os x)2 = 1+ 2 sin x cos x 1- 2 cos x - 3cos2 x = 1- 3cos x
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- Two trigonometric identities are given by:
- (sin x + cos x)2 = 1+ 2 sin x cos x
1- 2 cos x - 3cos2 x = 1- 3cos x
sin2 x
1- cos x
For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation using MATLAT, substituting x=200
- Find the solution to the systems
|
... .. .
y + 3 y + 2 y y u
Where y (0) =0; y’ (0) =0. u (t) is a square wave.
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- Write a computer program to evaluate the Taylor series expansion for cos(x) to evaluate theseries starting at x0 = 0 radian with h = 0·1 to x = 1 radian· Use one term, two terms, three termsand four terms of the series· Evaluate the error in each value and discuss the effect ofincrementally adding the terms to the series· Compare your results with the true solutionUse Matlab to solve the following equations for x, y, and z as functions of the parameter c. x-5y-2z=11c 6x+3y+z=13c 7x+3y-5z=10c Then, plot the solutions x,y,z versus c on the same plot for -10<=c<= 10.Using Matlab, code the following:The paper cup has Radius R2 = l.5(R1), height (h), volume V = 716 cm3 ,and surface area (S). The height, volume, and surface area of the cup are given by: V =πh(R1^2+R2^2+R1R2)/3 S = π R1^2+ π (R1+R2)√(R2 − R1)^2 + h^2 Determine R1, R2, and S of the paper cups with heights h = 8, 10, 12, 14, and 16 cm. • Method 1: Simulate Equations without using a for loop. • Method 2: Simulate Equations using a for loop. Display results to the screen tabulated Hint: You may need to transpose the vectors before printing to the screen.
- Demonstrate the validity of the following identities by means of truth tables: The distributive law: x + yz = ( x + y ) ( x + z )The electric flux density D at the point M (0,4,0) in the region about a uniform line charge of 1 nC/m lying along the z axis in free space is: Select one: a. None of the above b. 0.6366 nC/m c. 0.2387 nC/m d. 0.039 nC/m e. 0.1 nC/mThe equations given below are the mathematical models of the three mixed tanks that are connected in series. Solve the following equations using MATLAB programme using numerical methods and plot the graphics (C, t) for all tanks. Data: Q=constant= 300 L/min, V= constant= 50 000 L, t=0; C=Co, Differential equations : dCA1 / dt = -0.006 CA1 (CA1 - CA2 ) = 167 (dCA2 /dt) d CA3 /dt = 0.006 (CA2 - CA3 )
- The equations given below are the mathematical models of the three mixed tanks that are connected in series. Solve the following equations using MATLAB programme using ode23 and plot the graphics (C, t) for all tanks. Data: Q=constant= 300 L/min, V= constant= 50 000 L, t=0; C=Co, Differential equations : dCA1 / dt = -0.006 CA1 (CA1 - CA2 ) = 167 (dCA2 /dt) d CA3 /dt = 0.006 (CA2 - CA3 )PLEASE SHOW STEPS:What Boolean equation is represented by the following K-Maps: ~y~z ~yz yz y~z ~x 1 1 1 x 1 1 1 1Solve in PYTHON OR JUPYTER Consider the differential equation dy/dt = y(a −y^2) for the values a = −1, a = 0 and a = 1 and determine their critical points. Sketch for each of these differential equations their direction field and phase lines. Use these plots to determine whether the critical points are asymptotically stable or unstable.