The ratio of carbon 14 to carbon 12 in a piece of paper buried in a tomb is R = 1/3^11. Estimate the age of the piece of paper.

Q: A cubical crystal is growing in size. Find the approximate change in the length of a side when the…

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Q: What is the relationship between the angle of refraction and the index of refraction? Is it linear…

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain…

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Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

Q: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain…

A: Half life = 1590 years Inititial amount of sample (a0) = 300 mg Final amount of sample (af) = ?

Q: ind the half-life of a radioact

A: Given that: Rate = 12 %

Q: A stone dropped into a still pond sends out a circular ripple whose enclosed area increases at a…

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Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

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Q: The radioactive element Carbon-14 has a half-life of approximately 5730 years. A fossil is measure…

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain…

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Q: Approximate to 3 decimal place accuracy

A: Maclaurin series can be given as below : take

Q: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

Q: The mass reaches 75 grams after t= years.

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Q: The half-life of radium in a piece of lead is 1600 years. What percentage of the original amount of…

A: Given that, the half-life of radium in a piece of lead is 1600 years. Note that, the formula for…

Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

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Q: What rate is required to grow 750 to 7500 in 14 years?

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Q: In order to compare amounts of two different substances, it is necessary to figure out the amount of…

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Q: Find the volume of the largest cube of wood that can be cut from a log of circular cross section…

A: Given that, the radius of circular cross section is 6 inch.

Q: The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain…

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Q: A sample of radioactive material decayed to half of its original amount in 4 years. How long did it…

A: Given: A sample of radioactive material decayed to half of its original amount in 4 years To…

Q: The altitude of a triangle is increasing at a rate of 2.62.6 centimeters/minute while the area of…

A: Given, Area of a triangle, A=8484 cm2 Altitude of a triangle, h=1010 cm The rate of increase of…

Q: A bacteria decreases at a rate of 15% continuously when exposed to ultraviolent light. If a culture…

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Q: The radioactive element Carbon-14 has a half-life of approximately 5730 years. A fossil is a measure…

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Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: If I am blowing up a balloon at a rate of 3 cubic feet per minute, what is the rate of change of the…

A: Since, it is given that a person is blowing up a balloon at a rate of 3 cubic feet per minute, then…

Q: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain…

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain…

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Q: The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the…

A: Half life of the plutonium isotope is 24,360 years. If 10g of plutonium is released into the…

Q: The radioactive element Carbon-14 has a half-life of approximately 5730 years. A fossil is measured…

A:

Q: The radioactive element Carbon-14 has a half-life of approximately 5730 years. A fossil is measure…

A: Given : Half life of carbon- 14 is 5730 years

Q: The volume of a cube decreases at a rate of 0.75 ft3/min. What is the rate of change of the side…

A: Consider a cube with side 'a' The rate at which the volume of cube is decreasing is 0.75 cubic feet…

Q: A fire has started in an open field and is spreading in the form of a circle, with its radius…

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Q: The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain…

A: Radioactive decay

Q: When the lid is left off an ink bottle, the ink evaporates at a rate of 2.5 x 20 "cm" bottle…

A: Given that: Rate at which ink evaporates=2.5×10-6cm3s and Total volume of ink in the bottle is 36…

Q: Find the effective rate of interest for 10% compound continuously.

A: The continuous rate is calculated by raising the number "e" (approximately equal to 2.71828) to the…

Q: The half -life of carbon-14 is 5,730 years. Suppose a fossil is found with 20% as much of its…

A: Given that the half-life of carbon-14 is 5,730 years. So, h=half life=5730 Let the initial amount=P=…

Q: A wooden artifact from an ancient tomb contains 60 percent of the carbon-14 that is present in li…

A: The solution is given below

Q: A toxic radioactive substance in the amount of 7 miligrams per square centimeters is detected in the…

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Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: The half-life of radium-225 is approximately 14.9 days. How much of a 15 gram sample of radium-225…

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Q: The​ half-life of radium is 1690 years. If 40 grams are present​ now, how much will be present in…

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Q: A cube's volume increases at a rate of 108 ft3/min. At what rate is the cube's edge length changing…

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Q: The half-life of Carbon-29 is 1300 years. If 15 grams are present now, how much will be present in…

A: Let A(t) be the amount of Carbon-29 remaining in t years, then

Q: An unknown radioactive element decays into non-radioactive substances. In 880 days, the…

A: The half life of a radioactive element is the time it takes to decay half of its original isotope.…

Q: How many kilometers can a train moving at an average velocity of 25 m/s southwest be displaced in 2…

A: Given, average velocity of train = 25 m/s 2 hours = 2x60x60 = 7200 seconds

Q: If the area of a circle decreases constantly by half a square foot per second, at what rate is its…

A: Here, given that the area of the circle decreases constantly by half s square foot per second. That…

Q: The​ half-life of radium is 1690 years. If 40 grams are present​ now, how much will be present in…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.