A biologist observes that a certain bacterial colony is multiplied by 4 every 7 hours and after 28 hours occupies 1 square centimeter. (a) How much area was occupied by the colony when first observed? (b) What is the doubling time for the colony?

Q: A pick up truck is fitted with new tires which have a diameter of 41 inches. How fast will the pick…

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Q: (b) If its' owner uses 3 pipes of radius 4cm, with water flowing at a rate of 30cm/s, how long will…

A: (a) Area of circuler face= pi*r2  =pi*102 = 314 cm2.                    (pi=3.14)

Q: "An engineer is using a machine to cut a flat square of Aerogel of area 144 sq. c.m. If there is a…

A: Square have an area of 144 cm2, hence the side is 12 cmGiven that ε=8, a=12 and L=144The engineer…

Q: A cylindrical jar 6 inches in diameter and 8 inches high, contains 50 spherical balls of 1 inch…

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Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: An open box is to be made from a 16 inches long and 10 inches wide rectangular pieceof metal by…

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Q: A ball bounced 4 times, reaching three-fourths of its previous height with each bounce. After the…

A: We draw the situation roughly. Let the height when the ball was dropped is = h cmSo height after…

Q: A 20" by 14' piece of metal has squares cut from corners and thn is folded to create an open box.…

A: Length of metal sheet= 20 inches Breadth = 14 inches Let squares of side x inch have been cut from…

Q: A tank, measuring 30cm x 40cm x 50cm, contains 2 identical cubes. Water is then poured into the tank…

A: Given data is : A tank, measuring 30cm x 40cm x 50cm, contains 2 identical cubes Volume of…

Q: An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal…

A: according to our guideline we are supposed to answer only the first question if we want any…

Q: 10 ft-lb of work is required to stretch a spring from its natural length of 12 inches to 36 inches.…

A: Let F be the force and K be the spring constant. If x is the change in length of the spring from its…

Q: If an open box is made from a tin sheet 11 in. square by cutting out identical squares from each…

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Q: A force is applied to a particle, which moves in a straight line, in such a way that after each…

A: A geometric series is convergent if common ratio is less than 1. Sum of infinite geometric series is…

Q: A 500-lb cable is 300 feet long and hangs vertically from the top of a building. How much work (in…

A: Given:  Weight w=500-lb Length L=300 ft

Q: In October, Diana planted a tulip bulb 6 inches deep in the soil. The next spring, when the tulip…

A: Distance below the surface level = 6 inches Distance above the surface level = 13 inches Total…

Q: Starting with a 200-foot long stone wall, a farmer would like to construct a rectangular enclosure…

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Q: The wheel of the car of diameter 80 cm each,how any complete revolutions does each wheel in 10 mnts…

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Q: The rectangular tank shown here, with its top atground level, is used to catch runoff water. Assume…

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Q: The volume of a cube is growing at a rate of 225 ft3/min, and the length of a side is 5 ft. What is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose a cyclist was using a 150-millimeter-diameter chainring and an80-millimeter- diameter…

A: Given: Let, dc  and rc denotes the diameter and radius of Chainring respectively and ds  and  rs…

Q: The U.S. currently imports 9.5 x 10° barrels of oil each day. If a cylındrical stórage tank were to…

A: Given data: The given volume of oil import is V=9.5x106 barrels. The given dimension of the base is…

Q: A8 in thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 76…

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Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: A car has wheels are 80 cm in diameter.How many complete revolutions does each wheel make in 10…

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Q: A ball returns two-thirds of its preceding height on each bounce.  If the ball is dropped…

A: Here, the ball is dropped from a height of 6 m., it will rebound to a height of 23rd of initial…

Q: A certain process can plate out 80.6 um3 of gold onto a metallic surface per second. How long will…

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Q: How many milliseconds are in 31 days? show work in a step-by-step, please?

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Q: A limestone stalactite grew in length at a rate of – of a millimeter per year. At this rate, how…

A: Given the limestone is growing at a rate of 18mm per year i.e. 0.125 mm every year

Q: A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach. If the…

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Q: A rectangle has one side of 6 cm. How fast is the area of the rectangle changing at the instant when…

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Q: A rubber ball is made to fall from a height of 70 feet and is observed to rebound 3/4 of the…

A: The sum, S, of the infinite geometric series, a+ar+ar2+ar3+⋯ is defined as S=a1-r. Here a is the…

Q: 4. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast…

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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: What mass of glucose would you need (in g) to have 0.8 mol, given that the molar mass of glucose is…

A: Number of moles = Mass in gram / Molar mass Given Number of moles = 0.8 mol Molar mass = 180 g / mol…

Q: Estimate your volume in cubic meters by pretending you are shaped like a board. Pretending that…

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Q: A tire in Steve's car has just sprung a leak and is losing pressure at a rate of 5% every hour. If…

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Q: Spherical balls with diameter 12 in are arranged in a triangular pile. What is the total height in…

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Q: 8. A 50-ft. cable is stretched from the top of an antenna to an anchor point on the ground 15ft.…

A: Length of cable =50 t Distance of point from =15 ft BASE OF ANTENNA

Q: How many cubic meters must be hauled from PIT 1 in order to meet the engineer's needs? Round-off to…

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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: the minute hand of a clock is 15 mm long and the hour hand is 12 mm. How fast is the distance…

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Q: A chain lying on the ground is 16 ft long and weighs 90 lbs. How much work is required to raise one…

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Q: What is m∠MNT?

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Q: Each side of a square is increased 8 inches. When this happens, the area is multiplied by 25. How…

A: assume that the length of the original square is "x" inches.

Q: Suppose that you just completed a nonstop bicycle trip of 5.5 km. You know that each wheel of your…

A: Given Data: The distance covered by the bicycle is: d=5.5 km=5500 m The radius of the wheels of a…

Q: Find how fast the area of a triangle increases as the length of the base of the triangle increases…

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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.