Find an exponential equation y=Ce^kxt hat passes through the points (0,2) and (5,25). For what value of k is dy/dx=kx true for this y?

Q: A cylindrical rod made of ice is melting at a rate of 8 cm3 per minute. When the length of the rod…

A: The formula for the volume of the cylindrical rod is, V=πr2h where r is the radius of the…

Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

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Q: A balloon leaves the ground 30 m from an observer. If it rises at the rate of 2 m/s, how fast is it…

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Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

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: A fighter plane 2000 km away is spotted by a gunner in the ground. If it maintains its altitude at…

A: Pythagoras theorem: In a right angle triangle, Hypotenuse2=Base2+Perpendicular2 Differentiation…

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Given: Since the height is decreasing.     To determine:

Q: Suppose we have a rectangular aquarium with dimensions of length 8m,width 4m and height 3m .Suppose…

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Q: A point P is moving along the line whose equation is y = 4x. How fast is the between Pand the point…

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Q: Jay and John used to travel together but because of the pandemic, they decided to go separately…

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Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: First I have draw the graph of given problem and then solved them using Pythagoras theorem. The foot…

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

A: Decreasing:- We know that if something is decreasing then it is going down.

Q: One side of a right triangle is 150 m long and its adjacent angle is π/3 radians, with π/60 radians…

A: Possible error

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

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Q: 9. A man 5 n tall is walking toward a building at the rate of 3 A/sec. If there is a light on the…

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Q: A spherical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. At what…

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

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Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

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Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: A rectangle has a length of 1 inches and a width of 12 inches whose sides are changing. The length…

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Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: 1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A rectangle has a length of 11 inches and a width of 5 inches whose sides are changing. The length…

A: In the given rectangle  Width b = 5 inches Length l = 11 inches Length increasing rate dl/dt = 9…

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

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Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

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Q: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline…

A: Given a lighthouse which is located on a small island 3 km away from the nearest point P

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

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Q: A point is moving along the graph of x3y2 = 200. When the point is at (2, 5), its x-coordinate is…

A: Given that a point is moving along the graph x3y2=200 and it's x-coordinate is changing at the rate…

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

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Q: As an object cools, its rate of cooling slows. Explain how this follows from Newton’s Law of…

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Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

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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 surface…

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given a certain radioactive material is known to decay at a rate proportional to the amount present.…

Q: A rectangle has a length of 11 inches and a width of 10 inches whose sides are changing. The length…

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Q: Sand flows out of an hourglass at a rate of 4 cubic inches per second and forms a conical pile. How…

A: Write the expression for volume of cone take the derivative with respect to time t than put the all…

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

Q: A quantity with an initial value of 110 grows continuously at a rate of o.5% per hour. What is he…

A: Given, Initial value of quantity = 110  It is growing continuously at a rate of 0.5%  per hour.  We…

Q: A 10 m ladder leans against a vertical wall and the bottom of the ladder slides away from the wall…

A: Let L be the length of the ladder, h be the height of the wall and b be the distance between the…

Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

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Q: At 2:00 PM a car’s speedometer reads 30 mi/h. At 2:10 PMit reads 50 mi/h. Show that at some time…

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Q: When we take measurements of the same general type, a power law of the form y = ax often gives an…

A: (b)   Given that X´=log(X) and Y´=log(Y)   X Y X´ Y´ 2 1.81 0.30103 0.257679…

Q: A lighthouse is located on a small island 3 km away fromthe nearest point P on a straight shoreline…

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

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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.