For many species of fish, the allometric relationship between the weight W and the length L is approximately W = kL3,where k is a constant. Find the rate of change of the weight as a corresponding rate of change of the length.

Q: Given the area of a circle A=πr^2, find the rate of change of diameter d if dA/dt=3cm/min and the…

A: To find: The rate of change of the diameter d. Given: The rate of change of area is dAdt=3…

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per…

A:

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A: We will find the above mentioned as shown below

Q: Find the rate of change in the area (A) of a circle with respect to its radius (r) when r = 9. 9TT…

A:

Q: The length of a rectangle is given by 4t + 9 and its height is √t, where t is time in seconds and…

A: Given:

Q: b. find Find the rate of the volume of a sphere with respect to its diameter D when the diameter is…

A:

Q: Of a rectangle are chonging at the tates of 1m/s and 2m/s. Sides its When its sides are 30 m and Ao…

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Q: Find the rate of change of the speed of sound v (in m/s) with respect to air temperature T (in…

A:

Q: The weight of a limb of a tree is given by W = 3t°-444, where t is time. Find the relative rate of…

A:

Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

A: Please check step 2 for the solution.!

Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

A:

Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

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Q: The Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r). Find the…

A:

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

A:

Q: The radius, r, of a circle is decreasing at a rate of 4 cm/sec. Find the rate of change of the area,…

A:

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar h where r is the radius…

A:

Q: What is the rate of change of the volume of a ball (V = (4/3)pai r3 ) with respect to the radius…

A:

Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

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

Q: Assume a circle is expanding with time, where r = t + 2. What is the formula for the rate of change…

A: Given: r = t + 2   We know that the area of the circle: A = π r2   where r is radius.

Q: Given a cube with sides x inches, let x(t) = t + 2. What is the instantaneous rate of %3D change of…

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Q: If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A:

Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

A: Topic = Derivative As per guidelines, At a time only one question can be answered out of different…

Q: 2. Find the rate of change of a volume V of a cube with respect to (a) the length w of a diagonal of…

A: Consider a cube of a side a , and diagonals z and w  We know that Pythagorean theorem , Hypotenuse 2…

Q: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

Q: The altitude () of a right triangle is always twice the base (). Find the rate of change of the area…

A:

Q: find the rate of change. Speed of sound v (in m/s) with respect to air temperature T (in kelvins),…

A: We have been given the equation  v=20T            (1) where v is the speed of sound (in m/s) and T…

Q: The volume of a right-circular cone of radius r and height h is represented by V = (1/3)r2h.…

A: Given that, The volume of a right circular cone of radius r and height h is represented by V=13πr2h…

Q: Find the rate at which the volume of a right circular cylinder of constant altitude 10 ft changes…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: During a certain 12-hour period the temperature at time t (measured in hours from the start of the…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: The volume of a cube with sides of lengths is given by=s. Find the rate of change of volume with…

A:

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A: We use trigonometry formula of right angle triangle to solve the problem.

Q: The velocity, in feet per second, of a running rodent is modeled by v(t) = 5√t − 2t. What is the…

A:

Q: The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and…

A: Given that the volume V of a right circular cylinder is given by the formula V =(pi)r2h, where r is…

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A: Z is the distance from kite to person. We use Pythagoras Theorem

Q: The volume V = 3 "Tr° of a spherical balloon changes with the radius. 3 a. At what rate (in°/in)…

A: We know that the volume of the sphere  is V=43πr3 To find the rate of change in volume with respect…

Q: The velocities (in mi/hr) of an automobile moving along a straight highway over a 2-hr period are…

A: Given that the velocities(in mi/hr)of an automobile moving along a straight   highway over a 2-hr…

Q: 18. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change…

A: Topic:- Application of Derivative  Correct option = a

Q: The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the…

A: Consider the given equation: V=43πr3 Where V is the volume and r is the radius. Differentiating the…

Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: A kite is rising vertically at a constant speed of 2 m/s from a location at ground level, which is 8…

A:

Q: The centripetal force of an object of mass is given by F(r) where v is the speed of rotation and r…

A:

Q: Let A be the area of a circle with radius r that is increasing in size with respect to time. If the…

A: We have to find rate of change of the radius when radius is 6 cm and rate of change of area is given…

Q: Assume a circle is expanding with time where r = t + 3. What is the formula for the rate of change…

A: The chain rule: fgx'=f'gx·g'x The Power rule: ddxxn=nxn-1   (1). As we know that; The area of the…

Q: The area of a square with sides of length s is given by A = s2. Find the rate of change of the area…

A:

Q: The volume V of a right circular cone of radius r and height h is given by V = Tr²h. Find a formula…

A: To find the instantaneous rate of change:

Q: Assume a spring is oscillating and the length of the spring can be described as sin (t) L (t)=- What…

A:

Q: Assume that a rocket is lifting off 10 miles away, with a position h(t) = 5t². What is the rate of…

A: Topic = Derivative

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.