The edges of a cube increase at a rate of 5 cm/s. How fast is the volume changing when the length of each edge is 10 cm? Write an equation relating the volume of a cube, V, and an edge of the cube, a. Differentiate both sides of the equation with respect to t. dV %3D dt da (Type an expression using a as the variable.) dt

Q: The edges of a cube increase at a rate of 2 cm/s. How fast is the volume changing when the length of…

A:

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

A:

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A:

Q: What is the velocity (in ft/s) of a sandbag 1.5 s after it is released from a hot-air balloon that…

A: Given that t=1.5 sTo find : Velocity of sandbag1.5 s after it is relesed from a hot air balloon that…

Q: The sides of a square increase in length at a rate of am/s. At what rate is the larea of the square…

A: Area of square with side 's' isA=s2Differentiate with respect to xdAdt=2sdsdt Substitute dsdt=2,…

Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12². dV…

A: Given query is to find rate of change of volume.

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Topic- application of derivatives

Q: The length of a rectangle is increasing at a rate of 7cm/s and its width is increasing at a rate of…

A:

Q: The value V of a machinet years after it is purchased is inversely proportional to the square root…

A:

Q: (1) The rate of healing for a skin wound in cm² per day is given approximately by A'(t) = -0.9e-01t.…

A: dAdt = -0.9e-0.1t Now, integrate this equation A =∫-0.9e-0.1tdt So, A = -0.9e-0.1t-0.1 + C   but, we…

Q: A certain drug breaks down in the human body at a rate of 12% per hour. The initial amount of the…

A:

Q: Find the average rate of change of y = log1/2 x over the interval 1 < x < 4. Write your answer as a…

A:

Q: dv = 312 + dt 3. The rate of change of the volume of a balloon is given by 4 cubic feet per sec. If,…

A:

Q: 2. The volume of a cube is increasing at the rate of 6 cm /min. How fast is the surface area…

A:

Q: A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held…

A: Area of the triangle is given by;A = 12 ×base×height

Q: A 10​-foot ladder is leaning against a vertical wall​ (see figure) when Jack begins pulling the foot…

A: Here we have to find the rate of change.

Q: The volume of water in a tank is V cubic meters when the depth of the water is h meters. If the rate…

A:

Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A:

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10…

A:

Q: Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge…

A: (a) Given that, the velocity of the tip of the bore is V=kh0.5. Let h be the initial height and V be…

Q: ht h(t), in feet, of an airborne tee-shirt t seconds after being la ld a tee-shirt be airborne if it…

A: The height h(t) in feet, of an airborne tee-shirt t seconds after being launched is approximately…

Q: The volume of a cube decreases at the rate of 74 m³/ sec. The rate at which the side of the cube…

A:

Q: At noon, a city park manager starts filling a swimming pool. IfV(t) is the volume of water (in ft3)…

A: Given that a city park manager is filling his swimming pool. Volume of the swimming pool is V=43πr3.…

Q: What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at…

A: Let the model is given by Gt=G0ertGivenG0=348 gt=75 minGt=21.75

Q: The radius of a sphere decreases at the rate of 2 m/s. when the radius is 7m, then the rate of…

A: In this question we have to find the rate of change in the surface area of a sphere decreases.

Q: The radius of a circle is increasing at a constant rate of 0.2 meters per second What is the rate of…

A: Given that the radius of a circle is increasing at a constant rate of 0.2 meters per second. To find…

Q: A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following…

A: The volume of the region can found by integrating. The integration is dependent upon the function…

Q: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week.…

A: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week…

Q: ft -) is the radius of the puddle decreasing when the radius is 2 ft? hour A circular puddle is…

A:

Q: The area of a circle increases at a rate of 3 cm2 /s. a. How fast is the radius changing when the…

A: Given that: The area of a circle increases at a rate of 3 cm2/s To find: (a) How fast is the radius…

Q: The area of a circle increases at a rate of 5 cm2 /s. a. How fast is the radius changing when the…

A: Definition used -              Area of the circle  -                                   A =πr2…

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

A: Given: A tank partially filled with gasoline is seeping through the sides, at a rate proportional to…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A:

Q: Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge…

A:

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: A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following…

A: The volume of the region can found by integrating. The integration is dependent upon the function…

Q: Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and…

A:

Q: The volume of a cube is decreasing at a rate of 120 mm³ /s. What is the rate of change of the cube's…

A: Use  formula of volume and surface area of cube and then differentiate

Q: A 10-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: Given data- AC= 10 foot. AB=X=6 ft. dxdt=0.7ft/sec. We have to find dydt.

Q: he rate of growth dP/dt of a population of bacteria is proportional to the square root of t, wi nd t…

A: The given equation is: dP/dt = k√t.

Q: the volume of the sqhere is increasing at a rate of 10cm^3/sec. Find the rate of change of its…

A:

Q: The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of…

A:

Q: The volume of a cube is decreasing at a rate of 420 mm³ /s. What is the rate of change of the cube's…

A:

Q: If it begins to decelerate at the rate of a=(-0.5v/2) m/s², where v is in m/s, determine the…

A: To find the distance travels by the particle before it stops. Given that: Initial velocity of the…

Q: The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the…

A: Given that Radius of the sphere is decreasing at a rate of 2 cm/sec. drdt=-2 cm/sec, where r is…

Q: palloon is inflating at a constant rate of 3 cm' per second. When the volume of the balloon is T…

A: Here we have, inflating rate of a balloon dVdt=3 cm3/sec The volume of the ballon is V=43π cm3

Q: The distance between two charged particles is d and the electrostatic force F, measured in newtons,…

A:

Q: ,A large cube of ice melts such that it maintains its shape. The surface area is decreasing at the…

A: