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QUESTION 16 Cognitive behavioral therapy has been shown to work well for older adults who are experiencing: A. sensory impairment B. dementia C. balance problems D. anxiety and sleep disorders

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3. (a) Consider the following total utility schedule: Quantity Consumed 0 1 2 3 4 5 6 7 8 9 Total Utility 0 8 13 17 20 22 23 23 22 20 (i) Draw the total utility schedule and derive the marginal utility schedule from it. (ii) If the marginal utility of money (λ) is 0.5, plot the demand curve from marginal utility schedule. (iii) Find the equilibrium quantity demanded if the price of commodity is ₹ 4 per unit. (b) Suppose Rahul always consumes 2 spoons of sugar with each cup of coffee. The price of coffee is ₹ 20 per cup and price of sugar is ₹ 5 per spoon. If Rahul has ₹ 600 to spend on coffee and sugar, how much coffee and sugar would he like to purchase? With the help of budget line and indifference curve show the optimal choice of Rahul in a diagram. (2+3+1)+(2+2)

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$m_1\ddot{x_1} + k_1x_1 + k_2(x_1 - x_2) = 0$ $m_2\ddot{x_2} + k_2(x_2 - x_1) = 0$ Write these coupled second order linear differential equations as (a) A single fourth order ODE in $x_1$ (b) A system of four coupled linear ODEs in terms of the positions and velocities of each mass. Please write this as a matrix ODE. (c) For the remaining parts, you may assume that $k_1 = k_2 = m_1 = m_2 = 1$. What are the eigenvalues of the matrix system of ODEs? You can use a computer to solve for these these. (d) Simulate the system from $t = 0$ to $t = 50$ using using Matlab ode45 or python solve\_ivp with a sufficiently small time-step, and plot the results; start with an initial condition $x_1(0) = x_2(0) = 1$ and $\dot{x_1}(0) = \dot{x_2}(0) = 0$. (e) Now simulate the system from $t = 0$ to $t = 50$ and plot the results for initial condition $x_1(0) = -0.5$, $x_2(0) = 0.5$, and $\dot{x_1}(0) = \dot{x_2}(0) = 0$. (f) Do the simulations agree with your intuition based on the eigenvalues? Briefly, how would you explain the solutions to a first-year physics class, without using any calculus?

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Determine the first three nonzero terms in the Taylor polynomial approximation for the given initial value problem.\ y''(0) + 5y(0)$^3$ = sin 0; y(0) = 0, y'(0) = 0\ The Taylor approximation to three nonzero terms is y(0) = + ...

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For a layer of liquid flowing in a laminar flow in the z direction down a vertical plate or surface, the velocity profile is: v_z = frac{ ho g delta^2}{2mu} left[ 1 - left( frac{x}{delta} ight)^2 ight] Where delta is the thickness of the layer, x is the distance from the free surface of liquid toward the plate, and v_z is the velocity at a distance x from the free surface. Consider the wall to have a depth of w in the y-direction and a length L in the z-direction. (a) Provide a sketch of the system described above with appropriate coordinates and origin point (b) What is the maximum velocity v_{z-max}? Show that the expression you get has the units of velocity. (c) Derive the expression for the average velocity v_{z-av} and relate that to v_{z-max} (d) Derive an expression for the total volumetric flow rate down the wall. Show that the expression you get has the units of m3/s. (e) Calculate the shear acting on the x-surface at x=delta. You are given the relationship between shear and velocities as: au_{xz} = -mu left[ frac{partial v_z}{partial x} + frac{partial v_x}{partial z} ight]. What are the units of shear you obtain? (f) Calculate the drag force on the wall. What is the unit of drag you obtain?

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6. A triangle has sides equal to 5 cm, 10 cm and 7 cm, respectively. Find its area (round your answer to 1 decimal place).

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1. Consider lists made from the letters T,H,E,O,R,Y, with repetition allowed. (a) How many length-4 lists are there? (b) How many length-4 lists are there that begin with T? (c) How many length-4 lists are there that do not begin with T? 2. Airports are identified with 3-letter codes. For example, the Richmond, Virginia airport has the code RIC, and Portland, Oregon has PDX. How many different 3-letter codes are possible? 4. Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such line-ups are there in which all 5 cards are of the same suit? 6. Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such line-ups are there in which exactly one of the 5 cards is a queen?

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3. Calculate the bending stresses about the X axis for the 2a, 2b and 2c problem if the cross-section of the beam is: -2a) Rectangular shape: base b=400mm, height h= 250mm -2b) W130 x130x28.1 structural steel (attached table) -2c) Composite shape: 4. Size the W beam (problem 2c) based on sectional module from the attached table, if the allowable bending stress is 200 MPa.

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Potential from Two Point Charges A +52 µC charge is placed 21 cm from an identical +52 µC charge. If you assume the potential at infinity is zero, then what is the potential midway between the two charges? How much work is done to move a 0.30 µC charge from a point midway between the charges to a point 10 cm closer to either of the charges?

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Determine the exponential function whose graph is given. f(x) =

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maria o.