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_1) Consider the curve f(x) = Acos(27x//). The wavelength of the wave will be: a. the...
A transverse wave on a wire is given by D(x, t) = 0.030 sin(27x - 567t)...
A transverse wave on a wire is given by D(x, t) = 0.030 sin(27x - 567t) where x is in meters and t is in seconds. a) Determine an expression for a wave with the same amplitude, wavelength, and frequency but traveling in the opposite direction. b) What is the speed of either wave?
3. Consider the vector field F(x,y) = (27x D = {(1,y): 0 < rº + y2...
3. Consider the vector field F(x,y) = (27x D = {(1,y): 0 < rº + y2 <2}. +ya) defined on the region D where a) Directly compute SF. Tds using the definition of the line integral, where C is the unit circle oriented counterclockwise. b). Use Theorem 3.3 (Test for Conservative Vector Fields) from the text to determine if F is conservative. Is your answer consistent with part a)? If not, what is the source of the discrepancy?
E. Consider a continuous random variable X with cdf F(x) = x3/8, 0 < x < 2.
E. Consider a continuous random variable X with cdf F(x) = x3/8, 0 < x < 2. (27) The pdf f(x) of X is (а) 6х (b) x3/8 (c) 3x2/8 (d) x2/4(28) E[X2+3X] is (а) 6.9 (b) 4.3 (с) 4.5 (d) 8.1 (29) The probability P(X > 1) is (a) 7/8 (b) 4/8 (c) 6/8 (d) 3/8
SECTION 4.3 Polynomial Division; The Factor the polynomial function f(x). Then solve the equation f(x) =...
SECTION 4.3 Polynomial Division; The Factor the polynomial function f(x). Then solve the equation f(x) = 0. 39, f(x) =x3 + 4x2 + x-6 40. fx) 5x - 2x 24 41, f(x) =x3-6x2 + 3x+10 42. f(x)-x3 + 2x2-13x + 10 43, f(x) = x3-x2-14x + 24 44.f(x) = x3-3x2 In Ex given. a): Fi b) C in gi - L 二 10x +24ー丁only, this one d) C gi ase 45' f(x) =x4-7x3 + 9x2 + 27x-54 plecs( 46, f(x)...
part (e),(f) and (g) 3. Wave functions (40 marks) Consider particle described by wave function (x)...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
32. Multiply or find the special product (x-3) a. - 9x +27x+27 b. x-9x®-27x-27 c. X-9x...
32. Multiply or find the special product (x-3) a. - 9x +27x+27 b. x-9x®-27x-27 c. X-9x +27x-27 d. x +9x +27x+27 e. +9x°-27x+27 33. Find the product. The expression is not polynomial, but the formula can still be used.) (3+ *)(3-6) a. 3-X b. 9+x c. d. e. 1-9 9-X 3+x 34. Completely factor the difference of two squares. - 16 a. (x+4)-(-4) b. (x+4) c. (x+4)(x-4) d. (x+4)+(x-4) c. (x-4) 35. Factor the perfect square trinomial. -16x + 64...
5. (8 pints) A String that lies along the +x- axis has a free en incident wave at)-Acos(lox + t) is reflected at th...
5. (8 pints) A String that lies along the +x- axis has a free en incident wave at)-Acos(lox + t) is reflected at the en (1) (2 points) Judge that end (x 0) (2) (4 points) Write down the standing wave function y (3) (2 points) Find th of the string. d at x=0 . An x=0 the standing wave has an antinode or a node at its free function y(x,tl) along the +x-axis. imum speed of the free end...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t (A) Determine the wave's (a) amplitude; (b) wavelength; (c) propagation speed (d) frequency (e) direction of propagation (B) An element of the string is located at x 2.25 m (a) Show that the motion of this element is a simple harmonic motion with a transverse displacement of the form y(t) Acos ( t + ф). (b) Determine the phase constant φ (c) Give its...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin (...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin ( 3173 107t + 4 Find: a. the wavelength of the wave; b. the period of the wave; c. the speed and direction of travel of the wave; Now consider the particle at x = 10 cm. d. Find the vertical displacement of the particle t = 0. e. Find the maximum transverse speed and acceleration of the particle. If the oscillator that is generating...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x)...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x) = 27x+6(7x – 6) b. $'(x) = 27x+617x + 6) C. $'(x) = 7e7x+6(x - 1) d. f(x) = _ 3x+47 – 6X2x + 6) Inx 13. Determine the derivative of the function. 1. sm) = 1-31(c) b. f'(x) = Lt nec. Sw)= d. S(0) = . sm)= Blanket
3. Consider the vector field F(x,y) = (27x D = {(1,y): 0 < rº + y2 <2}. +ya) defined on the region D where a) Directly compute SF. Tds using the definition of the line integral, where C is the unit circle oriented counterclockwise. b). Use Theorem 3.3 (Test for Conservative Vector Fields) from the text to determine if F is conservative. Is your answer consistent with part a)? If not, what is the source of the discrepancy?
SECTION 4.3 Polynomial Division; The Factor the polynomial function f(x). Then solve the equation f(x) = 0. 39, f(x) =x3 + 4x2 + x-6 40. fx) 5x - 2x 24 41, f(x) =x3-6x2 + 3x+10 42. f(x)-x3 + 2x2-13x + 10 43, f(x) = x3-x2-14x + 24 44.f(x) = x3-3x2 In Ex given. a): Fi b) C in gi - L 二 10x +24ー丁only, this one d) C gi ase 45' f(x) =x4-7x3 + 9x2 + 27x-54 plecs( 46, f(x)...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
32. Multiply or find the special product (x-3) a. - 9x +27x+27 b. x-9x®-27x-27 c. X-9x +27x-27 d. x +9x +27x+27 e. +9x°-27x+27 33. Find the product. The expression is not polynomial, but the formula can still be used.) (3+ *)(3-6) a. 3-X b. 9+x c. d. e. 1-9 9-X 3+x 34. Completely factor the difference of two squares. - 16 a. (x+4)-(-4) b. (x+4) c. (x+4)(x-4) d. (x+4)+(x-4) c. (x-4) 35. Factor the perfect square trinomial. -16x + 64...
5. (8 pints) A String that lies along the +x- axis has a free en incident wave at)-Acos(lox + t) is reflected at the en (1) (2 points) Judge that end (x 0) (2) (4 points) Write down the standing wave function y (3) (2 points) Find th of the string. d at x=0 . An x=0 the standing wave has an antinode or a node at its free function y(x,tl) along the +x-axis. imum speed of the free end...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t (A) Determine the wave's (a) amplitude; (b) wavelength; (c) propagation speed (d) frequency (e) direction of propagation (B) An element of the string is located at x 2.25 m (a) Show that the motion of this element is a simple harmonic motion with a transverse displacement of the form y(t) Acos ( t + ф). (b) Determine the phase constant φ (c) Give its...
A traveling wave is described by the equation: TT y(x, t) = (0.35 cm) sin ( 3173 107t + 4 Find: a. the wavelength of the wave; b. the period of the wave; c. the speed and direction of travel of the wave; Now consider the particle at x = 10 cm. d. Find the vertical displacement of the particle t = 0. e. Find the maximum transverse speed and acceleration of the particle. If the oscillator that is generating...
12. Determine the derivative of the function. f(x) = (x - 1)e7x + 6 a. f'(x) = 27x+6(7x – 6) b. $'(x) = 27x+617x + 6) C. $'(x) = 7e7x+6(x - 1) d. f(x) = _ 3x+47 – 6X2x + 6) Inx 13. Determine the derivative of the function. 1. sm) = 1-31(c) b. f'(x) = Lt nec. Sw)= d. S(0) = . sm)= Blanket
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