Suppose a snowball remains spherical while it melts, with the radius r shrinking at 3 inch(es) per hour.What is the numerical value of dr/dt when r is 4?

Q: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

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Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

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Q: A spherical balloon is inflating at a rate of 277T in³/sec. How fast is the radius of the balloon…

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Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

Q: .A ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

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Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

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Q: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity of 125 ft/s.…

A: Given that: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity…

Q: The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: a.A surfboard 9 ft. long stands on the ground and leans against a wall. Due to a strong external…

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

Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

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Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

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Q: A 60-kg skydiver jumps out of an airplane. What is her terminal velocity, in meters per second,…

A: Given, Mass (m) of the skydiver = 60-kg, and k = 10-kg/s

Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

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Q: What is the velocity (in ft/s) of a sandbag 2.5 s after it is released from a hot-air balloon that…

A: Given that a sandbag is released from a hot-air balloon that is stationary in the air. Then we have…

Q: A cylindrical tank has a radius of 7.0 m and a depth of 17.0 m. It is being filled at a rate of 2.9…

A: Consider the given: Radius = 7 mDepth = 17 mRate at which the tank is filled = 2.9 m3/minVolume of…

Q: An egg is thrown off the roof of a 60ft. building with an initial velocity of 6.5 ft/s. How long…

A: Given initial velocity = 6.5fts

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: The height h and radius r of the base of a straight circular cone are varying at constant rates of…

A: Topic:- application of derivatives

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

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Q: A spherical ball is measured to have a radius of 6 cm with a possible measurement error of ±0.1rmcm.…

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Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

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Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

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Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: A spherical balloon is inflated with gas at the rateof 800 cubic centimeters per minute. (b) Explain…

A: To find the rate of change of the radius, differentiate the volume of the sphere, V=43πr2 with…

Q: A Fluid flows in an inverted conical tank, 14 in diameter on top and 24in deep at a rate of…

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Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

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Q: The surface area of a sphere, initially zero, increases uniformly at 4 square inches pe second. Find…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: at what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec?

A: The volume of a cube is: Where, a is the edge of the cube. Formula used:

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: A car is moving at 60 mi/hr (88 ft/s) on a straight road when thedriver steps on the brake pedal and…

A: Given: u=88 feetsec, a=-10 fts2, t=3 seconds we know that s=ut+12at2…

Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…

A: Remaining capacity of tank is 50-10 = 40 gallons.

Q: A 20 foot ladder leans against a vertical wall. If the base of the ladder is pulled away from the…

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Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

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Q: D A child is rolling a spherical snowball with an outer 1) Tayer of ice so that the volume Of the…

A: As per bartleby answering guidelines we are supposed to answer only first question in case of…

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

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Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

Q: Show that the period of motion of an undamped vibration of a mass hunging from a vertical spring is…

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Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

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Q: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

Q: The spherical balloon is being filled with air at the constant rate of ( 2cm3  ) / (sec). How fast…

A: Given: The spherical balloon is being filled with air at the constant rate of 2cm3/sec We know that,…

Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

A: we know that surface areaS.A. and volumeV of cube is given by S.A.=6l2…

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.