A water tank has the shape of an inverted circular cone (point down) with a base ofradius 3 feet and a depth of 8 feet. Suppose that water is being pumped into the tankat a constant instantaneous rate of 4 cubic feet per minute. Say that r is the radius and h the depth of the water at a given time, t. What equation relates the radius and height of the water, and why?

Q: Consider a tank in the shape of an inverted right circular cone that is leaking water. The…

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Q: A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second base…

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Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

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Q: The length x of a rectangle is decreasing at a rate of 5cm/seconds and the width y increasing at a…

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Q: A 5 meter (m) ladder leans against a wall. The bottom of the ladder is 1.3 meters from the wall at…

A: Given- length of ladder=5m, the bottom of ladder is 1.3 m from the wall at time t=0 and the height…

Q: Water is running out of a conical funnel at the rate of 1000 cu mm/sec. If the radius of the funnel…

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Q: The radius of a conical tank is 4.4 meters and the height of the tank is 9.8 meters. Water is…

A: Given that the radius of a conical tank is 4.4 meters and height of the tank is 9.8 meters. The rate…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 16 cm/min.…

A: Given that - A spherical balloon is to be deflated so that its radius decreases at a constant rate…

Q: A high-speed bullet train accelerates and decelerates at therate of 4 fts 2 . Its maximum cruising…

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Q: Two particles are initially at the point (0,0) (the origin) of a coordinate system. Particle A moves…

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Q: The length of a rectangle is given by 4t - 3 and its height is 2t, where t is time in seconds and…

A: Given the rectangle whose length and height are given L=4t−3H=2t3

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Given;  dh/dt=0.7 cm/sec , r=6cm , h=6cm V=πr^2h

Q: The position from its starting point of a small plane preparing for takeoff is given by x(1) = 1.412…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 5…

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Q: Analyse and solve the following problems and explain the reasons for each element of your solutions.…

A: Given:  --------------------------------------------------------------------------------- Relation…

Q: An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per…

A: The rate at which water level is rising when the level is 5cm is 25cm/sec.

Q: Suppose you are climbing a hill whose shape is given by the equation z = 2,000 - 0.005x - 0.01y,…

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Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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Q: accumulates in a conical pile with a radius that is always four times its height. Suppose the height…

A: Rate of change

Q: A. Find an equation that relates the total length of the elastic x to the distance y that the button…

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Q: Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 8 centimeters…

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Q: 11. An airplane is flying parallel to the ground at an altıtude of 2 km and at a speed of 4 km/min.…

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Q: In one of the warehouses of a construction firm, cement is being released from an elevated storage…

A: Given: Cement is being released from an elevated storage bin at a rate of 29 feet3/min. i.e. The…

Q: Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 10…

A: From the given information, the radius of the cone is 5 centimeters and height(depth) of the cone is…

Q: Two cylindrical swimming pools are being filled simultaneously at the same rate of cubic meter per…

A: Two cylindrical  are being filled simultaneously at same rate Smaller pool has radius = 5m   water…

Q: An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per…

A: Finding the rate at which water level rises in a pyramid at a particular height

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Q: A water tank in the form of an inverted cone is being emptied at the rate of 6 m³/min. The altitude…

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Q: The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The…

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Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Volume of a cylinder is constant ⇒ dVdt=0                                 V=πr2h ⇒ 2rhdrdt+r2dhdt=0

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Given: speed of waterdVdt=55 cm3second, b1=b2=6cm, h=13cm

Q: An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per…

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

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Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A: Given inverted square pyramid has length of square base b=2 cm and height h=5 cm Water is being…

Q: An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per…

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Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

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Q: A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of…

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Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A: We know, Volume of a figure = Area of a base × Height

Q: A woman at a point A on the shore of a circular lake with radius 2mi wants to arrive at the point C…

A: Aim: To find path from AC with minimum time of travel.  Given : Radius of lake = 2 mi Walk rate, w…

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 9400.0 cubic centimeters per min at…

A: Explanation: Start by ignoring the leakage and determine the rate of inflow required to achieve the…

Q: A cylindrical container has initially 400cm^3 of water and is being filled at the constant rate of…

A: The cylindrical container has 400cm3 of water. The rate of being filled per second is 100 cm3. And…

Q: A hemispherical dome has a diameter of 100 m. A searchlight was placed at point A located at the…

A: Length of curve s = 2 π r (θ/360°)

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

A: Let s cm be the side of the square formed by the water surface in the inverted and h cm be the water…

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A: Given : height of the pyramid = 7 cm Sides = 2 cm

Q: A surveyor is walking at the rate of 4 ft/sec along the diameter of a circular courtyard. A light at…

A: Here I am attaching image so that you understand each and every step.

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.