The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when the side is 3 m. O -189 m /sec 3 252 m / sec 126 m / sec

Q: The hypotenuse is √7 br. a right triangle, which is rotated around one of its perpendicular sides.…

A:

Q: The diagram below shows a cup in the shape of a right circular cone and some of its measurements. 5…

A:

Q: . Find the rate at which the volume increases when the radius is 30 cm. (Hint: Volume 4 of the…

A:

Q: The volume of a spherical balloon changes with respect to the radius r. At what rate (in ft°/ft)…

A:

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: Given data: The side of a cube is decreases at the rate of 8 m/s. The objective is to find the rate…

Q: fit the largest possible cone inside a sphere, what fraction of the volume of occupied by the cone?…

A: In this question we have to find the fraction of the volume of the sphere is occupied by the cone.

Q: 12 m 11.5 m 11.5 m 5 m 10 m

A:

Q: Week 16 Quiz Find the surface area and the volume of the solid. x Clear 9 Undo - Redo 4 cm SA: V: 9…

A:

Q: The volume V = (4/3)πr3 of a sphericalballoon changes with the radius.By approximately how much does…

A: To find the rate at which the volume changes, you must find the derivative of the volume function.…

Q: A tumor is approximately spherical. If the radius of the tumor changes from 14 mm to 16 mm, find the…

A: A sphere has radius 14mm and 16mm

Q: 2. What formula should be used to minimize the lateral surface area of a cone, where the volume of…

A: I am attaching image so that you understand each and every step.

Q: A metal ball has a mass of 2 kg and a volume of 6m3. What is its density?

A: Density of the substance is mass per its unit volume. ⇒Density, ρ=mV

Q: The side of a cube increases at the rate of 6 m/sec. The rate at which the volume of the cube…

A: Given, The side of a cube increases at the rate of 6 m/sec. The side of the cube is 4 m is m³/sec.

Q: What is the volume of the cylinder

A: Given ,  We have to find volume of the cylinder

Q: The side of a cube increases at the rate of 5 m/sec. The rate at which the volume of the cube…

A: let side of cube is x then rate at which side increase is 5 m/secie.  dxdt=5 m/sec

Q: The hypotenuse is √7 br. a right triangle with one of its right sides rotated. Occurring How many…

A:

Q: The circumference of a sphere is measured to be 84 cm with a possible error of 0.5 cm.  a. What is…

A:

Q: A ring that weighs 80 grams is made of gold and silver. By measuring the displacement of the ring in…

A: Let ring contains x grams of gold. Density of gold = 19.3/cm3. So, the volume of gold ring =…

Q: Find the change in volume dV if the sides of a cube change from 6 to 6.1. Do not round.

A: SOLUTION-

Q: The surface area of a sphere increases at a rate of 66 m2/sec. Then the rate at which the radius…

A:

Q: Find the volume of the cone below. 12 km 10 km

A:

Q: F. Determine the specific gravity of the substance having a volume of 9.85 ft x 13.12 ft x 59 ft if…

A:

Q: Find the volume of this cyinder. 6.5 m 10 m V = Trh 9

A: The volume of the cylinder is calculated by using the formula, V=πr2h ,where  r  is the radius of…

Q: The shaded pyramid in the diagram is cut from a rectangularsolid. How does the volume of the pyramid…

A: Let the length, width and height if the rectangular solid be l,band h. Then the volume of the…

Q: Given the diagram below: 10 Find the volume of the solid formed by rotating the green triangle…

A: Given: Formula used: The volume of the right angled triangle=12×base×height Volume of the rectangle…

Q: 8. 9. 2- -5 5. 10 -2-

A:

Q: The dimensions of a box are 0.4 m depth, 7.0 dm width and 50. cm height. What is the volume of the…

A: Depth= 0.4 m = 4 dmWidth = 7.0 dm = 7 dmHeight = 50 cm = 5 dm

Q: 11. Describe an effective way to show students the relationship between the volume of a cone and…

A: Write volume formula of cone and cylinder and relate

Q: Approximate the change in the volume of a sphere when its radius changes from r= 50 ft to r= 50.02…

A: Given that the radius changes from r = 50 ft to r = 50.02 ft.   find the change in volume of sphere…

Q: The volume of a right circular cone is found using the equation V = r²h. Which equation represents…

A: Simplify by multiplying and dividing.

Q: Which best compares the volumes of cylinder X and cylinder Y?

A: Cylinder X volume Vx = pi x r2 x h

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: A chunk of Platinum is mixed with other metals to make a piece of art. Roughly, 43% of a 60-gram…

A:

Q: Given the funcion: ((x^2)/9)+(((y^2)/9)e^0.2x)=1    revolve around the x-axis to create an egg. Find…

A: The given equation is x29+y29e0.2x=1.We can plot the solid of revolution as

Q: The volume of the solid is (Тур

A:

Q: ZSM-5, a catalyst material, has a surface area of 425 m³/g. What is the surface area of this…

A:

Q: The volume of the solid given by tl

A: Given,             z=8-3x2+y2            z=x2+y22-2

Q: The side of a cube increases at a rate of 10 m/sec. Find the rate at which the volume of the cube…

A: Use the formula for volume of cube and take its derivative than substitute the given values.

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: Volume of the cube =side^3 If side decreased  then volume also decreased

Q: Find the volume (in units3) of the solid created after a hole of radius  a = 1  is bored down the…

A: Given: the radius of the cone= 9 units height of the cone=9 units the radius of the hole(cylinder)=1…

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: Topic- Application of Derivative

Q: 2. Approximate the change in the volume of a sphere when its radius changes from r = 5ft to r =…

A: Given that  Radius changes from 5ft to 5.01ft To find the rate of change of volume of the sphere

Q: The surface area of a sphere increases at a rate of 77 m2/ sec. Then the rate at which the radius…

A:

Q: Given the function: ((x^2)/9)+(((y^2)/4)e^0.2x)=1  revolve around the x-axis to make an egg and find…

A: The given curve is as follows: The equation of the curve is x29+y24·e0.2x=1.  Thus, the curve…

Q: A eight foot rod has a density of D(x) = 2 +√3 x (kg/ft), where x represents the distance (in ft)…

A: Given that, the length of the rod is 8 foot, and density of the rod from one end to the point x is…

Q: The volume of the solid is cubic units

A:

Q: The surface area of a sphere increases at a rate of 52 m2/sec. Then the rate at which the radius…

A: Let A is the surface area of Sphere.

Q: A frustum of a cone has an area of 2m2 and 5m2 for the upper and lower base respectively, If the…

A: Given:- A frustum of a cone has an area of 2m2 and 5m2 for the upper and lower base respectively, If…

Q: The volume of the open cylindrical tank is

A:

Q: The side of a cube increases at the rate of 10 m/sec. The rate at which the volume of the cube…

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.