A rubber ball is made to fall from a height of 70 feet and is observed to rebound 3/4 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner?

Q: A radioactive substance decays at a rate proportional to the amount present, and half the original…

A: given radioactive substance that its half life is 1500 years. we have to find time after which the…

Q: Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel…

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Q: 1. A 17 feet ladder is leaning against a wall. If the bottom of the ladder is pulled along the…

A: Given : dx/dt = 5 y = 8 Now we find the dy/dt = ?

Q: An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining…

A: There is an exponential decay with rate of 28.8%.

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Simple rate of decay of radium problem....

Q: if water rises 1/2 inch in 3/7 of a week in a water reservoir, at what rate is the water rising per…

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Q: Consider an object in a surrounding with constant temperature of 25°C. If the temperature of the…

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Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A: Given the rate of change= 0.6+4/(t+2)2 feet per year To find the total number of feet grown during…

Q: Ask The population of Northern Cascadia is growing at a rate of 20% every 3 years. Assuming that it…

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Q: Consider an object in a surrounding with constant temperature of 25°C. If the emperature of the…

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Q: A 17 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: Given, length of ladder = 17 ft But given that ladder is leaning against a wall ⇒  the ladder and…

Q: An isotope of cesium has a half life of 29 years. If 1300 grams of cesium disintegrates over a…

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Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: A certain radioactive material loses mass at a rate proportional to the mass present. If the…

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Q: If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude…

A: We have to determine the relationship between the intensities of the two earthquakes .

Q: Consider an object in a surrounding with constant temperature of . If the temperature of the object…

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Q: A ball is thrown upward from the ground with an initial speed of 25m/s. at the same instant, another…

A: Solution   Given a ball is thrown upward from the ground with an initial Same from Speed of 25m/s,…

Q: (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km…

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Q: Based on an appropriate regression model, the distance traveled by the caterpillar after 8.5 minutes…

A: From given data, X Y X*Y X*X 1 15.3 15.3 1 2 30.1 60.2 4 3.5 50.6 177.1 12.25 4 58.1…

Q: A runner starts at the beginning of a runners' path and runs at a constant rate of 5 mi/hr. Fifteen…

A: First, we need to calculate the relative speed which is, the difference between the speed of the…

Q: due to the current. How far did he actually swim from his starting point? Round to the nearest…

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Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

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Q: An element with mass 490 grams decays by 28.6% per minute. How much of the element is remaining…

A: There is a decay of element at the rate of 28.6% per minute. Initially the mass of element given is…

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

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Q: Find how much more energy was released by an earthquake of magnitude 6.9 than by an earthquake of…

A: Solution: use formula Log E = 11.8+1.45M

Q: A vehicle purchased for $29800 depreciates at a constant rate of 6%. Determine the approximate value…

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Q: When Apollo 15 astronaut David Scott dropped a hammer and a feather on the moon to demonstrate that…

A: An astronaut dropped a hammer and feather on the moon.These are dropped from about 4 ft above the…

Q: A 17 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

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: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: An

A: Given,element with mass = 510 gramsdecay rate = 26.3% per minuteour aim is to find how much of the…

Q: A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: From the given problem the representative diagram is as shown below. Apply the Pythagorean theorem:…

Q: If paper napkin 0.10 inch thick could be folded so that it was half as large but twice as thick,…

A: paper napkin 0.10 inch thick could be folded so that it was half as large but twice as thick,…

Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

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Q: An element with mass 640 grams decays by 7:3% per minute. How much of the element is remaining after…

A: Given intial mass =640 gmsRate of decay=7.3% per miniutetime =8 minute

Q: A certain radio isotope has a half-life of 12 years. Find the mass that remains from a 220mg sample…

A: Half life = 12 yrs 220 mg is the initial mass Therefore decay constant = ln2 / half- life

Q: An element with mass 310 grams decays by 8.9% per minute. How much of the element is remaining after…

A: Given   mass = 310 gm  Rate = 8.9 %  Time = 19 min

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: A hypothetical square grows at a rate of 8 m^2/min. How fast are the diagonals of the square…

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Q: was an earthquake in South America with magnitude 4.3 that caused only minor damage. How many times…

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Q: An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining…

A: We need to find the exponential function representing the decay of the element.

Q: If a 250 meters long train is traveling at an average speed of 60 kph, how long it would take that…

A: According to the question, Speed of train 60 kph To convert the speed of train in meter per second,…

Q: Suppose that a ladder of length 25 ft is placed on a vertical wall. It was then found out that the…

A: length of the ladder= 25ft According to Pythagoras theorem:…

Q: On the planet Gzyx, a ball dropped from a height of 20 ft hits the ground in 2 s. If a ball is…

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Q: Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that…

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Q: It is estimated that t months from now, the population of a certain town will be changing at the…

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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: A certain illness is spreading at a rate of 10% per hour. How long will it take to spread to 1200…

A: Assuming exponential growth    31.1t=1200