(4) The mass (in grams) of an insect after t days is given by m(t) = 3+t2, while the volume (in cm³) after t days is given by V(t) = 1+t. (a) Find a function for the density after t days, p(t). (b) Compute p(t). (c) When is the density increasing? When is the density decreasing?

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A: see the calculation below

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A: We will use directional derivative.

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A: We have to find the change in the volume of cone using total differential.

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A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: A detailed solution is given below.

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A: Given  , Rate if drain: dV/dt = - 1.8L/min By integrating the equation we get the volume.

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: Given: Let A is the area of a circle with radius r Then we have A = πr2

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A:

Q: a. Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone…

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Q: (а) The flow (in cm³/s ) of blood from an artery into a small capillary can be modeled by CTx…

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Q: 03/ The dimensions of a rectangular solid at a given instant (t.) are : L(t) 13 cm. W(t)-9 cm. H(t.)…

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A: The solution to the above question is in the images below.

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

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Q: A flexible cable suspended between two vertical supports is hanging under its own weight. The weight…

A:

Q: A)If A is the area of a circle with radius r and the circle expands as time passes, find  dA dt  in…

A: a) Given A is the area of a circle of radius r A=πr2 Then, dAdt=2πrdrdt...(1)

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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.