AREA OF CONCENTRATION-FINAL EXAM FEBRUARY 2013

ENGINEERING MATHEMATICS 1 (EMT 201) PROBLEMS

These are the areas of concentrations. Try to solve by yourself as part of the review on the Final Exam in February 2013 . Similar problems will be coming out.

- Bacteria are growing at the rate equal to 10.60 % of its population each week. If in the beginning there are 2000 microorganisms, how many organisms are present after

A) 4 weeks b) 2 months

2. An engineering student deposited N400, 000.00 at an annual rate of 18.55 % compounded continuously, how long will it take the account to triple in value?

3. A tank contains 222 liters of water. A bitter lemon solution containing 3 kg/liter of sugar enters the tank at the rate of 6 liters/min and runs out at 5 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 1 hour.

**4. **Determine the value of current** I** flowing in a resistor R= 100 ohms, an inductance L = 7 henrys and a battery E = 100 volts connected in series.

5. A Madonna University canteen serves a cup of tea at 96C to an engineering student. After 3 minutes, the tea has cooled to 78C . If the canteen temperature is 18C , how many minutes that the student must wait to cool the tea to 46C?

6.Solve y” + y’ -2y = e ** ^{3x}** using a) undetermined coefficient method

b) Variation of parameter method

7. Solve y’ + 6y = 0, y=2 when t=0. Solve by Laplace transform.

8. How much will be left after 600 years for a radioactive element carbon 14 which has a half life of 5750 years if the initial amount is 50 grams? Solve by Laplace transform.

9. Determine the equation of motion of a 40 kg mass suspended to a coiled spring with k = 2000 N/m, initially displaced a distance of 1 meter from equilibrium position, and released with zero velocity and subjected to no damping or external forces. Solve by Laplace Transform.

10. A student deposited N200, 000.00 at an annual rate of 8.25 % compounded continuously, how long will it take the account to double in value? Solve by Laplace.

11.Find the area bounded by a parabola y=x^{2} from x =0 and x=6 by vertical and horizontal elements methods.

12.Determine the accumulated amount of N22000.00 after 12 years if invested at a nominal interest of 4 % is compounded continuously?

13. A hemispherical tank 8 meters in radius contains mercury to a depth of 4 meters. Find the volume of mercury in the tank.

14. The watermelon is ellipsoid in shape with major axis 44 cm and minor axis 36 cm. Find its volume.

15. Solve y” + 5x (y’)²=0.

Good luck!

**DR. VICTOR E. ODARVE BSME, MEP-ME, MAED, EDD**

**PHILIPPINES, SOUTHEAST ASIA**