Q4) growth of a spherical tumor modeled as a function of the population of germs (g in Million) in tumor, v(g) = 1.5 g?, When the diameter of the tumor is 2v15, and population of germs is 20m and it is growing at a rate of 2m /day. How fast is the diameter of the tumor changing at that time? %3D

Q: 5. A spherical balloon is being inflated at a rate of 10 cubic centimeters per second. dr A. Find an…

A:

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

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A:

Q: A point is moving on the graph of y = z?. When the point is at (-64, 16), its y coordinate is…

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Q: When treating cancer, it is an advantage to know the rate of growth of the cancer tumor. A…

A: Since the tumor is spherical, its volume is given by, V=43πR3 Substitute diameter D=2R in the above…

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A:

Q: 9) Sand falls from an overhead bin, accumulating in a conical pile with a radius that is always…

A:

Q: Sand is pouring from a hole at the rate of 25 cubic feet per second and is forming a conical pile on…

A: Solved below

Q: Q4) growth of a spherical tumor modeled as a function of the population of germs (g in Million) in…

A: Given function f(x), we can find the rate of change in f w.r.t to other variable t as dfdt=dfdxdxdt

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A: Given that: x = number of people who have the information is treated as a differentiable function of…

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A:

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.

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A:

Q: A tree trunk is approximated by a circular cylinder of height 50 meters and diameter 4 meters. The…

A: Volume of cylinder = πr2h r = radius of cylinder h= height of cylinder

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A: (a) Consider the given statement of the question,

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Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

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Q: 3 of its radius. 4 Mohamad Salah poured orange juices into a cylindrical red tank whose height f the…

A: Topic:- application of derivatives

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A: V=43πr3

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A: Explained below

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A: Given :- The length of a rectangle is increasing at a rate of 5 cm per second and its width is…

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Q: The radius of a circular ink blot is increasing at a constant rate of 0.2 cms¯'. (i) Calculate, in…

A: Given - The radius of a circular ink blot is increasing at a constant rate of 0.2 cms-1 To find -…

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Q: An executive conference room of a corporation contains 4500 ft3 of air initially free of carbon…

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Q: 2. Gravel is being dumped from a conveyor belt at a rate of 30 1S and its coarseness is such min…

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Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

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Q: The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the…

A: Here,             We have given  the rate of proliferation for the cells in a tumor varies depending…

Q: A cell culture contains 10 thousand cells, and is growing at a rate of r(t)=11e0.06tr(t)=11e0.06t…

A: A cell culture contains 10 thousand cells, and is growing at a rate of r(t)=11e0.06tr(t)=11e0.06t…

Q: Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20%…

A:

Q: Consider a tank used in hydrodynamic experiments. After one experiment the tank contains 200 L of a…

A: y=amount of salt at time t  ............the water is fresh

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: he measure of the angle subtended at

A: Given: A picture 40 cm high is placed on a wall with its based 30 cm above the level of the eye of…

Q: : 20 A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away…

A: We have to use Pythagoras theorem and calculus to obtain our result.

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A: Given , Length of ladder is 6m Let height of ladder on wall is x m, and base length of ladder from…

Q: 5. Sand is pouring from a hole at the rate of 25 cubic feet per second and is forming a conical pile…

A: Solution ) dv/dt = 25 ft3/ sec  h = d/4  d = 4h  [ d = r/2 ] r/2 = 4h  r = 2 × 4h  r = 8h  h = 5…

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given- dldt=5cm/sec, dwdt=-3cm/sec To find- The rate of changing of the area when the length and…

Q: 3. After long study, tree scientists (dendrologists) conclude that a eucalyptus tree will grow at a…

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Q: Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200…

A: Consider Q(t) be the amount of dye present in the tank at any time t.Given that initial the tank…

Q: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

A:

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.