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1. Consider the initial value problem (x + 5) y' + {2 / x-π) y= In x, y(1) = -10. Without solving the equation, what is the largest interval in which a unique solution is guaranteed to exist?
2. A fish tank is initially tilled with 400 liters of water containing 2g/liter of dissolved oxygen. At t 0. oxygenated water containing 10 g liter of oxygen flows in at n rate of 4 liter min. live well-mixed water is pumped out at a rate of 3 liter min from the tank. Write an initial value problem (do not solve) that describes. Q(t). the amount of dissolved oxygen in the tank at any time r > 0 (until the time when the tank, eventually, overflows).
3. Newton's Law of Cooling says that the rate at which the temperature of a body changes is proportional to the difference of the temperature of the body and the temperature of the surrounding medium. Suppose a cup of coffee at 100o C is placed in a room where the temperature is 25o C. Write an initial value problem (do not solve) to describe the temperature of the cup of coffee at any lime t > 0.
Saly and marbel Had the same number of cards at first. Aafter saly sold 18 of her cards,mabel had four times as many cards as saly. How many cards did each girl have at first?
The tension T at each end of the chain has magnitude 15 N. What is the weight of the chain?
Parametric equations for the line through {1,2,3} parallel to the vector {5,6,-4} are, A friend taking the old-fashioned course tells you that the xyz-equations for this line are
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value does not exist, enter NONE.)
1. evaluate the derivatives of the followinga. f x x sincosx2b. f x x32 - x tanxc. f x tan2x2dx2. a square piece of
Front range cabinet distributors in colorado springs, colorado, sells to its contractors with a 42% markup on cost. if the selling price for cabinets is $9,655, what is the cost to contractors based on cost?
the charge to rent a car is 29.95 per day plus .08 per mile. write an expression that shows the cost of renting a car
To attend a friend's wedding, you must buy an airplane ticket and rent an automobile. If you can spend a total of $685 and the plane ticket will cost $325, how much can you spend on car rental?
The zoo is building a new polar bear exhibit, and wants to put a semi-circular window in the concrete wall of the swimming tank. Find the hydrostatic force on the window.
Raw materials A and B are used to make one of the target company's product the product must contain no more than 9units of A and at least 18units of B, it must cost no more than 300$, how much of each raw material should be used to maximize the we..
Suppose that at a certain instant the volume is 540 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 11 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
Using the following integral and the facts that v(t) = x'(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Answer the questions a - c.
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