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Q: An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the…

A:

Q: The area of a circle is increasing at a rate of 10 ft2/min. Find the rate of change of the diameter…

A: Area of a circle is increasing at a rate of 10ft2/min. To find: Rate of change of diameter, given…

Q: is pedaled so that the tires rotate at a rate of 200 revolutions per minute. A 20-inch bicycle is s…

A: Question: A 26 inch bicycle padaled so that the tires rotates at the rate of 200 revolution per…

Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the…

A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r…

Q: centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8…

A: The volume of a pyramid isBh3 , where B is the area of the base and h is the height of full pyramid.…

Q: An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the…

A:

Q: Hooke’s law states that the distance that a spring is stretched by hangingobject varies directly as…

A: Let distance= y Mass of the object= x According to the question y=kx  k=constant  Given that y=20…

Q: The radius r of a circle is increasing at a rate of 4 centimeters per minute. Can you help me find…

A: The radius r of a circle is increasing at a rate of 4 centimeters per minute. That is, drdt=4

Q: A mixing blade on a food processor extends out 3 inches from its center. If the blade is turning at…

A: Given that

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

A: In the question it is asked to calculate speed of the top of ladder sliding down when foot of ladder…

Q: 10. A ladder 15 m long leans against the wall. The ladder slides down the wall at a rate of 1.5 m/s.…

A: Here we use the property of right angle triangle.

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

A:

Q: The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of…

A: Given that : The radius of a circle is increasing at a rate of 4 centimeters per minute. That is,…

Q: baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with…

A:

Q: The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of…

A: Given query is to find the rate of change of area of a circle whose radius is increasing with rate…

Q: At noon Ben is Ikm west of Jerry. Ben is heading South at a due rate of 4 km/h and Jeny heads East…

A:

Q: A balloon's volume is increasing at 15 ft /sec at the same moment as its surface area is increasing…

A:

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

A: Recall: Pythagoras Theorem:        Pythagoras theroem states that In a right angled triangle , the…

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

A: The ladder makes a right triangle with the wall.  So using Pythagorean theorem:

Q: An jet travels horizontally at a speed of 500mph at an altitude of 3 miles above the ground. A…

A: We need to find the rate at which the angle of elevation is changing.

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

A:

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

A: Given: Length of ladder = 13-foot Distance between foot of ladder & foot of wall=12 - foot The…

Q: a light is placed on the ground at a distance of 31 feet from the point at which a javelin will be…

A: Distance between light and javelin is AB=31 feet,  At some moment, height of javelin is BC=28 feet…

Q: An observer is 20 m above the groundfloor of a large hotel atrium looking at a glass-enclosed…

A: Let The height of the elevator above the ground level = x m…

Q: A mixing blade on a food processor extends out 2 inches from its center. If the blade is turning at…

A: This question can be solved using the concept of trigonometry.

Q: A mixing blade on a food processor extends out 3 inches from its center. If the blade is turning at…

A: 1 foot  =  12 inches     1 inch  =  112 foot 3 inches  = 312 feet                 =  14 feet

Q: A piston is seated at the top of a cylindricalchamber with radius 5 cm when itstarts moving into the…

A: From the given data:

Q: A spotlight at a building corridor is fastened to a wall 8 m above the floor . A lady 1.75 m tall…

A: Refer the diagram below. Let x be the distance between the spotlight and the lady and y be the…

Q: A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: In this we are going to use formula for area of triangle and then differentiation of that. So I'm…

Q: One ship is approaching a port from the east, traveling west (to the left) at 15 miles per hour,…

A: Let x be the distance between pole and the one ship and y be the distance between the pole and the…

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A: We use here first Pythagorean theorem then we use application of derivatives. Note: I used here…

Q: The area of a square is increasing at a rate of 16 centimeters squared per second. Find the rate of…

A: Area of square =(side)2

Q: Air is pumped into a balloon at a rate of 64cn^3/min. Find the rate of change of the radius when the…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: t) A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A: solution

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: NOTE: Refresh your page if you can't see any equations. . the volume of the cylinder is given by…

Q: A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. (a) Find the…

A:

Q: O H.W 1: Two cars leave from the same position at the same time. One travels due North at 30 km/h,…

A:

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A:

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A:

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A: Assume distance of the airplane from the radar is s (say) height h(say) and horizontal distance of…

Q: A street light is at the top of a pole that has a height of 15 ft. A woman 5 ft tall walks away from…

A: Consider a function y = f(x) .Then f '(x) is the rate of change of y with respect to x.

Q: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

A: Volume of the sphere is given by :V=43πr3where r = radius of the sphere

Q: A cone that is. filled with water has a radius of 4 feet and a height of 10 feet. The water is…

A:

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: A hunter is moving away from a tree at the rate of 2 ft/sec. A 3 ft-tall eagle is resting on a…

A: Solve for the angle

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.