2/T = cos cos--Cos 4. 16 12+2cos 7/2 /2+2 cos a /4 V2 +2 cos T /16 elido vZ VZ+ vZ V2+ V2+ v2 2+ V2 + v2 12. Vièta solved the quadratic equation x2 +ax = b by substituting x = y – a/2. This produces a quadratic in y in which the first-degree term is missing. Use Vièta's method to solve the quadratic equations: %3D %3D - x² + 8x = 9. x² + 10x = 144. (b) x² +12x = 64. (c) 3x² + 10x = 32. [Hint: Multiply both sides by 3 (d) and let z = 3.x.] barieh (a) %3D %3D %3D %3D 7). 13. To solve the equation x² + ax = b² geometrically, René Descartes would have used the method as Mndi described. Draw a line segment AB of length b and at A erect a perpendicular AC of length a/2. With C as center, construct a circle of radius a /2 and draw a line through B and C , intersecting the circle at points D and E. Prove that the length of the segment BE is the value of x that satisfies x² +ax = b². %D until

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A:

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

A:

Q: Suppose that x1(t) = et and x2(t) = e-t are two solutions of a homogeneous linear differential…

A: The answer is found in step-2

Q: Use (18) in Section 6.4. x²y" + xy' - (x²x² + ²y = 0 (18) Find the general solution of the given…

A:

Q: Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х +…

A: OPTION D IS CORRECT.

Q: Determine whether {1, sin 2x, cos 2x} is a set of linearly independent solution of the linear…

A:

Q: Use the method of undetermined coefficients to solve the initial value problem. Oy y = y= y = y = 3…

A:

Q: a) Find the general solution to the following third-order differential equa- tion 2- dz3 + 2y = 3e…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A:

Q: 2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use…

A: Furst we rewrite the equation as in the theorem, then Use the given theorem

Q: 5. Find two solutions (not multiples of each other) of the Bessel equation of order x*y" +xy' + (x²…

A: The general form of the Bessel equation is ,                                          x2y" +xy'…

Q: Solve the diffevential cauationm. du e cosn=0,0 X2015,40)-a. Alam - Moislton method with h=0.4.

A: The given differential equation is, dydx+y-e-xcosx=0

Q: 1. Solve the following partial differential equations by direct partial integration. (i) = 4ty [u=…

A:

Q: Find a formula involving integrals for a particular solution of the differential equation y" – 18y"…

A: Consider the provided question,

Q: Suppose we are given y₁ (x) and y2(x) (with y₁ y2), which are two different solutions of a…

A:

Q: Use the annihilator operator (not undetermined coefficient) for the right hand side and use it with…

A:

Q: 7. Obtain the solution of (D² – 4)y = 16 + cos 2x using the method of undetermined coefficients %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: function is given by: f(x)1 − 4x cos(x) + 2x2 + cos(2x). Find the solution of f(x) = 0 within 10-5…

A:

Q: 14. A form of a particular solution for the DE (using undetermined coefficient method) + 3yl4 + 5v"…

A:

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = + 10e',…

A:

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 6e¹,…

A: Given differential equation is y'' + 4y = t2 + 6et,   y(0) = 0, y'(0) = 7

Q: If y, = u1 (t) cos(5t) + u2(t) sin(5t) is a particular solution of the differential equation y" +…

A:

Q: 3. Rewrite y" - 2y' + y² = cos x as two first-order equations and then use Euler's method to…

A:

Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

A:

Q: The differential operator D2 +12D+ 40 has the form D -2aD+a? + B2 where a = - and B= 2 Therefore D2…

A:

Q: 1. Solve for x(t) and y(t), given that x(0)=D4 and y(0)=3 dx dy + x + 4y = 10; a dt dt x(t) 2+2e cos…

A: Solution :-

Q: 7. When the given differential equation is Solved using Laplace transform Method, the equivalint…

A: Given  differential equation isy''+2y'+y=te-tand given conditions are y0=1 and y'0=-2find the…

Q: 15. A form of a particular solution for the DE y(4) + 3y + 5y" = 72 using undetermined coefficient…

A:

Q: 1/2 Q2. a) Using Hilbert-Schmidt method, solve y(x) = cos 2x + 2 f,"´ K (x, t)y(t)dt, where Ssin x…

A:

Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

A:

Q: 4.Find two solutions (not multiples of each other) of the Bessel equation of order 3232…

A:

Q: 3- Find the solution of given initial value problem: y" +y= u3(t), y(0) = 1, y'(0) = 0 y(t) = sint +…

A:

Q: Q6: Determine a particular solution of the equation dzy +4y 4x2 cos 2x dx2 Using D-operator method

A:

Q: 8. The auxiliary roots of the auxiliary equation associated with a certain homogeneous LDE are m =…

A:

Q: Solve the initial value problem dx 2x = cos(4t) dt with x(0) = 1. x(t) = sqrt(-1/4sin(4t)+1)

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A:

Q: Show that the kinematic differential equations of the (2-3-2) Euler angles is 0 = [B(0)]» %3D where,…

A: Let us first find the kinematic differential equations of the (2-3-2).

Q: How do you solve this problem?

A: Note: As the question is very lengthy, we have showed the important calculations leaving the basics.…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A:

Q: The van der WVaals equation of state is given by 3. (P +) (v- b) = RT In this equation, v (V/n)…

A: This is a multipart question having 3 or more interrelated subparts. So, as per the company policy,…

Q: Solve the following initial value problem for r as a function of t. dr Differential equation:…

A: To solve the given initial value problem.

Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

A:

Q: a) By using convolution theorem, show that 1 1 (sin 3t – 3t cos 3t). 54 L- (s² + 9)² b) Using…

A:

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . h"…

A: Given: h''-4h'+5h=0 , h(0)=0 , h'(0)=-1 To determine: Solution of the differential equation.

Q: efe* cos 2t dt 1. 5. e 3 sin 2t 9. t S* sin at dt 2. 6. e' - cost 10. t e 3t | tsin 2t dt 1- cos 3t…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Prove that the general solution of the differential equation √√1+cos(t) d0=(√1 + cos(t) — t sin(t)…

A:

Q: se the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1 + 8e',…

A: Method of Undetermined coefficients  We have to find general solution of given differential…

Q: Which of the following is the general solution of the fifth-order homogeneous linear differential…

A: The solution is given as

Q: Verify that the indicated pair of functions is a solution of the given system of differential…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.