Count Iblis

Most popular questions and responses by Count Iblis

Original qustion posted here: http://www.jiskha.com/display.cgi?id=1239379999 If you do computations Modulo some number, say Modulo 11, then you identify numbers from the ordinary number system that differ by a mulitple of 11. A rigorous mathematical

2. Math

i^6 = (i^2)^3 = (-1)^3 = -1 The square, not the square root of -1 is 1. :) B.t.w., can you prove that -1 times -1 is 1? Hint, try to prove first that for any number X: -1 times X equals -X How do you find the square root of -1? The square of any real

This is a reply to the question posted here http://www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we

4. Physics plzzzzzzzzz help

Ideal Gas Law: PV = N k T ---> N = PV/(k T) N = 1.387*10^(29) mass of one helium atom is approximately 4*u = 6.642*10^27 kg 4u*N = 921 kg A Goodyear blimp typically contains 4770 m3 of helium (He) at an absolute pressure of 1.10 x 105 Pa. The temperature

5. Calculus

RP^2=RQ^2 + QP^2 -2(RQ)*(QP)cosQ (1) QP = 24 (km/min) t (2) Diffentiate both sides w.r.t. the time t: 2 RP* d Rp/dt = 2 t [24 (km/min)]^2 -2(RQ)* 24 (km/min) cosQ (3) Using (1) and (2) you find out what RP is at t = 4 minutes. You plug that into (3) and

6. Third Side, Reply to Jen

Hi Jen, I've seen the drawing. My site is down at the moment. Draw a line from Venus (either of the two positions) to the line Earth-Sun at right angles. Let's call the distance Earth Venus d. Then you have a right angle triangle with a hypotenuse d, the

7. maths

Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

8. Cos(pi/4 + h) = 2^(-½)[1 - h - h^2/2 + h^3/6 +..]

This reply to some student got deleted, so I'm reposting it. Cos(pi/4 + h) = Cos(pi/4)Cos(h) - Sin(pi/4)Sin(h) = 1/sqrt(2)[1 - h - h^2/2 + h^3/6 + h^4/24 - h^5/120 - h^6/720 + ...] Note that the way students like you are asked to solve this and similar

9. calc

correction: 9/25(u+7)u^11 du = 9/25(u^12 + 7 u^11) du and you can easily integrate this indefinate integral of 9x(5x-7)^11 dx using the u substitution method: i know u= (5x-7) but when i use this the x in the 9x doesn't cancel thus x= (u+7)/5. however when

10. A Math Equation...Plz Help...

|2x + 4| is always larger than or equal to zero. This means that the left hand side of the equation is always 6 or less, so there are no solutions. 6 - 3|2x + 4| = 12 So I just put NO Soution? No solutions, or if you have to write down the solution in the

11. Science

momentum What is a kilogram meter per second? vesc=(2GM/R)1/2

1. Discrete Math

You can use generating functions. Consider the function f(y) = sum over x1,...x5 of y^(x1 + x2 + x3 + 2x4 +x5) where the summation over x1,...,x5 is from 0 to infinity. This then factors into geometric series, the result is: f(y) = 1/(1-y)^4 1/(1-y^2) =

posted on November 26, 2016
2. maths plz help

sin^2(theta) = 1-cos^2(theta) Therefore: sin^8(theta) = [1-cos^2(theta)]^4 = 1 - 4 cos^2(theta) + 6 cos^4(theta) - 4 cos^6(theta) + cos^8(theta)

posted on September 21, 2016
3. Maths

If a number X is divisible by Y, then the remainder of X after division by Y is zero. Calculating the remainder after division can be greatly simplified, you often don't need to actually divide X by Y to calculate the remainder. The remainder after

posted on August 10, 2016
4. resolve the partail fraction and then integrate

The fraction is: p(x)/(x-5)^3 with p(x) = 3x^2-34x+97 Then let's expand p(x) in powers of (x-5). If we put x = 5+t then we have: p(5+t) = 2 - 4 t + 3 t^2 Therefore, partial fraction expansion is: 2/(x-5)^3 - 4/(x-5)^2 + 3/(x-5)

posted on August 30, 2015
5. physics

Put T = 1 hour. Then in the rest frame of an observer on the ground, the spacecraft will travel distance of v T, during a time of T, this means that the space-time interval between two points on the trajectory a time T apart is given (in c = 1 units)by s^2

posted on August 13, 2015
6. physics

p = gamma(v) m v where gamma(v) = 1/sqrt[1-v^2/c^2]

posted on June 20, 2014
7. maths

Do a partial integration twice, e.g. integrate the exponential function, and then in the integral of e^(5 t) sin(5 t), you again integrate the e^( 5 t) factor (and not the sin(5t) ). You then get the the same integral back but with additional terms. You

posted on May 25, 2014
8. Calculus

You just look at the expression and then try defining a function u(x) such that in terms of u the integral will simplify. There is no "wrong choice" because the integral in terms of u will always be the same as the original one. However, the goal is to

posted on May 20, 2014
9. physics

We have: |+> = 1/sqrt(2)[|0> + |1>] |-> = 1/sqrt(2)[|0> - |1>] M = 3|+>

posted on May 15, 2014
10. physics problem

The bulk modulus K used here is the so-called adiabatic bulk modulus and this is related to the pressure P according to: K = gamma P where gamma = cp/cv = approximately 1.4 for air. So, you know the pressure and the density and then you can find the

posted on April 19, 2014
11. lotto,5 of ninety numbers

Assuming the lottery is fair, all combinations of numbers have equal probability. The only thing to consider when choosing a set of numbers is then to choose a set that no one else is likely to choose. Then when you do win, you won't end up having to share

posted on April 6, 2014
12. Math

Good old Pythagoras's theorem says that: ds^2 = dx^2 + dy^2 We can write: dx = [-5 sin(t) + 5 sin(5t)] dt dy = [5 cos(t) - 5 cos(t)] dt ds^2 = dx^2 + dy^2 = (using sin^2(x) + cos^2(x) = 1 twice for x = t and x = 5t) 25 [2 - 2 sin(t) sin(5t) - 2 cos(t)

posted on April 5, 2014
13. science

The force on the ball is unbalanced, the floor exerts a force on the ball which causes the ball to accelerate away from the floor. However, this doesn't explain why the ball changes its shape. If you hold the ball in your hands and compress it, it will

posted on April 4, 2014
14. Calculus

g'(x)=af'(x). Try to prove this using the definition of the derivative.

posted on April 2, 2014
15. probability

The probability that X is in the interval between x and x + dx is equal to dx. The proabability that Y is in the interval between y and y + dy is equal to dy. It then follows that the proability that X is in the interval between x and x + dx and Y is in

posted on March 28, 2014
16. college physics 2

At a fixed angle from the slits, if you decrease the distance between the slits the path length difference decreases. So, the angle needs to increase to get back to the same path length difference (half the wavelenght for a fringe).

posted on March 22, 2014
17. PROBABILITY

Method 1: Assign a different number to each student ranging from 1 to 90, numbers 1 to 30 go in group 1, 31 to 60 go to group 2 61 to 90 go to group 3. All possible partitions are obtained with equal probablity by a random assignment if these numbers, it

posted on February 19, 2014
18. MATH

Our time and energy used by our computers and the internet servers.

posted on February 19, 2014
19. Math : Probability

The probablity of any specific sequence of heads and tails is (1/2)^4, because the probability of getting a head at each throw is 1/2. So, the probability of getting exactly 2 heads is 1/16 times the number of ways of having two heads in a sequence of 4

posted on February 17, 2014
20. Math

You get a contradiction, i.e. a false statement. This is because you are writing down a set of equation, which already supposes that there does exist at least one solution. So, if there are no solutions that supposition is false, so you must get a

posted on February 17, 2014
21. Calculus

int y dy/(y^2-2y-3) = int 1/2 2y dy/(y^2-2y-3) = int 1/2 (2y - 2 + 2) dy/(y^2-2y-3) = 1/2 Log(y^2 - 2 y - 3) + int dy/(y^2-2y-3) int dy/(y^2-2y-3) = int dy/[(y-3)(y+1)] 1/[(y-3)(y+1)] = 1/4 [1/(y-3) - 1/(y+1)] -----> int dy/(y^2-2y-3) = 1/4

posted on February 17, 2014
22. Calculus

(4n-7)/(4n+9) = [(4n+9) -16]/(4n+9) = 1 - 16/(4n+9) The limit thus exists and is equal to 1. Clearly, for every epsilon > 0, there exists an N such that A_n will be within epsilon of the limiting value for all n > N, taking N = 4/epsilon will do.

posted on November 16, 2013
23. Calculus

|a_n| = |sin(2/n)| Since |sin(x)| N the absolute value of the difference of a_n and the limit is less than epsilon.

posted on November 16, 2013
24. Physics

If f(x1,x2) is a function of x1 and x2 which have independent uncertainties sigma1 and sigma2, then the uncertainty in f(x1,x2) is: sigmaf = sqrt[sigmaf1^2 +sigmaf2^2] where sigmaf1 and sigmaf2 are the contributions to the uncertainty in f coming from x1

posted on November 11, 2013
25. dynamics

In the co-rotating frame, define an angular variable alpha such that the channel is at alpha = 0. You can enforce that the ball is at alpha = 0 using a Langrange multiplier, so you treat the alpha coordinate as a dynamic variable for the ball. The kinetic

posted on November 10, 2013
26. Probability

Each card has equal probability to end uop in the hand of the different players. So, for each ace you have 4 equaly likely choices for the players they will end up at, there are thus 4^4 = 2^8 ways the aces can end up in the hands of the players. There are

posted on November 9, 2013
27. Science

http://www.columbia.edu/~vjd1/carbon.htm "some examples: If CO2 concentration increases in the atmosphere because of an increased rate of outgassing, global temperature will rise. Rising temperature and more dissolved CO2 will lead to increased weathering

posted on November 7, 2013
28. Calculus

sin(x) = sin[2(x/2)] = 2 sin(x/2) cos(x/2) Draw a right triangle with one angle equal to x/2. If you make the length of the side opposite to that angle equal to t = tan(x/2) then the length of the side side orthogonal to it that connects to that angle will

posted on October 31, 2013
29. physics

Without the hole the field would be sigma/epsilon_0 directed in the radial direction. Then instead of cutting a hole, you can put a surface charge of -sigma there. The field is then sigma/epsilon_0 plus the field due to the additional surface charge

posted on October 24, 2013
30. Calculus

sqrt(x^2+6x+3) = x sqrt(1 + 6/x + 3/x^2) Using the series expansion: (1+y)^p = 1 + p y + p (p-1)/2 y^2 + ... for p = 1/2 gives: sqrt(1 + 6/x + 3/x^2) = 1 + 3/x + O(1/x^2) Where the O(1/x^2) means that there exists an R and a constant c such that for x

posted on October 22, 2013
31. Linear Algebra

a) If you take two polynomials p1(t) and p2(t) that have a constant term 1 and take the linear combination a p1(t) + b p2(t) then what is the constant term of that linear combination? For arbitrary a and b does this then belong to the set of all the 4th

posted on October 22, 2013
32. calculus

The secoind derivative of a product of two functions f(x) and g(x) is: f''(x) g(x) + 2 f'(x) g'(x) + f(x)g''(x) If you take f(x) = x and g(x) = arcsin(x) then the first term is zero, so you only have to evaluate the last two terms. If you add them up you

posted on October 21, 2013

http://www.jiskha.com/display.cgi?id=1382331843

posted on October 21, 2013
34. Physics

The charge between radii r and r + dr on the disk is: sigma 2 pi r dr The contribution to the potential from this charge is: sigma/(4 pi epsilon) 2 pi r dr/sqrt(r^2 + x^2) Integrating over r from 0 to R gives: V(x) = sigma/(2 epsilon) [sqrt(R^2 + x^2) - x]

posted on October 21, 2013
35. Quantum Physics

None of them. Unless ψ1 and ψ2 are solutions with the same energy eigenvalue (in which case we say that this eigenvalue is degenerate), the linear combination aψ1+bψ2 won't be a solution to the time independent Schrödinger equation.

posted on October 21, 2013
36. Quantum Physics

The Klein-Gordon equation.

posted on October 21, 2013
37. calc

Determine on what intervals you have that: |x^2 + x | = x^2 + x and where do you have that: |x^2 + x | = -(x^2 + x) You can then compute the derivative on these intervals and see if what you get is the same as |2x + 1| for all x.

posted on October 20, 2013
38. Essentials of meteorology

The cloud would be able to rise higher were it not for the fact that the troposphere ends at a certain height in the atmosphere (between 10 to 20 km altitude, at the equator it's 20 km near the poles it's 10 km). What happens is that the temperature

posted on October 18, 2013
39. physics

See here for the correct solution: http://www.jiskha.com/display.cgi?id=1381448688

posted on October 15, 2013
40. Quantum Physics

Hadamard transform is defined as: U|0> = 1/sqrt(2) [|0> + |1>] U|1> = 1/sqrt(2) [|0> - |1>] The state is: 1/sqrt(2)|00> + e^iphi/sqrt(2)|10> We then have that: = 0 You can evaluate the l.h.s. by letting U act on the bra vector. Since U equals its own

posted on October 15, 2013
41. Calculus

Hint: What is g(0)?

posted on October 14, 2013
42. College Physics

m = 938.3 MeV/c^2 v = 7500 km/s m v = 938.3 MeV/c^2 7500 km/s = 938.3 MeV/c (7500 km/s)/c = 23.47 MeV/c

posted on October 13, 2013
43. probability

This is 1 - probability that each person will stay in a different hotel. There are 6!/2! ways to assign hotels to the four persons such that each person stays in a different hotel. The total number of ways to assign hotels to the person without any

posted on October 13, 2013
44. Physics

Correction of the last part: The kinetic energy at the start of the rough surface is thus: E = E1 [cos(theta) - mu_1 sin(theta)]^2 The distance the block will slide is thus given by: d = E/(mu_2 m g) = L/mu_2 [cos(theta) - mu_1 sin(theta)]^2* [sin(theta) -

posted on October 11, 2013
45. Physics

The height is L sin(theta). The decrease in the gravitational potential energy is thus m g L sin(theta). The magnitude of the component of the gravitational force orthogonal to the incline is m g cos(theta), therefore the normal force is equal to m g

posted on October 10, 2013
46. combination,Math

This amounts to coloring 9 balls with 4 colors. We can represent a coloring as a string of 9 o's and 3 |'s. E.g. 000|00|000|0 represents 3 balls with color 1, 2 balls with color 2, 3 balls with color 3 and 1 ball with color 4. The number of different

posted on October 8, 2013
47. physics

http://www.jiskha.com/display.cgi?id=1381249499

posted on October 8, 2013
48. PHYSICS

The tension in a point of the rope is defined as follows. It is the magnitude of force that the part of the rope on one side of the point exerts on the part of the rope on the other side of the point. The direction of the force then depends on which sides

posted on October 8, 2013
49. MATH - URGENT!!!

It's the number of ways you can put precisely 3 girls next to each other plus the number of ways you can put preciesly 4 next to each other. To get precisely 3 girls next to each ther, you can choose the 3 girls and the order in which they will take their

posted on October 6, 2013
50. physics

Put v = 19 m/s and alpha = 41°. v cos(alpha) is the horizontal speed of the ball and v sin(alpha) is the vertical speed of the ball. The equations for the vertical and horizontal motion of the ball are independent of each other. This allows you to

posted on October 6, 2013
51. Easy math

http://www.random.org/ 0.1526961 -0.4481168 -0.6982344 -0.6276160

posted on October 6, 2013
52. Math Factoring with 3 VARIABLES?!?!

You just need to recognise the square of a sum of two terms like (x+y)^2 via the term 2 x y. If you do that, you will find all the squares and then you can see the difference of the squares. So, in the expression: a^2-b^2+8bc-16c^2 you have the term 8 bc.

posted on October 5, 2013
53. physics

M G/r^2 = a where M is the mass, a the acceleration, and r is the radius. The mass is given by: M = 4/3 pi r^3 rho with rho the density, so: 4/3 pi G rho r = a -----> rho = 3 a/(4 pi G r)

posted on October 1, 2013
54. Astronomy

R = 2 M in natural units. To convert to SI units, you have to insert c and G in here, that's most easily done as follows. In Si units M^2 G/R has the dimensions of an energy and Mc^2 also has the dimensions of an energy, the ratio of the two is thus

posted on September 17, 2013
55. Logarithms

For small arguments, you can use the series expansion of the exponential function. For large arguments, you can subtract a multiple of log(2)to make the argument smaller and then use the series expansion on that smaller argument. E.g.: exp(7) = 2^10 exp[7

posted on September 17, 2013
56. Quantum Mechanics

I'm going to assuming that: |+> = 1/sqrt(2) [|0> + |1>] |-> = 1/sqrt(2) [|0> - |1>] Then there is a unitary operator U that relates output to input as: |output> = U|input> You can then calculate the output without having to expand everything in one basis,

posted on September 12, 2013
57. Quantum Computing

You haven't specified H.

posted on September 4, 2013
58. thermodynamics

I don't agree with what Graham's says about the more efficient lighting systems. All the energy produced by the lights is eventually going to heat the room (if you ignore the amount of light energy that leaves the room via the windows). It doesn't matter

posted on September 1, 2013
59. math

If u is a primitive element of Z_{37}, then: u^(36/2) = -1 We thus have that: 36! = Product from k = 0 to 36 of u^k = u^(36*37/2) = (-1)^37 = -1. So, we have: 33! = -34^(-1) 35^(-1)36^(-1) = 2^(-1) 3^(-1) 2^(-1) = 1/2 = 38/2 = 19 3^(-1) = 1/3 = 75/3 = 25

posted on August 12, 2013
60. physics

Magnitude of the electric field just outside the outer surface is: E = 49,000 N/C (4.10/3.75 )^2 equate this to sigma/epsilon_0 to find the surface charge density.

posted on August 7, 2013
61. Physics

See here for details: http://en.wikipedia.org/wiki/Paschen's_law You can use that the mean free path for electrons in air is about 5*10^(-7) meters. You always have ions and electrons in the air, so what needs to happen is that an electron has to be

posted on August 2, 2013
62. Maths

If you compute Modulo (x^2-1), then you have: x^2 = 1 x^3 = x So, we have: ax^3+bx^2+cx+d = (a + c) x + b + d Equating this to 10x+11 for all x, gives: a + c = 10 b + d = 11 Modulo (x^2+x+1), we have: x^2 = -(x+1) x^3 = -x(x+1) = -x^2 - x = 1 So, we have:

posted on July 31, 2013
63. Calculus-Series

Integral from 1 to infinity of (x^3)* (e^(-x^4)) dx = 1/4 exp(-1)

posted on July 29, 2013
64. calculus

I have reduced that to a trivial problem. The whole point of this problem is to find out how to solve it, not to get the correct answer, although I know that this is part of the Brilliant competition and the correct answer does matter here, which simply

posted on July 21, 2013
65. calculus

The integral is from -x to x, so you can replace the integrad by its even part. Since cos(t) is an even function, you can replace the factor 1/[1+exp(t)] by its even part: 1/[1+exp(t)] + 1/[1+exp(-t)] = 1/[1+exp(t)] + exp(t)/[1 + exp(t))] = 1 So, the even

posted on July 20, 2013
66. Math (Combinatorics)

The symmetry group here is D_5, see here: http://en.wikipedia.org/wiki/Dihedral_group So, you have 10 different rotations and reflections (the identity, i.e. doing nothing is one of these operations). If you don't take into account this symmetry, you would

posted on June 30, 2013
67. trig

z = 2(cos 240° + i sin 240°) = 2 exp(4/3 pi i) z^5 = 2^5 exp(20/3 pi i) = 32 exp(2/3 pi i) = -16 + 16 sqrt(3) i

posted on June 28, 2013
68. Math (Algebra)

N^3−6 is zero Modulo (N-6). If we compute Modulo (N-6) then obviously: N-6 = 0 -----> N = 6 Here and in the following the equals sign means equality modulo N - 6. We then have: N^3 -6 = 6^3 - 6 = 210 Therefore: 210 = 0 Reverting back to the ordinary

posted on June 28, 2013
69. heeeeeeeelp physics

This problem is fundamentally flawed, because you cannot treat the collision as elastic (in the sense that all the energy stays in the center of mass motion). You can't on the one hand consider the effect of the finite elasticity coefficient making the

posted on June 26, 2013
70. Maths

The boxes are indistinguishable, which means that two configurations are identical if they can be obtained from each other by permuting the boxes. If you label the boxes by the number of balls they contain, then it is clear that any partition of 7, see

posted on June 25, 2013
71. heeeelp math

If you write p(x) = q(x) r(x) then either |q(xi)| = 1 or |r(xi)| = 1, the maximum number of points xi is thus 8 if p(x) factors into 2 second degree polynomials or a third degree and a first degree polynomial.

posted on June 23, 2013
72. math

S(x) = 1 + x + x^2 + x^3 +... = 1/(1-x) dS/dx = 1 + 2 x + 3 x^2 + 4 x^3 +... = 1/(1-x)^2

posted on June 18, 2013
73. math

z = −ã2/2+ã2/2 i = exp(3/4 pi i) -z^(-52) = -exp(-39 pi i)= 1

posted on June 18, 2013
74. Math

Each permutation can be decomposed in terms of cyclical permutations. The GCM of the cycle lengths is the number of times you need to apply the permutation to get the same result back. This number is, of course, different for each permutation, so we need

posted on June 18, 2013
75. calculus

Log(e^2 + 1/10) = Log(e^2) + Log[1+e^(-2)/10] We can compute this using the series expansion: Log(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ... But we can speed up the convergence of the series as follows. Replacing x by -x in the series gives: Log(1-x) = -x -

posted on June 16, 2013
76. maths

n^3 - (n-2)^3 = 6 n^2 + .... so, A = 1/6.

posted on June 16, 2013
77. physics

http://www.jiskha.com/display.cgi?id=1370324553

posted on June 9, 2013
78. pls heeelp math

Read this: http://en.wikipedia.org/wiki/Telescoping_series Then sum both sides of: 1/H_{n} - 1/H_{n-1} = -1/[n H_{n}H{n-1}] from n = 4 to infinity, the left hand side is then a telescoping series.

posted on June 7, 2013
79. pls heeelp math

I reduced this problem to a primary school level problem here: http://www.jiskha.com/display.cgi?id=1370534461

posted on June 7, 2013
80. pllllls heeeeeeeeelp math

It's trivial: 1/H_{n} - 1/H_{n-1} = [H_{n-1} - H_{n}]/[H_{n}H_{n-1}] = -1/[n H_{n}H{n-1}]

posted on June 6, 2013
81. calculus 2

The nth term in the summation can be written as: 1*3*5...(2n-1)/(2*5*8...(3n-1) = Product i = 1 to n of (2 i-1)/(3i-1) Then because 3/2 (2i-1) = 3i - 3/2 < 3i-1 we have that: (2 i-1)/(3i-1) < 2/3 Therefore: Product i = 1 to n of (2 i-1)/(3i-1) < (2/3)^n

posted on June 5, 2013
82. Maths

a) It's 1-probability of not choosing Jaspal = 1 - (9/10)^2 = (100-81)/100 = 19/100

posted on June 5, 2013
83. Calculus

sin(x) cos(x)/(sin^2(x)-4) = -sin(x) cos(x)/(cos^2(x) + 3) -sin(x) is the derivative of cos(x), therefore, so d(cos(x)) = -sin(x) dx Integral of -sin(x) cos(x)/(cos^2(x) + 3) dx = Integral of cos(x)/(cos^2(x) + 3) dcos(x) = Integral of u/(u^2+3) du = 1/2

posted on June 5, 2013
84. heeeeeeeeeeeelp physics

http://www.jiskha.com/display.cgi?id=1370324553

posted on June 5, 2013
85. heeeeeeeeeeelp math

Use the symmetry w.r.t. interchanging heads and tails. P(4 or more heads) = P(4 or more tails) = P(less than 5 heads). So: 2 P(4 or more heads) = P(4 or more heads) + P(less than 4 heads) + P(4 heads) = 1 + P(4 heads) ------> P(4 or more heads) = 1/2 + 1/2

posted on June 5, 2013
86. physics

If the entropy of the objects at some T0 is S0 then the total entropy of the objects is: S(T1,T2,T3) = 3 S0 + C [Log(T1/T0) + Log(T2/T0) + Log(T3/T0)] We choose T0 such that the heat capacity can be taken to be constant for T > T0. Note that the heat

posted on June 4, 2013
87. Phyics Toughest question on earth

Let's call the angular velocity with which the Earth rotates around its axis omega and the average angular velocity with which it rotates around the Sun, alpha. Then the average angular velocity at which the Sun moves in the sky is omega - alpha and this

posted on June 4, 2013
88. plllllls heeeeeeelp math

3^(57x) = y 27 y - 9 y^2 + 1/27 y^3 - 1 = 0 y^3 - 3^5 y^2 + 3^6 y - 3^3 = 0 (y-y1)(y-y2)(y-y3) = 0 -y1 y2 y3 = -3^3 Log(y1) + Log(y2) + Log(y3) = 3 Log(3) 57 Log(3) S = 3 Log(3) S = 1/19

posted on June 4, 2013
89. Math Geometric Series

S = 7 + 14 + 28 + ... + 3584 2 S = 2 (7 + 14 + 28 + ...1792 + 3584) = 2*7 + 2*14 + +...+ 2* 1792 + 2*3584 = 14 + 28 + ...+ 3584 + 7168 = S - 7 + 7168 = S + 7161 2S = S + 7161 ---------> S = 7161

posted on June 3, 2013