Fully Factor  

Solve the quadratic equation  

You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman–you don’t know which is which, but the guards do know. One of the guards always tells the truth and the other always lies. You don’t know which one is the truth-teller or the liar either. However both guards know each other. You have to choose and open one of these doors, but you can only ask a single question to one of the guards. What do you ask to find the door leading to freedom?

Existence-Uniqueness Theorem: If f(x, y) and df/dy are continuous on a rectangle R in the xy-plane containing the initial condition y(x0)=y0, then the initial value problem y’=f(x,y), y(x0)=y0 has a unique solution in R. 6pts Determine whether the Existence-Uniqueness Theorem can be used to determine if the initial value problem: y’ = 1/x + y1/3,    (1,1)  has a unique solution.  Please indicate the largest possible rectangle R from the Theorem.   21pts First order ODEs: Solve the following. Provide solutions in explicit form if possible. Theorem: M(x,y) dx + N(x,y) dy = 0 is an exact equation if dM/dy = dN/dx. a.  (y4 + 1)cos x dx – y3 dy = 0 b.  (12x – y)dx – 3x dy = 0 c.  (x3 + y/x)dx + (y2 + ln x) dy = 0   8pts Homogeneous ODE: Solve y iv + 5y ‘’ – 36y = 0.   10pts Nonhomogeneous ODEs: Solve the following with either undetermined coefficients or variation of parameters to solve  3y ‘’ – y’ – 2y = 4x + 1, y(0) = 1 and y’(0) = 0   10pts Systems: Solve the following.                   x1’ = 2×1 – 4×2                                      x2’ = 2×1 – 2×2   15pts Solve the initial value problem for y(t) using the method of Laplace transforms. y ’’ + 4y’ + 3y = 1 y(0)=0,   y’(0) = 0   Taylor polynomial about 0: pn(x) = f(0) + f’(0)x + f ‘’(0)/2! x2 + f ‘’’(0)/3! x3 +  … + f (n)(0)/n! xn   15pts Determine the first three nonzero terms in the Taylor polynomial approximations for the given initial value problem y ’’ – 2y’ + y = 0;          y(0)=0,   y’(0) = 1   Theorem: Consider the differential equation A(x) y” + B(x) y’ + C(x) y = 0.  If the functions p(x) = B(x)/A(x) and q(x) = C(x)/A(x) are analytic at x =0, then the general solution is produced by the power series centered at x=0: y(x) = a0 + a1x + a2 x2 + a3 x3 + …   15pts Determine the first four nonzero terms in the power series expansion about x=0 for a general solution in the given ODE y ’’ + xy’ + y = 0           

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Dystocia is largely due to

What is the outermost part of a tooth’s crown called?

An occupational therapist closely examines the steps a client must perform to load clothes into a washing machine.The therapist notes specific physical and cognitive actions such as: Bending down to pick up the laundry basket Gripping and lifting the basket with both hands Maintaining balance while carrying the basket across the room Opening the washing machine door using fine motor skills Selecting the correct wash cycle by turning a knob with appropriate hand strength and motor planning The therapist is focused on breaking down the specific motor and process skills required for each step. This type of analysis is BEST described as ________. 

True or False: Section GG scoring is a factor in the determination of payment in post-acute settings such as Inpatient Rehabilitation Facilities and Skilled Nursing Facilities.

An occupational therapist conducts a satisfaction survey to evaluate the quality of OT services in an outpatient program. The questionnaire developed by the therapist asks respondents to rate their responses to quality statements according to a 4-point Likert scale of agreement. Which statement best reflects an accurate measure of satisfaction?