balloon is 30 meters above the ground when a car, running at 40 kph passes directly below it. If the balloon is rising at 5m/s. how fast is the distance between the balloon and car changing 10 seconds after the car is directly below the balloon.

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: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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

Q: The altitude of a triangle is increasing at a rate of 22 centimeters/minute while the area of the…

A:

Q: A 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

A:

Q: The altitude of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is…

A:

Q: The length of the rectangle is decreasing at a rate of 5 centimeters per second, and its width is…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A: Let height of triangle = h Base = b Then, we are given that:

Q: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight…

A:

Q: Two cars start moving from the same point. One travels south at 40 mph and after one hour, the other…

A:

Q: A ship moving 8 mph sails north for 30 minutes then turns east. If a searchlight at the point of…

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: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A:

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Here we use the formula of area of triangle. First we differentiate area with respect to time and…

Q: An airplane, flying horizontally at an altitude of 1km, passes directly over an observer. If the…

A: Given: y = altitude = 1km  constant speed of plane dx/dt = 240kph

Q: A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled away from…

A: .

Q: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

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

A:

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

A: Please see the answer below.

Q: A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping…

A: Given ,dydt=-2ft/s     negative sign because as ladder is slipping down, y decreasesby Pythagor…

Q: A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline…

A:

Q: The sides of a cube are increasing at a rate of 1cm/s. How fast is the diagonal of the cube changing…

A: Explanation: Given that,  The sides of a cube are increasing at a rate of 1cm/s. The objective is to…

Q: Suppose that Stuart is 6 feet tall and is walking towards a 20-foot streetlight at a rate of 4 feet…

A:

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A: Definition used -        Pythagorean theorem - In a right angle triangle, The Square of the…

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

A: Given that increasing altitude of the triangle dh=2cm/min The increasing area of the triangle dA =…

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

A: Consider the given information

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

A: Given

Q: Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west…

A:

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

A:

Q: A man on a wharf is pulling a rope tied to a raft at a rate of 0.6 m/s. If the hands of the man…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A:

Q: Suppose that two boats leave a dock at different times. One heads due north, the other due east.…

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

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: Suppose a tank contains 600 gallons of salt water. If pure water flows into the tank at the rate of…

A: Given a tank contains 600 gallons  of salt water. Pure water flows into the tank at the rate of 7…

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: area = altitude*base289 = 9.5*base2base = 18.73 cm

Q: A boat traveled north by 5 km then turned west. if the speed of the boat is 10 km/hr at what rate…

A: Given that,  the boat traveled north by 5 km then turned west and the speed of the boat is 10 kn/hr…

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: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A:

Q: A dead fish was found inside a compartment that is able to maintain a constant temperature of 373…

A: let D be the body temperature at t seconds according to question, initially , at time t=0D=900…

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

A:

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

A: Formula of area of triangle 12bhWhere b is the base and h is the altitude Chain rule (uv)'= u'v+uv'

Q: A rectangle’s length is growing at 3 inches per second, while its width is shrinking at 5 inches per…

A:

Q: A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast…

A: Time , distance and speed is related using a formula time=distancespeed .At the same time , both the…

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

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

A:

Q: A 5m long ladder has its upper end leaning against a vertical wall and lower end on a perfectly…

A: To determine the rate at which the ladder is moving down in cm/sec when the lower end is 3 m away…

Q: A tiger is 45 ft directly south of a herd of elephants. The tiger starts to slink towards the…

A:

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

A: We can sketch the situation roughly as follows. Here, CE and DF both are the positions of the…

Q: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same…

A: Given: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the…

Q: Suppose that two boats leave a dock at different times. One heads due north, the other due east.…

A: