Suppose a train is moving along a trackwith a velocity of v(t) = t^2 − 3t. In the first four seconds, calculate in simplified fractions the train's displacement and its total distance traveled.

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: An aeroplane left 30 minutes later than its scheduled time; and in order to reach its destination…

A: let the usual speed of aeroplane = x km/hr and the increased speed = (x+250) km/hr total distance…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Let y be height of wall upto ladder and x be distance between bottom of wall and bottom of ladder…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

Q: Each side of an equilateral triangle measures 3 cm, with a possible error of 0.1 cm. Using…

A: This question is taken from the differentiation in which we have to find the relative error in the…

Q: A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide…

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Q: A light is hung 6 meters above a straight horizontal path.  If a man 2 meters tall is walking toward…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

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Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: all details are given in below. please check it

Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the…

A: Given query is to find the rate of chnage of diameter.

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

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Q: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

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Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Let the length be: l Let the width be: w

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

Q: As a bicyclist moving at 6m/s passes a point, a balloon 8m directly above him rises at the rate of…

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Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

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Q: Suppose that a car skids 15 m if it is moving at 50 km/h when the brakes are applied. Assuming that…

A: Given that car skids, 15 m if it is moving at 50 km/h when the brakes are applied. That is,

Q: The original 24 m edge length of a cube decreases at the rate of 2 m divided by two minutes When x=1…

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Q: The length of the rectangle is increasing at a rate of 5cm/s and its width is decreasing at a rate…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75degrees with…

A:

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

Q: A man 2m tall is walking at the rate of 2m/s away from a lamp post 7m high. At what rate is the tip…

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Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: A certain cube with side equal to 5 inches is said to have an incremental error of 0.1 inch in its…

A: Topic :- Application of Derivative  Volume of cube = (side)3

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given,  A ladder slides down a vertical wall at a rate of 0.675 m/s  When the bottom of the ladder…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A:

Q: A girl is using a straw to drink coke from a right cylindrical glass at a rate of 6 cubic…

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Q: A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.15m/s. At the moment when the bottom…

A: We have given; the rate of change when ladder slides down i.e 0.15m/s The rate of change when it…

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A:

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: A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on…

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Q: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

Q: A spacecraft is launched from the surface of a 6.7 x 1024 kg planet. If the spacecraft is moving at…

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Q: Suppose a 10-foot ladder is leaning against a building. The bottom of the ladder slides away from…

A: Solution:-

Q: A patient is drinking  0.6 pint of orange juice every two hours. At this rate, how many quarts of…

A: Dimensional analysis: A method of analysis in which physical quantities are expressed in terms of…

Q: The base of a 20-foot ladder is sliding toward a wall at a rate of 1.5 feet per second. How fast is…

A: We solve the above problem.

Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.