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7. An element decomposes at a rate proportional to its amount at any instant. In 100 years, 100 mg of the amount of element decomposes to 96 mg. In 100 years, determine the amount left. a. 88.60 O b. 92.16 O c. 95.32 O d. 90.72

7. An element decomposes at a rate proportional to its amount at any instant. In 100 years, 100 mg of the amount of element decomposes to 96 mg. In 100 years, determine the amount left. a. 88.60 O b. 92.16 O c. 95.32 O d. 90.72

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. An element decomposes at a rate Which of the following equations is a variable separable DE? proportional to its amount at any instant. In 100 years, 100 mg of the amount of element decomposes to 96 mg. In 100 years, determine the amount left. O a. 2y dx = (x² + 1) dy 88.60 O b. (x+ x? y) dy = (2x + xy?) dx о с. у? dx + (2х - зу) dy - 0 O b. 92.16 Oc. 95.32 o d. (x+ y) dx – 2y dy = 0 o d. 90.72 8. 10. The solution of the differential equation (x* +1) +(x² +1) = 0 The solution of differential equation dr dy dr ! + tan 1-x y=. 1+x Oa. Ob. y=2+x O a. cos(y/x)=xc Oc. 1+x y=: 1-x O b. sec?(y/x)=xc od. y=x(x-1) Oc. sin(y/x)=xc O d. cot(y/x)=xC
Transcribed Image Text:7. An element decomposes at a rate Which of the following equations is a variable separable DE? proportional to its amount at any instant. In 100 years, 100 mg of the amount of element decomposes to 96 mg. In 100 years, determine the amount left. O a. 2y dx = (x² + 1) dy 88.60 O b. (x+ x? y) dy = (2x + xy?) dx о с. у? dx + (2х - зу) dy - 0 O b. 92.16 Oc. 95.32 o d. (x+ y) dx – 2y dy = 0 o d. 90.72 8. 10. The solution of the differential equation (x* +1) +(x² +1) = 0 The solution of differential equation dr dy dr ! + tan 1-x y=. 1+x Oa. Ob. y=2+x O a. cos(y/x)=xc Oc. 1+x y=: 1-x O b. sec?(y/x)=xc od. y=x(x-1) Oc. sin(y/x)=xc O d. cot(y/x)=xC
1. 3. 5. A tank contains 80 gals. of pure water. A A container has 100 liters of brine containing 50 kg. total of dissolved salt. Pure water is An organic compound decomposes at a rate proportional to the amount present. If the half of the original amount disappears after 1000 years, what is the percentage lost in 100 years? brine solution with 2 lbs/gal of salt enters at allowed to run into the container at the rate of 3 L/min. Brine runs out of the tank at the 2 gals/min, and the well-stirred mixture rate of 2 L/min. The instantaneous leaves at the same rate. Find (a) the amount concentration in the tank is kept uniform by of salt in the tank at any time stirring. How much salt is in the tank at the end of one hour? O a. 4.30% a. 80 lbs a. 15.45 kg Ob. 19.53 kg O. 12.62 kg od. 20.62 kg O b. 4.50% O b. 41.3 Ibs Oc. 5.35% Oc. 23 Ibs O d. 6.70% o d. 27.73 Ibs 2. 6. Determine the solution of the differential An island has population that doubles in 50 equation dy dr +y cot x = coSX years. Determine how long will the population be five times as much? Assume Newton's law of cooling states that, the rate at which a substance change temperature in air is directly proportional to the difference that the rate of increase is proportional to the sin'z +c Oa. O a. ycos x = between the temperatures of the substance number inhabitants. and that of air. If the temperature of the air is 30° and the substance cools from 100* to Ob. ob. ycos x = sin²z 70° in 15 minutes, how long will it take to cool 100* to 50*? O a. 100 years O c. ysin x = cosz +c b. 98 years a. 33. 59 min O b. 43.60 min O. 35.39 min o d. ysin x = sin²z ос. 120 years O d. 116 years o d. 45.30 min
Transcribed Image Text:1. 3. 5. A tank contains 80 gals. of pure water. A A container has 100 liters of brine containing 50 kg. total of dissolved salt. Pure water is An organic compound decomposes at a rate proportional to the amount present. If the half of the original amount disappears after 1000 years, what is the percentage lost in 100 years? brine solution with 2 lbs/gal of salt enters at allowed to run into the container at the rate of 3 L/min. Brine runs out of the tank at the 2 gals/min, and the well-stirred mixture rate of 2 L/min. The instantaneous leaves at the same rate. Find (a) the amount concentration in the tank is kept uniform by of salt in the tank at any time stirring. How much salt is in the tank at the end of one hour? O a. 4.30% a. 80 lbs a. 15.45 kg Ob. 19.53 kg O. 12.62 kg od. 20.62 kg O b. 4.50% O b. 41.3 Ibs Oc. 5.35% Oc. 23 Ibs O d. 6.70% o d. 27.73 Ibs 2. 6. Determine the solution of the differential An island has population that doubles in 50 equation dy dr +y cot x = coSX years. Determine how long will the population be five times as much? Assume Newton's law of cooling states that, the rate at which a substance change temperature in air is directly proportional to the difference that the rate of increase is proportional to the sin'z +c Oa. O a. ycos x = between the temperatures of the substance number inhabitants. and that of air. If the temperature of the air is 30° and the substance cools from 100* to Ob. ob. ycos x = sin²z 70° in 15 minutes, how long will it take to cool 100* to 50*? O a. 100 years O c. ysin x = cosz +c b. 98 years a. 33. 59 min O b. 43.60 min O. 35.39 min o d. ysin x = sin²z ос. 120 years O d. 116 years o d. 45.30 min
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