A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being brought in at the rate of 4 feet per second. If the angle of elevation does not change, how fast is the hot air balloon losing altitude?

Q: A hot-air balloon is 150 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Let x be the distance the motorcycle has traveled. Let y be the height of the balloon above the…

Q: The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity…

A:

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

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

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

A:

Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

Q: A kite 100 feet above the ground moves horizontally at a speed of 10ft/s. At what rate is the angle…

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

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

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: A 6 ft tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

A:

Q: A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2 feet per…

A:

Q: What constant acceleration is required to increase the speed of a car from 20 mi/h to 45 mi/h in 5…

A:

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away fromher at a…

A:

Q: When a rocket is 2 kilometers high, it is moving vertically upward at a speed of 300 kilometers per…

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Q: Assuming there is no sag in the string, find the rate at which the kite is moving when 125

A: Considering a right triangle with the data given, the hypotenuse 'c' is 125 feet, base 'b' and the…

Q: An 8 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A kite flies at a constant height of 30 meters above the ground in a wind that blows it horizontally…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

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

A:

Q: A 15-meter ladder is resting against a vertical wall, If the bottom of the ladder is being pushed…

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

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

A:

Q: A boat is pulled toward a dock by means of a rope wound on a drum that is located 3 ft above the bow…

A: a rough sketch of the problem will be as follows:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: Please refer the attached image for complete solution. THANK YOU !

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A:

Q: Jamal is flying a kite on a string, and it is 100 ft above the ground. At the point that Jamal has…

A: Jamal is flying a kite on a string, and it is 100 ft above the ground. At the point that Jamal has…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A:

Q: If a ladder of length 20ft which is leaning against a vertical wall has its upper end sliding down…

A: Given : Length of the ladder = 20 ft

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at…

A: Given A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from…

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: An 8 ft. ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: A streetlight is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

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

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

Q: c. A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post that…

A: Definition uses-       Similar triangles -        If two triangles are similar then their…

Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

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

A: To determine the rate of change of angle between the ladder and the ground.

Q: An aircraft is climbing at a 300 angle to the horizontal. How fast is the aircraft gaining altitude…

A: An aircraft is climbing at a constant 30 degree angle to the horizontal and the speed is 500 mph…

Q: A ladder 15 ft. long leans against a vertical wall. If the top slides down at 2 ft/sec, how fast is…

A:

Q: A searchlight, 1/2 mi from a straight shore, rotates at the rate of 2 rev/min. How fast is the spot…

A: Let the angle formed by line AB with the line AC is x  in the triangle ABC,   So, from the tangent…

Q: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at…

A: Form the situation on a right triangle and use trigonometric ratio than differentiate.

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

A:

Q: A ladder 10 ft long leans against a vertical wall. If the bottomof the ladder slides away from the…

A: Given - A ladder 10 ft. long leans against a vertical wall. If the bottom of the ladder slides away…

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

A: Let, the angle θ is an acute angle made by telescope and the vertical. The distance between the boat…

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at 180…

A: To  Determine: How fast will your camera angle u be changing when the car is right in front of you?…

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

A: Rate of change

Q: A ladder 20 ft long is leaning against an embankment inclined 60° to the horizontal. If the bottom…

A: Let x= distance of ladder from the embankment, y= vertical height. Given: dxdt=-1 ft/sec To find:…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A:

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

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

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

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

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.