(4) (Section 3.11 - Related Rates Problems) A cube starts with an initial edge length of 1 cm. The edges of the cube increase at a rate of 2 cm/s. How fast is the volume changing when the length of each edge reaches 50cm?

Q: section: Additional Techniques of Integration.

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Q: 6. ) If the edges of a solid cube grow at 2 inches per second, how fast is the volume of the cube…

A: 6. The rate at which the edges of the solid cube changing is, dxdt = 2 in/sec where, x is the edge…

Q: 4. Two circles have the same center. The inner circle has radius r which is increasing at the rate…

A: According to the given information, Let r be the radius of inner circle and R be the radius of outer…

Q: Example 4: A water trough is 10 m long and a cross section has the shape of isosceles trapezoid as…

A: Given that,  Let V be the volume of the water inside the through and h be the height of the water…

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

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Q: 4. . A balloon is at a height of 50 meters, and is rising at the constant rate of 5 m/sec. A…

A: Let us consider a right angled triangle  ∆ABC, right angled at B. The height of balloon is h meter…

Q: 6. A spherical balloon is being inflated so that its diameter is increasing at a rate of 2 cm/min.…

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Q: . An open hemispherical container has radius 20 feet. Honey begins flowing into the tank in such a…

A: To calculate the rate at which the top circular surface area of the honey changing and how fast is…

Q: (a) If the bee is hovering at the point (0, 0, 0), what temperature is they experiencing? (b) If…

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Q: hand-tossed pizza base starts off as a ball of dough with a volume of 400π cm3 . First, the cook…

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Q: A population of the yeast cell Saccharomyces cerevisiae (a yeast used for fermentation) developswith…

A: The growth rate formula is  P(t)=P(0)ekt where P(t) is the population at time t, P(0) is the initial…

Q: The metal frame of a rectangular box has a square base. The horizontal rods in the base are made out…

A: To find the rate of change of the volume of the box

Q: 10. A tank contains a brine solution. Fresh water enters the tank at a rate of 5 gal/min while the…

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Q: a) If the bee is hovering at the point (0, 0, 0), what temperature is they experiencing? (b) If the…

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Q: 1. A spherical hot air ballooon is bieng inflated at a rate of 1.5 cubic feet per second. a) Find…

A: Given that a spherical hot air balloon is being inflated at a rate of 1.5 cubic feet per second.…

Q: 9. A rectangle initially has dimensions 2 cm by 4 cm. All sides begin increasing at a rate of 1…

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Q: 5. (5 points) A board 5 feet long slides down a wall. At the instant the bottom end is 4 feet from…

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Q: 4) A piece of land is shaped like a right triangle. Two people start at the right angle of the…

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

A: Let x be the distance from the bottom of the wall to the bottom of the ladder Let y be the distance…

Q: Example 5: A spherical balloon is inflated with helium at a rate of 100TT ft/min. a) How fast is the…

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Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How…

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

A: This question is based on application of derivative

Q: 16. A point P(x, y) moves along the graph of the equation y = x³ +x²+1, the x-values are changing at…

A: Given: y = x3 + x2 +1 The value of x changes at a rate of 2 units per second. that means x is…

Q: 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m'/min. At what…

A: Let r be the radius of the balloon and D be the diameter.

Q: 5. The length a,b, and c of the edges of a closed rectangular box are changing with time. At the…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: 3. A (right circular) cylinder is expanding in such a way that its height is increasing three times…

A: This question is about application of derivative.

Q: Example 42. A train travels first 300 kilometres at an average rate of 30 k.p.h. and further travels…

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Q: A tank originally contains 100 gal of fresh water. Then water containing Ib of salt per gallon is…

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Q: Water leaks from a cylinder, with axis vertical, through a small orifice in its base at a rate…

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Q: 7. The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the…

A: let r be the radius of cylinder    h be the height of cylindergiven drdt = 1 mhrdhdt = -4 mhrwhen r…

Q: A pyramid has height h and a square base with side x. The volume of a pyramid is V = xh. f the…

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Q: 5. A ladder 25 feet long leans against a vertical wall. The bottom of the ladder slides away from…

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Q: All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the volume…

A: Given:- All edges of a cube are expanding at a rate of 7 centimeters per second  To find:- (a) How…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

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Q: 8. Suppose that you are standing on the shore of a calm lake on a beautiful spring day. Without the…

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Q: Situation 1 A tank initially contains 100 gal of brine where there is dissolved 20lb of salt.…

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Q: 5. a) All edges of a cube are expanding at a rate of 3 cm per second How fast is the volume changing…

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Q: 5) A thin sheet of ice on a lake is in the shape of a circle. If the ice is melting such that the…

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Q: The radius of a sphere, initially zero, increases at rate 6 ft per seconds. Find how fast the volume…

A: By using differentation and integration and rate of change

Q: 3) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches…

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Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

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Q: spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

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Q: A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: Let's find.

Q: The length of a rectangle is decreasing at a rate of 8cm/sec and its area is increasing at a rate of…

A: Area of rectangle = l×w Where l is length and w is width of the rectangle.

Q: A weight is attached to one end of a 33-foot rope which passes over a pulley 18 feet above the…

A: Given: Distance between pulley and ground = 18 feet. Other end of the rope is attached to a truck…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: Let s ,in centimeters,  be the length of edge of cube . All edges of a cube are expanding at a rate…

Q: The metal frame of a rectangular box has a square base. The horizontal rods in the base are made out…

A: Given: horizontal rods expand at the rate of 0.004cm/hr. vertical rods expand at a rate of 0.008…

Q: Part A. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing…

A: Volume of sphere =(4/3)πr3   surface Area of sphere =4πr2

Q: 3. A balloon is released from the ground 100 meters from an observer. The balloon rises directly…

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.