Two people start from the same point. One walks east at 6 mi/h and the other walks northeast at 5 mi/h. How fast is the distance between the people changing after 15 minutes? (Round your answer to three decimal places.)

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: From the Pythagorean theorem, BC2+AB2=AC2

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

Q: At a given moment, a plane passes directly above a radar station at an altitude of 6 km. (a) The…

A:

Q: A man 6.00 ft tall approaches a street light 14.0 ft above the ground at the rate of 8.00 ft/s. How…

A:

Q: Two people start moving from the same point. One heads east, at 24 km/h, the other south at 18 km/h.…

A:

Q: A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is the…

A:

Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A:

Q: A man 5.5 feet tall is walking at a rate of 4 feet/sec away from a light that is 24 feet above the…

A:

Q: Two people start from the same point. One walks east at 5 mi/h and the other walks northeast at 4…

A:

Q: A 20-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: A bicyclist accelerates at a constant rate from a standstill to 25 km/hr in 36 sec. a) How fast is…

A: We will solve the problem

Q: An 8-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

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

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

Q: A 10-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: From Pythagorean theorem in the right triangle,  the length of the ladder is h2+b2.

Q: The base of a 40-foot ladder is being pulled away from a wall at a rate of 14 feet per second. How…

A:

Q: Two people start from the same point. One walks east at 2 km/h and the other walks northeast at 3…

A:

Q: The height of a triangle is increasing at a rate of 4 cm/s while the area of the triangle is…

A: Let the height, base and area of a triangle be 'h', 'b' and 'A' Given, dhdt=4 cm/sdAdt=56 cm2/s

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s. How fast does the tip of…

A:

Q: 9. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 mi/hr. How fast does the…

A:

Q: The base of a 20-foot ladder is being pulled away from a wall at a rate of 11 feet per second. How…

A: application of derivative

Q: A man, 1.65 m tall is walking on a horizontal street at 2.3 kph away from a vertical street light,…

A:

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: Each side of a square is increasing at a rate of 6 cm/s. At  what rate is the area of the square…

A:

Q: An ice cube that is 3 cm on each side is melting at a rate of 2 cm3 per min. How fast is the length…

A: Given: Length of cube L=3cm Rate of melting =-2cm3

Q: A balloon is 30 meters above the ground when a car, running at 40 kph, passes directly below it. It…

A: Given,         A balloon is 30m above the ground when a car, running at 40kph passes directly below…

Q: Two people start from the same point. One walks east at 2km/h and the other walks northeast at 3…

A: Given

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

A:

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A: Let y be the distance of lighthouse from nearest point on the shoreline and at time t, the beam…

Q: Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 9…

A: We sketch the situation roughly  Let x= distance of the person on the East y=distance of the person…

Q: C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south…

A: We use Pythagoras theorem

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A:

Q: A 16-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Let us consider that, lowermost end of ladder is y foots away from wall and height of wall is x…

Q: Charley stands 34 meters west of Robert. Robert starts walking north at a speed of 2 m/s, and…

A:

Q: A bicyclist accelerates at a constant rate from a standstill to 15 km/hr in 90 sec. a) How fast is…

A: a) Consider the given information: u=0 km/hrv=15 km/hrv=15 ×10003600m/sv=4.17m/st=90sec From…

Q: 4. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: A man 5.00 ft tall approaches a street light 14.0 ft above the ground at the rate of 7.00 ft/s. How…

A: Explained below

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square…

A: If the area of a square, A, is x2 units , then the length of its side is x unit .

Q: An observer on the ground is 12m away from the foot of the tower 40 m high. A stone is dropped from…

A:

Q: A 10-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Height = 10 foot 3 feet/sec Ladder is 3 feet from the wall

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: Two people start from the same point. One walks east at 3mi/h and the other one walks northeast at…

A:

Q: Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north…

A: At t = 0 { initial position } , distance between ships.Let the distance between ship A and ship B be…

Q: A man 7.00 ft tall approaches a street light 16.0 ft above the ground at the rate of 6.00 ​ft/s. How…

A: Given data: The height of the man is CD=7 ft. The height of the street light is AB=16 ft. The rate…

Q: A man, 1.84 m tall is walking on a horizontal street at 3.9 kph away from a vertical street light,…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.