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At a certain factory, output Q is related to inputs 2 and y by the equation...
At a certain factory, the total cost of manufacturing q units is C(q) = 0.4q2 +...
At a certain factory, the total cost of manufacturing q units is C(q) = 0.4q2 + q +800 dollars. It has been determined that approximatelyq (t) = 12 + 60t units are manufactured during the first 1 hours of a production run. Compute the rate at which the total manufacturing cost is changing with respect to time 3 hours after production begins. Three hours after production begins, cost is changing at the rate of approximately SI per hour. Round your...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
Assume that I and y are both differentiable functions of t and are related by the...
Assume that I and y are both differentiable functions of t and are related by the equation y=cos (2x) dy Find when 11 given . -3 when = Enter the exact answer. = Number Hint Penalty Hint1 0.0 View Hint Memaining Time: 37:32:32 The volume of a sphere is increasing at a rate of 15 cubic centimeters per second. Find the rate of change of the radius when it is 5 milimeters. Round your answer to two decimal places. The...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
problem 1) Find the differential equation describing the amount of salt,Qb, in the tank for times...
problem 1) Find the differential equation describing the
amount of salt,Qb, in the tank for times t in the interval t>=T.
Then solve to obtain Qb(t) for t>= T
A Water Tank Problem with Discontinuous Source A water tank contains V > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r >0 liters per minute with a salt concentration of q> 0 grams...
The pressure P and volume V of a gas are related by the equation p^5v^7=c where c is a constant. At a certain instant of time, the pressure is 100 lb/ft^2, the volume is 4ft^3 and the pressure is dece...
The pressure P and volume V of a gas are related by the equation p^5v^7=c where c is a constant. At a certain instant of time, the pressure is 100 lb/ft^2, the volume is 4ft^3 and the pressure is decelerating at a rate of 5 lb/ft^2/sec. Find the rate of change at which the volume is changing.
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r > 0 liters per minute with a salt concentration of q> 0 grams per litter, and we let the well-stirred water leave the tank at the same rate. After T > 0 minutes the process is stopped and fresh water is...
_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2)...
_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2) B (0) C2) D.(0.2) (0,3,-3) D_7. The set of critical points (or equilibrium points) of the equation y'=yl - 9y is: A (0) C.-99) D_8. Which of the following is a stable point of ' (-1)? A0 B. 1 C andu1 D. Neither is stable F 9 True or False) The equation y + xy +x+yi b le Writer for true or F forse...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
At a certain factory, the total cost of manufacturing q units is C(q) = 0.4q2 + q +800 dollars. It has been determined that approximatelyq (t) = 12 + 60t units are manufactured during the first 1 hours of a production run. Compute the rate at which the total manufacturing cost is changing with respect to time 3 hours after production begins. Three hours after production begins, cost is changing at the rate of approximately SI per hour. Round your...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
Assume that I and y are both differentiable functions of t and are related by the equation y=cos (2x) dy Find when 11 given . -3 when = Enter the exact answer. = Number Hint Penalty Hint1 0.0 View Hint Memaining Time: 37:32:32 The volume of a sphere is increasing at a rate of 15 cubic centimeters per second. Find the rate of change of the radius when it is 5 milimeters. Round your answer to two decimal places. The...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
problem 1) Find the differential equation describing the
amount of salt,Qb, in the tank for times t in the interval t>=T.
Then solve to obtain Qb(t) for t>= T
A Water Tank Problem with Discontinuous Source A water tank contains V > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r >0 liters per minute with a salt concentration of q> 0 grams...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r > 0 liters per minute with a salt concentration of q> 0 grams per litter, and we let the well-stirred water leave the tank at the same rate. After T > 0 minutes the process is stopped and fresh water is...
_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2) B (0) C2) D.(0.2) (0,3,-3) D_7. The set of critical points (or equilibrium points) of the equation y'=yl - 9y is: A (0) C.-99) D_8. Which of the following is a stable point of ' (-1)? A0 B. 1 C andu1 D. Neither is stable F 9 True or False) The equation y + xy +x+yi b le Writer for true or F forse...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
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