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  1. H

    ##\int (\sin x + 2\cos x)^3\,dx##

    Homework Statement $$\int (sinx + 2cos x)^3dx$$ Homework Equations The Attempt at a Solution $$\int (sinx + 2cos x)^3dx$$ $$\int (sinx + 2cos x)((sinx + 2cos x)^2dx)$$ $$\int (sinx + 2cos x)(1 + 3cos^2x+2sin2x)dx$$ How to do this in simpler way?
  2. H

    Find induced current, magnetic force, work in inclined plane

    Homework Statement A conducting bar slides down without friction on a pair of conducting rails separated by distance d. Connected to resistor R and there magnetic field B directed upward, perpendicular to the ground over the entire region through which the bar moves. 1) find the current 2)...
  3. H

    Electric Force on a Charge in a Solenoid

    Homework Statement Since i only know the field direction, increasing go into page. Why the answer is C? Why the answer "a" ? The R and r on the pic is respected to what? Homework Equations The Attempt at a Solution Right hand rule : finger tip = current Thumbs = force Palm = B Or...
  4. H

    Find the minimum distance between 2 particles

    Homework Statement A point particle of mass m and charge q(>0) approaches to a point particle Q(>0) at a fixed position. When the distance between the two particles is L, the speed of the moving particle is v. The permittivity of the vacuum is denoted as Epsilon0. Find the minimum distance...
  5. H

    New wave after superposition (interference)

    Homework Statement 1. Homework Statement [/B] The displacement y of standing wave that is obtained by a superposition of waves : Y1 = 3 sin (2##\pi##(0.5t - 0 25 x)) Y2 = 3 sin (2##\pi##(0.5t + 0 25 x)) Homework Equations Formula for standing waves Y = 2Asinkx coswt The Attempt at a Solution...
  6. H

    Find the change in the Kinetic energy of an Ideal Gas

    Homework Statement Let 3/2kT be the kinetic energy of ideal gas per molecules. T the absolute temperature and N the avogadro number. Answer the following questions : 1) when the volume doubled at constant temperature. How many times the kinetic energy per molecule become greater than before...
  7. H

    Find the force between 2 blocks

    1. The problem statement, all variables and given/known data Homework Equations The Attempt at a Solution B at rest. A moves 7m/s and bump into B. Object A is frictionless. Object B not, coeff of friction = 0.2. g = 9.8 m/s2 After collision both objects moves together with speed 2 m/s to the...
  8. H

    Frequency for resonance to occur

    Homework Statement That is a speaker. Sound wave is sent out from spesker S into pipe of uniform thickness. Piston P move to left 1st resonance at 0.045 m 2nd resonance at 0.151 m Frequency of the sounx 1620 Hz Piston is stopped at the position that 2nd resonance occur Then, frequency...
  9. H

    Magnetic field and flux

    Homework Statement [/B] There is lead XY shaped as straight wire. Next to it, circular lead with radius 0.10 m. They are in the same plane. XY to center of circle, O is 0.20 m. Curent flowing through XY is 15.7 A Homework Equations The Attempt at a Solution 1) find magnetic field (B) at...
  10. H

    ##\lim_{n \to \infty} ## for the sequence at ##a_n##

    Homework Statement ##a_1## = 3 ##a_{n+1}## = ##\frac{2}{3} a_n + \frac{1}{4} ## Homework Equations [/B] The Attempt at a Solution Sequence i got : ## a_1, a_2, a_3, a_4, a_5 ## ## 3, \frac{9}{4}, \frac{7}{4}, \frac{17}{12}, \frac{43}{36} ## I tried to find the formula of ##a_n## ##a_n =...
  11. H

    How to solve this trigonometry equation

    Homework Statement ##\sin a + \cos b## = ##\frac{-1}{2}## ##\cos a + \sin b## = ##\frac{\sqrt 3}{2}## 0 < a < ##\pi/2## ##\pi/2## < b < ##\pi## a + b = ? By calculating sin (a+b) Homework Equations The Attempt at a Solution I tried : ##\sin a + \cos b =...
  12. H

    Find the angle between 2 vectors

    Homework Statement |a| = 2 |b| = ## \sqrt3## |a - 2b| = 2 Angle between a and b Homework Equations The Attempt at a Solution ##\theta## is angle between a and b So angle between a and -2b is 180-##\theta## [/B] ##|a-2b|^2## = |a|^2 + |2b|^2 -2|a||2b|cos(180-##\theta##) ##2^2## = 2^2 +...
  13. H

    Find the transient current in this circuit

    Homework Statement Homework Equations The Attempt at a Solution I often do circuit. But still there is always stuff i dont get.. I was asked to find 1) I1 I2 I3 immidiately after S closed 2) I1 I2 I3 after sufficient of time 3) I1 I2 I3 immidiately after S opened Just give me clue please...
  14. H

    Find the speed of a satellite at a distance R from Earth

    Homework Statement Gravitational force exerted on mass m is GMm/r^2 2. Relevant equations Orbital velocity at distance R from earth = ##\sqrt gR## Escape velocity = ##\sqrt 2gR## gR = GM/R Fc = mV^2/R F =m.a The Attempt at a Solution 1) express acceleration of gravity in terms of G, M , and...
  15. H

    Heat and work when temperature increases by 1 degree

    Homework Statement Kinetic energy per mol is 3/2KT Homework Equations Q = nC##\Delta##T U = Q + W W = -P##\Delta##V The Attempt at a Solution 1) internal energy = 3/2NKT 2) heat needed to increase temperature of 1 mol ideal gas by 1 degree at constant volume? Since constant volume, W = 0 Q...
  16. H

    What is the necessary and sufficient condition?

    Homework Statement |x-2| < a is a necessary condition for x^2 -3x -10 < 10 . What is the range value of a? |x-2| < a is a sufficient condition for x^2 -3x -10 < 10. What is the range value of a?[/B] The options are a>= 4 a>=3 0<a<=2 0<a<=3 0<a<=5 The Attempt at a Solution Range of x for x^2...
  17. H

    Magnetic field at the center of 3 wires carrying current?

    Homework Statement each wire carrying 10 Amps a = 0.3 meter point o located in the center Homework Equations B = permeability constant * I / ( 2 ##\pi## r) r = distance between O and the wire r perpendicular to B and I A = carrying current into the page B and C = out of the pages The...
  18. H

    Electrostatic energy after a metal piece is inserted between 2 capacitor plates

    Homework Statement fig 1 : Area of each plate is S, separated by 2d, charge Q in the capacitors fig 2 : uncharged conductors of area S, thickness d, inserted parallel between plates What is the ratio of electrostatic energy in fig 2 to electrostatic energy in fig 1? Homework Equations Q =...
  19. H

    Find the Voltage in the parallel resistor-capacitor circuit

    Homework Statement C1 = 4 micro F C2 = 8 mF R1 = 4 ohm R2 = 8 ohm V = 12 Questions : 1) Find current I when S not closed 2) find Vb, when Vc is 0 3) find Vd, when Vc is 0 4) total charge move from B to D Homework Equations Vf - Vi = F.d/q (not sure this below is useful equations) I = E/Z E...
  20. H

    How to find the power consumed by the light bulb

    Homework Statement (Is the image read-able now? ) The fig 1 shows the relationship between voltage and current when voltage is applied to a certain light bulb. Next, in fig 2, the bulb is connected in series with a 12-V battery and a 5 ohm resistor. Question : what is the amount of power...
  21. H

    How to solve this integral of an absolute function?

    Homework Statement Homework Equations The Attempt at a Solution I think the answer for number 1 , graph somewhat like this I get trouble for 2, 3, etc I (k) = ##\int_{-1}^{1} f(x) dx ## f(x) = ## \mid x^2 - k^2 \mid## 2) k < 1 for negative side ##\int_{-1}^{-k} (x^2 - k^2) dx +...
  22. H

    Find the limit as h --> 0 for this trigonometery equation

    Homework Statement ##\lim_{h \to 0} \frac{f(x - 2h) - f(x + h)}{g(x + 3h) - g(x-h)}## While f(x) = cos x g(x) = sin x Homework Equations The Attempt at a Solution Using L Hopital i couldn't make it more simple. I tried to divide it by cos and sin Can you give me clue?
  23. H

    Find the current induced in a wire loop by a nearby current

    Homework Statement Homework Equations The Attempt at a Solution When the circuit moves creates magnetic force that moves the some charges in the wire and that is a current. That is what i thought. F = Q.v B sin theta B = ( permeability Of vacuum* I)/(2pi.r) But how to find the I? Thank...
  24. H

    Find the width increases when a monoatomic gas is heated

    1. The problem statement, all variables and given/known Homework Equations ## \frac {PV1}{T1} = \frac {PV2}{T2} ## The Attempt at a Solution I find that v2 = 330/273 V1 But how can this related to the distance of P travel? Also, as the A gas pressed to B, i think the B gas try to resist...
  25. H

    Rubber strings pulled and realeased -- find the max height

    Homework Statement Homework Equations The Attempt at a Solution I tried to find constant k f = k ##\Delta##x 1/2 * 9,8 = k * 0,1 k = 49 N/m is rubber string the same as spring? Ep + EK at 0,1 meter = Ek + EP at 0,3 m 1/2 k x^2 + 0 = 1/2 k x^2 + 1/2 mv^2 v^2 = 2*49(0,08) v = 7*0,4 = 2,8...
  26. H

    Find the forces on a table that is lifted in a tilted position

    Homework Statement Homework Equations The Attempt at a Solution what's the Fa and Fb? my logic is Fa = Wa - N = mg - ##\frac{N}{\cos \theta}## so is Fb... so the ratio is 1. But I know it's wrong. What will make the difference between Fa and Fb? can anyone give a clue please?
  27. H

    Find the time when the spring reaches its max height

    Homework Statement Homework Equations f = Spring's constant * ##\Delta x## Potential Energy = ##\frac{1}{2} kx^2## The Attempt at a Solution I try to find constant of the springs Fabove + Fbelow - W = 0 k*(0,2 m) + k*(0,2m) - ##\frac{1}{2}## * 9,8 = 0 0,4k = 4,9 k = 12,25 N/m can I use...
  28. H

    Find f(x) which satisfies this integral function

    Homework Statement find f(x) which satisfies f(x) = x + ##\frac{1}{\pi}## ##\int_{0}^{\pi} f(t) \sin^2{t} \ d(t)## Homework Equations The Attempt at a Solution to solve f(x), I have to solve the integral which contains f(t). And f(t) is the f(x) with variable t? if yes, I will get integral...
  29. H

    Find limit x to infinity from f(x) contains squareroot of x

    Homework Statement ##\lim x \to \infty \frac{\sqrt{x+1} - \sqrt{x}}{\sqrt{3x + 5} - \sqrt{3x + 1}}## Homework Equations The Attempt at a Solution ##\lim x \to \infty {\sqrt{x+1} - \sqrt{x}} * \lim x \to \infty \frac{1}{\sqrt{3x + 5} - \sqrt{3x + 1}}## ##\lim x \to \infty \frac{(x+1) -...
  30. H

    What's the current from this circuit? Is it a short circuit or not?

    Homework Statement Pic A, what's the I2? Pic B, what's the current across a-b ? Homework Equations V = I*R Voltage in series is different, the current is the same Current in parallel is different, the voltage is the same The Attempt at a Solution from Pic A, I found that I1 = 1A, I3 = 1A...
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