Air is being pumped into a spherical balloon at a rate of 4.5 cubic inches per minute. How fast is the radius of the balloon changing when the radius is 2 inches? (Recall: the volume of a sphere of radius r is given by V = 4 3 πr3 .)

Q: 1. The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea…

A:

Q: A gas balloon is being filled at a rate of 50π cm³ of gas per second. At what rate is the radius of…

A: Write the formula for the volume of the sphere and take the derivative.

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: The radius of the sphere is increasing at a rate of 5mm/sits diameter is 80 mm

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 60cm³/s. How…

A: To find the rate at which surface area is changing

Q: The edge of a cube is changing at the rate of 0.2 cm/sec. How fast is the volume of a cube changing…

A:

Q: dA dr in terms of dt (a) If A is the area of a circle with radius r and the circle expands as time…

A:

Q: SA Spherical ballon is ingiated With goas at the rate af 20 Cm3min. How fast is the fadtus af the…

A:

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: Air is being pumped into a spherical balloon so that its volumeincreases at a rate of 100 cu. cm /s…

A:

Q: A street light is at the top of a 29 ft pole. A 4 ft tall glri walks along a straight path away from…

A:

Q: A tank is shaped like an upside-down square pyramid, with base of 5 m by 5 m and a height of 14 m.…

A:

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

A: let the length of rectangle is l cm and width is w cm area of rectangle is(A) =lxw differentiate…

Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: Assume  horizontal distance from original position is x diagram according to problem

Q: The length of a rectangle is increasing at a rate of 11 cm/s and its width is increasing at a rate…

A: The area of a rectangle is the product of its length and width, A=l×w, where l is the length of the…

Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second…

A: To determine the velocity from the given conditions

Q: A The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when…

A:

Q: As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that…

A: To show that  the radius of rain drop decrease at a constant rate That is to show drdt  is a…

Q: 10. Gas is escaping from a spherical balloon at a rate of 2 cubic feet per minute. How fast is the…

A:

Q: Sand is being dropped at the rate of 5 n3/min onto a conical pile. If the height of the pile is…

A:

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm3/s. How…

A: Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm3/s. To…

Q: A ball is being inflated such that the volume is increasing at a constant rate of 100cm3/s How fast…

A: Given  and

Q: #Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is…

A: we have to find the rate change of surface area of the spherical balloon

Q: Sand is poured onto a surface at 11 cm³/sec, forming a con- ical pile whose base diameter is always…

A:

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: The radius of the first circle is modeled by w(t)=12-12e^-0.5t at what time t is the radius of the…

A: The given equation of circle is w(t)=12-12e-0.5tUpon differentiating: (As it is given rate, we…

Q: The length of a rectangle is increasing at a rate of 9cm/s and its width is increasing at a rate of…

A: To Determine: How fast is the area of the rectangle increasing? Given: we have the length of a…

Q: A baseball player throws a ball straight up into the air. At a height of 3.4 m above the release…

A:

Q: the hypotenuse AB of a right triangle ABC is constantly 5 in long. The side AC is increasing…

A: Given that the hypotenuse AB of a right triangle ABC is constantly 5 in long. and the side AC is…

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A:

Q: The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea decreases…

A: solution is given below

Q: A spherical snowball melts at a rate of 2 cubic centimeters per hour. How fast is the radius…

A: We know that the volume of a spherical snowball is v = 43πr3 where v is the volume and r is the…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 70cm³ /s. How…

A: Volume of the sphere , V =43πr3 ; where , 'r' is the radius of the sphere. Surface Area of the…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 20cm³ /s. How…

A: We have given the  Rate of change in volume = 20cm3/sec  We have to find the change in surface area…

Q: A spherical balloon is inflated with air flowing at a rate of 19 cm³/s. How fast is the radius of…

A: Use volume of sphere and differentiate wrt  t and put value

Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…

A: Remaining capacity of tank is 50-10 = 40 gallons.

Q: A conical cup is 6 inches tall, and the top of the cup has a radius of 3 inches. Water is being…

A: Given, The volume of a cone of height h and radius r is given by, v=13πr2h Here we use the units,…

Q: The Volume of a Sphere is increasing at the rate of 8 m³; how fast is its Radius increasing when the…

A:

Q: The brakes of a car are applied when it is moving at 100km/h and provide a constant deceleration of…

A:

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

A:

Q: 1. The side of a cube increases at a rate of 2.5m/s. Find the rate at which the surface area…

A: Let x be the legth of a side and S be the surface area of the cube We know that   S=6x2 Given that…

Q: dV If the volume of the cube increases at the rate of 15 m² / sec, then the value of is dt

A:

Q: j. A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a…

A: Given: Height of boat above water level=20 ft……1Length of rope=50 ft……2Rate at which boat is pulled…

Q: You are inflating a spherical balloon at the rate of 7 cm³/sec. How fast is it radius increasing…

A:

Q: A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400 – 20t, for…

A: Solve the following

Q: A spherical balloon is expanding at a rate of 60n in.3 How fast is the surface area of the balloon…

A: Use formula of surface area of shpare and take derivative of that than put given values.

Q: Helium is pumped into a spherical balloon at a rate of 2 cubic feet per second. How fast is the…

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: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second…

A: Given query is to find the velocity.

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.