1. 1 answer
2. 669 views
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
1. 1 answer
2. 436 views
Write the reciprocal and the anti-reciprocal of:That a quadrilateral has 4 equal sides, is a necessary condition for that it is
1. 1 answer
2. 493 views
Random variables X and Y are distributed according to the joint PDFfX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise. 1
1. 3 answers
2. 1,006 views
Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the
1. 4 answers
2. 1,295 views
A boat leaves point P on one side of a river bank and travels with constantvelocity V in a direction towars point Q on the other
1. 4 answers
2. 1,621 views
Alice and Bob each choose at random a real number between zero and one. We assume that the pair of numbers is chosen according
1. 9 answers
2. 9,243 views
Alice and Bob each choose at random a real number between zero and one. We assume that the pair of numbers is chosen according
1. 4 answers
2. 1,244 views
PROBLEM 4: PARKING LOT PROBLEM (3 points possible)Mary and Tom park their cars in an empty parking lot with n≥2 consecutive
1. 3 answers
2. 2,785 views
How do you toss a fair coin?
1. 3 answers
2. 3,929 views
PROBLEM 2: SET OPERATIONS AND PROBABILITIES (3 points possible)Find the value of P(A∪(Bc∪Cc)c) for each of the following
1. 4 answers
2. 3,363 views
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
1. 3 answers
2. 3,927 views
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
1. 3 answers
2. 832 views
In the lecture, we discussed the case of an isothermal atmosphere where the temperature is assumed to be constant. In reality,
1. 1 answer
2. 595 views
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
1. 13 answers
2. 1,242 views

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