mangaman81

How do I solve the following problems? (I don't want just the answer--I already have those. I want to know how to do these for the test) :

Determine whether the following set of vectors form a basis for R^3. Justify your answer.

a. {v1 = (1,1,0)^T, v2=(1,0,1)^T, v3=(0,1,-1)^T}

b. {v1=(3,-2,1)^T, v2=(2,3,1)^T, v3=(2,1,-3)^T}

Thanks!

Hey,

I managed to find the answers to these problems online, but that really doesn't help because I want to know how to do these, and I'm totally lost.. can someone show me the process for at least a few of these?

Which of the following are true and which are false, and why?

(a) √n^5 ∈ O(n^2)

(b) √n log √n ∈ O(n)

(c) log(n^3) ∈ O(n log n)

(d) 2/n + 4/n^2 ∈ Θ(1/n)

(e) (log_2(n))^.5 ∈ Θ(log(n))

(f) min(700, n^2) ∈ Θ(1)

How do I do these?

If I buy a Japanese PS2 (NTSC-J), then will it be able to be used with American power outlets and televisions?

Thanks

About a four days ago I noticed two little bumps on my (older) cat, and one on her back. My cat gets bumps from time to time, so I didn't really worry about it, and figured it would go away in a few days. The two bumps on her neck are near each other and have gotten bigger (they're not very big yet, but they're definitely bigger than the tiny bumps they were a few days ago.)

Does this seem like something that could be serious? My parents are out of town and I have to go to work in the morning. I'm going to keep checking to see if it gets bigger or anything like that.. Is this something I need to take her to the vet for? Also, she's showing no other symptoms--just acting like her self, but these have me worried.

Thanks so much!

PS: Before finishing writing this, I was petting her and noticed one more on her head (really, really small one.)

13. A whistle of frequency 540 Hz moves in a circle of radius 60 cm at an angular speed of 15 rad/s. What is the highest frequency that an observer a long distance away might hear?

or...

14. A whistle of frequency 540 Hz moves in a circle of radius 60 cm at an angular speed of 15 rad/s. What is the lowest frequency that an observer a long distance away might hear?

I'm thinking it is probably pretty simple, but I have no idea where to start. Thanks!

(n + 1)/(2n - 1)

and also:

sqRt(n)/(1 + sqRt(n))

Thanks!

I'm trying to study for my physics test, but I can't figure out part B (and I guess technically C or D) of this question:

2. Flywheels represent one method of storing energy for use during peak loads, and have seen limited use in buses. In one configuration a carbon-fiber cylinder of radius r = 0.5 m and moment of inertia I = 200 kg m2 operates at an angular speed of 24,000 rpm at full capacity. (a) (5 points) Calculate the energy stored in the flywheel.

(b) (5 points) Assuming that the torque applied in accelerating the wheel is 2000 N m, the time required to reach its maximum angular velocity is

(c) (5 points) The number of revolutions the flywheel rotates in reaching this velocity is

(d) (4 points) At full speed the acceleration of a particle on the outer surface of the cylinder is

I solved part A by doing 24000 rpm * 2 * pi/60 = ~2512

KE = 1/2 * I * w^2

.5 * 2512^2 * 200 = 6.31e8

But I have no idea how to do the rest. Anyone have any ideas?

Thanks!

Hiya!

The question is:

Solve the differential equation using the method of undetermined coefficients.

y'' + 2y' + y = xe-x

The auxiliary equation is:

r^2 + 2r + 1

The complementary solution is:

c1xe^-x + c2e^-x

But what is the general solution? I tried:

y = Axe^-x

Take the derivative:

y' = -Ae^-x(x - 1)

Take the second derivative:

y" = Ae^-x (x - 2)

Plug it back into the original equation:

1 * Ae^-x (x - 2) + 2 * -Ae^-x(x - 1) + 1 * Axe^-x = xe^-x

Axe^-x - 2Ae^-x - 2Axe^-x + 2Ae^-x + Axe^-x - xe^-x = 0

All of the things with A cancel, leaving just -xe^-x = 0...

What did I do wrong?

Thanks a lot!

Hello!

The question states:

Solve the initial-value problem.

y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1

So....

r^2 - 2r + 1 = 0

Using the quadratic formula to find the values:

(- - 2 +/- sqRt((-2)^2 - 4 * 1 * 1))/(2 * 1)

2 +/- sqRt(0)/2

2/2

1

In the book, it states that this means the general solution is:

y = c1e^rx + c2e^rx, where in this case r = 1.

So then I differentiate, but....

y' = c1e^x + c2e^x = y = c1e^x + c2e^x

Because they're the same, I can't solve for the constants.

What am I doing wrong?

Thanks!!

Hello,

I'm attempting to study for Physics, but I'm stuck on another problem:

A bullet of mass m = 20 gm [It says gm, I'm assuming it just means grams, so in kg = .02] is traveling at a velocity of 200 m/s perpendicular to the long axis of a wood block resting on a frictionless surface. The mass of the block is M = 10kg, and its length is L = 1 m. The bullet goes through the end of the block, emerging along its original path but with a reduced velocity of 100m/s.

Part b is just the easy conservation of momentum, mv of bullet = mv of bullet + mv block....

But part a is:

Determine the magnitude of the angular velocity of the block, assuming that the block is thin enough so that the moment of inertia about its center of mass is Icm = (1/12)ML^2.

I didn't really know how to do this, but I tried:

200m/s * .02 = 100m/s * .02 + 1/12 * 10 * 1^2 * omega

2 = 10/12 omega

2.4 = omega

The answer is, however, that omega = 1.2, which is half of my answer. Am I missing a 1/2 somewhere, or is this just a coincidence and I did everything totally wrong?

Thanks!

Hi!

We're having trouble understanding this problem:

7. A 3 kg particle is moving at a velocity of 5 m/s parallel to the x axis in the negative x direction. The line of action (path of the particle) is a distance of 4 m from the origin in a given coordinate system, P, and a distance of 8 m from the origin of a second coordinate system, P¢. The angular momentum of the particle about P¢ as compared to P is

(a) the same

(b) larger by a factor of 2

(c) smaller by a factor of 2

(d) larger by a factor of 5

(e) smaller by a factor of 5

L = Iw

I = .5mr^2

w = 5

Because everything but r is constant, the only difference is r^2

So we have 4^2 and 8^2 which yields 16 and 64, so the difference is 4x. However, the correct answer is 2x, why is this? It seems that it is just the 4 versus 8, but this doesn't make sense to me.

Thanks!

Hiya!

This question reads:

A particle of mass 0.40 kg is moving with velocity v = (5.0i + 6.0j) m/s.

(a) Find the angular momentum L relative to the origin when the particle is at r = (2.0j + 3.0k) m.

I'm meant to answer in terms of i, j, and k.

My understanding is that L = v * r * m

So that would give me m * (v x r), so I do the cross product:

[5 6 0]

[0 2 3]

I tried to find i, which would be 6 * 3 - 0 * 2 = 18 * .4 = 7.2, however this is not correct.

What am I doing wrong?

Thanks!

(a) Use Euler's method with step size 0.1 to estimate y(1.4), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places.

y' = x - xy

y(1) = 0

My work:

y(1) = 0

->y'(1) = 1 - 1 * 0 = 1

y(1.1) = y(1) + .1 * y'(1) = 0 + .1 * 1 = .1

-> y'(1.1) = 1.1 - 1.1 * .1 = .99

y(1.2) = y(1.1) + .1 * y'(1.1) = .1 + .1 * .99 = .199

-> y'(1.2) = 1.2 - 1.2 * .199 = .9612

y(1.3) = y(1.2) + .1 * y'(1.2) = .199 + .1 * .9612 = .29512

-> y'(1.3) = 1.3 - 1.3 * .29512 = .916344

y(1.4) = y(1.3) + .1 * y'(1.3) = .29612 + .1 * .916344 = .3877544 or in 4 decimal places .3878 ... this is not correct. The previous problem was the same question, except I was supposed to use step size of .2, and I got .392 (and it was correct), so I don't know what the problem is.

Thanks!

Question Part

Points

Submissions Used

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places.

y' = 1 - xy

y(0) = 0

So, my work is:

y(0) = 0

y(.2) = y(0) + f(0)*.2 = 0 + (1 - .2 * y(0))*.2 = (1 - .2*0)*.2 = .2

y(.4) = y(.2) + f(.2)*.2 = .2 + (1 - .2 * .2) * .2 = .392

y(.6) = y(.4) + f(.4)*.2 = .392 + (1 - .2 * .392) * .2 = .57632

y(.8) = y(.6) + f(.6)*.2 = .57632 + (1 - .2 * .57632) * .2 = .7532672

y(1) = y(.8) + f(.8) *.2 = .7532672 + (1 - .2 * .7532672) * .2 = .923136

But .9231 is not the answer. What have I done wrong?

Thanks a bunch!

A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

F = spring constant * d

So:

25N = const * .1 (20cm to 30cm is .1m)

const = 250

F = spring constant * d again

F = 250 * .05m (from 20cm to 25cm)

F = 12.5

Work = F * d

12.5 * .05 = .625J

Obviously that is way too small, and not correct. Also, WebAssign tells me it isn't correct. Why? What is correct?

Hey!

Can someone point out cards that are like Totally Lost in standard where they put a card on top of a player's library? (Like Azorius charm, but in the colors U/B). I'm trying to make a casual/for-fun Dimir deck, and I feel like there are a lot of fun combos to be had with that and Nightveil Specter and Duskmantle Seer.

Do the partners ever stop being useless? So far I only have Esther, but everytime I'm in a boss fight she's just a complete moron and stands in every attack and dies immediately. I've just been letting her die and beating the boss fight on my own. Is there something I'm missing?

I've been running a Boros Deck in standard (even though its not a thing yet) for awhile now, but here's what I'm currently considering for when Gatecrash comes out (excluding unannounced spoilers, of course) :

1 Mana:

4x Champion of the Parish

2x Legion Loyalist

2 Mana:

2x Ash Zealot

2x Lightning Mauler

3x Searing Spear

4x Boros Charm

3 Mana:

4x Silverblade Paladin

2x Frontline Medic

2x Fiend Hunter

2x Oblivion Ring

3x Aurelia's Fury (XWR)

4 Mana:

3x Resto Angel

2x Odric, Master Tactician

3x Spark Trooper

Sideboard:

3x Rest in Peace

2x Fiend Hunter

2x Oblivion Ring

2x Ash Zealot

2x Lightning Mauler

1x Aurelia's Fury

4x Skullcrack

Any suggestions?

Evaluate:

Integral( (2x^2 + 5) / (x^2 + 1)(x^2 + 4) dx)

Set it up with partial fractions...

(Ax + B)/(x^2 + 1) + (Cx + D)/(x^2 + 4)

Multiply through by denom..

Ax(x^2 + 4) + B(x^2 + 4) + Cx(x^2 + 1) + D(x^2 + 1) = 2x^2 +5

Multiply out..

Ax^3 + 4Ax + Bx^2 + 4B + Cx^3 + Cx + Dx^2 + D

Solve for variables..

4Ax + Cx = 0x

4B + D = 5

A + C = 0

B + D = 2

4A + C = 0

4B + D = 5

A = -C

4 * -C + C = 0

-3C = 0

C = 0

A = 0

D = 2 - B

4B + 2 - B = 5

5B = 3

B = 3/5

D = 7/5

Plug variables back in..

(0x + 3/5) / (x^2 + 1) + (0x + 7/5) / (x^2 + 4)

3/5Integral(1/(x^2 + 1) dx) + 7/5Integral(1/(x^2 + 4) dx)

Integrate..

3/5[arctan(x)] + 7/5[1/2arctan(x/2)]

3/5arctan(x) + 7/10 arctan(x/2) + C

This is not the correct answer.

Why?

What is the correct answer?

Does Calc 2 ever stop being impossible?

Integral ( (x^2 + 2x - 1) / (x^3 - 1) dx)

I know I need to do partial fractions, so I get the bottom to be (x - 1)(x^2 + x + 1),

but I'm really bad at setting these up...

Would it be:

A/(x - 1) + (Bx + C)/(x^2 + x + 1)? How do you know when to use Bx + C? How do you know when to just use Bx, and how do yo ukonw when you need to split up up further (like I know you do it when it is an x^2..?)

Thanks!