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Let z = 1+sqrt(3) * i (a) Express z in polar form (b) Hence evaluate z^(9) (c) Express z^(5) in cartersian form Thanks for any help!?
Let z = 1+sqrt(3) * i
(a) Express z in polar form
(b) Hence evaluate z^(9)
(c) Express z^(5) in cartersian form
Thanks for any help!
1 AnswerMathematics6 years agoYoung’s experiment is performed with monochromatic light. The slits are 1.40 mm apart, and the viewing screen is 6.30 m from the slits.?
Young’s experiment is performed with monochromatic light. The slits are 1.40 mm apart, and the viewing screen is 6.30 m from the slits. The distance between the 2nd and 4th dark fringes is determined to be 5.76 mm. What is the wavelength of the light?
The answer is 640Nm according to my lecturer - but I don't know what formulae to use. Cant get my head around it :/any help would be immensely appreciated guys thank you
1 AnswerPhysics6 years agoA worker repeatedly strikes one of the rails of a train track with a hammer. In the distance, a car sitting on the rail notices that a?
A worker repeatedly strikes one of the rails of a train track with a hammer. In the distance, a car sitting on the rail notices that a little after each blow the rail shakes, and then the sound of each blow arrives through the air 0.53s later. The cat then creeps 55 m along the rail towards the worker and sits again. Now the delay is reduced to 0.38s.
(a) How far along the rail is the cat sitting from the worker to begin with?
(b) What is the speed of sound in the rail?
(Use 343m/s as the speed of sound when needed)
Guys I FOUND the answers are for (a) 190m and (b) 5300m/s - but I don't know how to do the calculating physics around it. Any help an d input would be tremendously appreciated !
2 AnswersPhysics6 years agoA rusty bicycle is ridden at constant speed along a highway. The front wheel produces a sound at a frequency of 468 Hz.?
A rusty bicycle is ridden at constant speed along a highway. The front wheel produces a sound at a frequency of 468 Hz. The driver of a car travelling in the same direction notices that the frequency changes from 488 to 447 Hz as she overtakes the cyclist.
Find the speed of (a) the cyclist, and (b) the car.
I know the answers are for (a) 8.37m/s and (b) 23.4m/s but I don't know how to get my head around the physics behind getting these. Please help me out guys thanks :/
1 AnswerPhysics6 years agoAssume x,y,t > 0. Solve the differential equation: t*(dx/dt) = (1+2ln*t)tanx?
Assume x,y,t > 0. Solve the differential equation: t*(dx/dt) = (1+2ln*t)tanx
Thanks guys
1 AnswerMathematics7 years agoA cup of coffee is made with boiling water and stands in a room where the temperature is 20◦ C. If H(t) is the temperature of the coffee?
a) A cup of coffee is made with boiling water and stands in a room where the temperature is 20◦ C. If H(t) is the temperature of the coffee at time t, in minutes, explain what the differential equation
dH/dt = -k(H-20)
says in everyday terms. What is the sign of k?
(b) Solve this differential equation. If the coffee cools to 90◦C in 2 minutes, how long will it take to cool to
60◦C degrees?
Thanks guys
1 AnswerMathematics7 years agoUse separation of variables to find the solutions to the differential equations subject to the given initial conditions:?
Use separation of variables to find the solutions to the differential equations subject to the given initial conditions:
(a) dz/dt = te^(x), through the origin
(b) x(x+1)*(du/dx) = u^(2) where u(1) =1
Thanks guys
1 AnswerMathematics7 years agoFor the following system of linear equations, write the system as an augmented matrix, then use elementary row operations to?
For the following system of linear equations, write the system as an augmented matrix, then use elementary row operations to solve the system.
x1 + 5x3 = 2
3x1 + 5x2 + 15x3 = 8
-5x1 - 10x2 - 25x3 = -14
** The 1s, 2s and 3s after all the x variables are just numerals, not integers. So its just saying its the first term, then the seconf x term, and the third - I think its the same as jut x, y and z. But do I just solve it like a normal matrix? Thanks
1 AnswerMathematics7 years agoFor the following system of linear equations, write the system as an augmented matrix, then use elementary row operations to solve the?
For the following system of linear equations, write the system as an augmented matrix, then use elementary row operations to solve the system.
x1 - 2x3 = 3
3x1 + 3x2 - 8x3 = 2
4x1 - 6x2 - 3x3 = 25
** The 1s, 2s and 3s after all the x variables are just numerals, not integers. So its just saying its the first term, then the seconf x term, and the third - I think its the same as jut x, y and z. But do I just solve it like a normal matrix? Thanks
2 AnswersMathematics7 years agoDetermine whether the given planes are parallel: (a) x + 4y - 3z = 2 and 2x - 8y - 6z = 1 , (b) 4x - y + 2z = 5 and 12x - 3y + 6z = 8?
Determine whether the given planes are parallel:
(a) x + 4y - 3z = 2 and 2x - 8y - 6z = 1 ,
(b) 4x - y + 2z = 5 and 12x - 3y + 6z = 8
Thank you!
2 AnswersMathematics7 years agoGiven v=3i+4j and force vector F=9i+12j, find:?
Given v=3i+4j and force vector F, find:
(a) The component of F parallel to v
(b) The component of F perpendicular to v
(c) The work, W, done by force F through displacement v
THanks guys very unsure
2 AnswersMathematics7 years agoUse the method of Gaussian elimination to solve the following systems of linear equations:?
Use the method of Gaussian elimination to solve the following systems of linear equations:
Thanks guys i don't know how to do it with the extra variable
1 AnswerMathematics7 years agoConsider the three points a = (1,4,0), b = (2,1,5) and c = (3,5,2) in R3 . Find each of the following:?
Consider the three points a = (1,4,0), b = (2,1,5) and c = (3,5,2) in R3 . Find each of the following:
(a) the vector from a to b
(b) a parametric form of the equation of the line through a and b
(c) a parametric form of the equation of the plane through a , b and c
(d) a cartesian equation of the plane containing a, b and c;
(e) a vector perpendicular to the plane containing a, b and c .
Thanks guys hopeless with vector geometry!
1 AnswerMathematics7 years agoCalculate the volume of the “table leg” for which the radius r at height z is given by the following expression, with 0<=z<=12?
Calculate the volume of the “table leg” for which the radius r at height z is given by the following expression, with 0<=z<=12
r(z) = 4 + cos((pi*z)/2)
1 AnswerMathematics7 years agoUse the substitution x = tan u to evaluate the integral?
Use the substitution x = tan u to evaluate the integral:
1/(1+x^(2))^(5/2) between 0 and 1. (picture to represent the integral better)
2 AnswersMathematics7 years agoFind the values of the following improper integrals, if they converge:?
Find the values of the following improper integrals, if they converge:
(a) integral of xe^(-x^(2)) between - infinity and + infinity
(b) integral of 1/sqrt(3-x) between 0 and 3
Thanks guys, not sure what it means about converging?
2 AnswersMathematics7 years agoFind the values of the following improper integrals, if they converge:?
Find the values of the following improper integrals, if they converge:
(1) integral of xe^(-x^(2)) between - infinity and + infinity
(2) integral 1/sqrt(3-x) between 0 and 3
Thanks guys for your time!
3 AnswersMathematics7 years agoRotating the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = about the x-axis generates an ellipsoid. Compute its volume?
Rotating the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = about the x-axis generates an ellipsoid. Compute its volume
Thanks guys :)
3 AnswersMathematics7 years agoEvaluate the definite integral representing the area of the region enclosed by y=x^(2) and y=3x using vertical slices.?
Evaluate the definite integral representing the area of the region enclosed by y=x^(2) and y=3x using vertical slices.
Is this just simple integration by using pi or what? Thanks guys :)
1 AnswerMathematics7 years agoCalculate the integral: (dx)/(x^(2)+25) between - negative and + infinity?
Calculate the integral: (dx)/(x^(2)+25) between - negative and + infinity
If they converge, it is said I should appeal to the dominance of one function over the other , or also by applying l"Hopital's rule.
Any help is greatly appreciated!
3 AnswersMathematics7 years ago