Reference no: EM131007059
1. a. Check that y = ½x2 + x + 3 satisfies the differential equation dy/dx = x + 1.
b. Check that y = sin t satisfies the differential equation d2y/dx2 = -y.
2. Sketch a slope field corresponding to the equation dy/dt = 2t - y. Then sketch the solution that passes through the point (1,2).
3. Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy/dx = -2 Then determine f(x).
4. A curve y = f(x) has the property that the slope of tangent to the curve at every point is reciprocal to the y value of the curve. Write down a differential equation whose solution is y = f(x). Then show verification that y = √(2x + C) and y = - √(2x + C) satisfy this differential equation.
5. Determine the time it takes an amount of money to triple if compounded continuously at an annual rate of 15%.
6. I got a Guinness can whose temperature is 21o C. To enjoy it cold at the perfect temperature of 9oC, I set my refrigerator to 0oC. The temperature T(t) of the can at time t measured in seconds satisfies Newton's Cooling Law equation:
dT/dt = -.000iT.
How long will it take for the can to cool off to 9oC?
7. A cup of tea with initial temperature of I = 85oC is left in the room a constant temperature A = 21oC. In one minute the tea cools down to 84Cdegree. What will be the temperature of the tea after an hour? When will the temperature of the tea be 22o?
|
Physical units of production
: 1) Compute the physical units of production 2) Compute equivalent units of production for materials and conversion costs 3) Determine the unit cost of production
|
|
Company manufacturing cost and other expense data
: 1) Fabila Company specializes in manufacturing a unique model of bicycle helmet. The model is well accepted by customers, and the company has enough orders to keep the factory production at 10,000 helmets per month (80% of its full capacity). Fa..
|
|
Accounting rate of return
: The company anticipates a yearly net income of $2,850 after taxes of 30%, with the cash flows to be received evenly throughout of each year. What is the accounting rate of return?
|
|
Monterey average investment
: Monterey uses straight-line depreciation and assumes that the annual cash inflow from the machine will be received uniformly throughout each year. In calculating the accounting rate of return, what is Monterey's average investment?
|
|
What will be the temperature of the tea after an hour
: In one minute the tea cools down to 84Cdegree. What will be the temperature of the tea after an hour? When will the temperature of the tea be 22o?
|
|
Determining the normal selling price
: If it rebuilds the units, they will not be able to produce 750 new units with a unit cost of $3.00 and a normal selling price of $15.00 each. What should the company do?
|
|
Lawn fertilizer called fastgro
: Use the following information to answer this question. Cole Laboratories makes and sells a lawn fertilizer called Fastgro. The company has developed standard costs for one bag of Fastgro as follows:
|
|
Do these actions constitute systematic errors
: Suppose that Joe enjoys and repeatedly does stupid things like getting heavily into debt and insulting police officers. Do these actions constitute systematic errors? If he gets what he wants each time, are his stupid actions even considered to be..
|
|
Comparison of the statement with the cash account
: On May 31, 2011, James Logan Company had a cash balance per books of $6,602.94. The bank statement from Farmers State Bank on that date showed a balance of $6,375.10. A comparison of the statement with the cash account revealed the following facts..
|