(3) A rock thrown into a still pond causes a circular ripple. for the given x and y a) If the radius of the ripple is increasing by 2 feet per second, how fast is the area changing when radius is 10 feet? Use A = πR2 and π = 3.14 b) How fast is the circumference of a circular ripple is changing when the radius is 5 feet? Use C = 2πR and π = 3.14

Q: 1. Aman 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1).…

A: Given that dxdt=3 ft/slet height of streetlight = AB=18 ftheight of man DE =6 ft b.  dydtin ∆ABC…

Q: 1. A 25 feet long ladder is leaning against a wall and sliding toward the floor. If the foot of the…

A:

Q: The base x of the right triangle in Figure increases at a rate of 5 emfs, while the height remains…

A: Write the tangent ratio for angle .

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

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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 area of a circle increases at a rate of 4 cm? /s. a. How fast is the radius changing when the…

A:

Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a)  Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

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

A: Solution:- we have to find the rate of change of the area of the triangle when AC is 3 in.…

Q: 4. A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A: To find the solutions of given statements

Q: A hemispherical dome has a diameter of 100 m. A searchlight was placed at a point A located at the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

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Q: m Oil is running into an inverted conical tank at the rate of 37 -. If the min tank has a radius 2.5…

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Q: 9. A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from…

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Q: #13 The radius of a sphecical blloon is increasing at the cate of 3inches per second, How fast is…

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Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

Q: 13. A 10-meter ladder is leaning against a vertical wall with its foot on the same horizontal plane…

A:

Q: 2. A 15-meter-long ladder is leaning against a wall The bottom of the ladder is pushed horizontally…

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Q: 11. An airplane is flying parallel to the ground at an altıtude of 2 km and at a speed of 4 km/min.…

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Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

Q: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

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: The area of a circle increases at a rate of 4 cm2 / s. a. How fast is the radius changing when the…

A: I have given an answer in step 2.

Q: (b) Water runs into a conical tank at the rate of 9 m /min. The tank stands point down and has a…

A:

Q: . A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A:

Q: The edge length of a cube is 12 cm and increasing at a rate of 2 m. How fast is the Surface Area of…

A: Given dx/dt=2cm/hr X=12cm

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

A:

Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A:

Q: 1)A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground.…

A: ----------------------------------------------------------------------------------------------------…

Q: (2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A:

Q: A hemispherical dome has a diameter of 700 m. A search light was placed at a point A located at the…

A: The solution is given below

Q: 2. A man 1.8 meter tall walks away from a lamp post 4 meter high at a speed of 1.5 m/s. How fast is…

A: We'll answer one question since the exact one hasn't specified. Please re-submit the question you…

Q: A spherical balloon is being filled in such a way that the surface area is increasing at a rate of…

A:

Q: a-) The sides of a square increasing at a rate of 10 cm /sec. How fast the area enclosed by the…

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Q: A furniture Fis attached to a rope 50 meters long that passes over a pulley at point A, 20 meters…

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Q: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

Q: pouring

A: We will find the rate of change of height.

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: To solve the following problem.

Q: 5. A cone-shaped ice cream is melting at the rate of 2cm/s in a manner that maintains its original…

A:

Q: A man walks along a straight path of 4m/s. A searchlight is located on the ground 25m from the path…

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Q: 2. A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches…

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Q: 2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A: Solution

Q: 6. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 40 km/hr and ship B is…

A: Given query is to find the rate of change of distance.

Q: A hemispherical dome has a diameter of 100 m. A searchlight was placed at point A located at the…

A: Length of curve s = 2 π r (θ/360°)

Q: (a) A 5-ft ladder is leaning against a house when the base starts to slide away. by the time the…

A: First we use Pythagoras theorem and then we calculate dA/dt and solve it .

Q: 3. After the blast-off, a space shuttle climbs vertically and a radar-tracking dish, located 1,000…

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Q: g.) A ladder 14 ft long is leaning against a fence 8 ft high with the upper end projecting over the…

A:

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…