A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the angle e between the ground and the ladder changing, if the top of the ladder is sliding down the wall at the rate of rinches per second, at the moment that the top of the ladder is h feet from the ground? (You're looking here for an equation in terms of h and e.)

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

A: Let θ denote the angle between thw ladder and the ground

Q: A hot air ballon rises vertically upwards from a distance of 170m away. If the angle 0 at which you…

A: To Determine: how fast is the ballon rising when θ=π6 Given: A hot air balloon rises vertically…

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

A:

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given that, the length of the ladder is 10 ft and distance between the wall and ladder in base is 6…

Q: The bast x of the right triangie in the figure, increases at a rate of 5 cm/s, while the nei ght…

A:

Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: We have to find the rate of change of angle.

Q: How do you solve question 4?

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Given y be the height of the Ballon ,t be time and theta the angle between the line of sight and the…

Q: A kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle…

A:

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

A:

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

A: The diagram of the situation is shown below:

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: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A:

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

A: given: A 15-meter ladder is resting against a vertical wall. the bottom of the ladder is being…

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 picture 40cm high is placed on a wall with its base 30cm above the level of the eye of an…

A: Shown below

Q: A 5-ft-tall person walks toward a wall at a rate of 2 ft/sec. A spotlight is located on the ground…

A: 12. Let h be the height of shadow on wall using the similarity bof thr triangle,∆OAB, △OPQ,h40=540-x…

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: The objective of the problem is to find the speed at which the balloon is rising at the given…

Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

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

A:

Q: A man 2 meters tall walks at a rate of 1.2 meters per second away from a light that is 5 meters…

A: dy/dt = rate of moving of tip of shadow dp/dt = rate of change in length of shadow

Q: 21. For the camera and rocket shown in Figure 3.4.5, at what rate is the camera-to-rocket distance…

A: Given that the distance between camera and launching pad is 3000 ft., the distance between launching…

Q: kite 100 ft. above the ground moves horizontally at the speed of 8ft/sec. At what rate is the angle…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

A:

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

A:

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic- application of derivatives

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Here we will find how fast is the balloon rising,

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

A:

Q: 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A:

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

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A:

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

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: 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: Suppose you always keep your eyes fixed on the very top of a 100 m building. Suppose you start to…

A: Height of building = 100 m Let x be the base distance from the building Head angle = θ tanθ=100x

Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A: A Hot air balloon is rising vertically . Angle between observer's line of sight and ballon is pi/5.…

Q: A kite 100 ft above the ground moves horizontally at a speed of 4 ft/s. At what rate is the angle…

A: Here we use trigonometric formulas along with differentiation formulas.

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the…

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Rate of change

Q: A duck is 6 feet north and 8 feet east of a buoy. He is swimming due east at a rate of 3ft/sec. How…

A: Consider the value of x=3ft/sec. A duck is 6 feet north and 8 feet east of a boy. We have to find…

Q: 9. A balloon, leaving the ground 60 ft. from the observer, rises 10 ft. per sec. How fast is the…

A: 9- Given- The ballon leaving the ground 60ft. from the observer rises 10 feet per second. To find-…

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

A: From the given information we use trig ratio ,  tan(θ)=oppositeadjacent…

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

A:

Q: 1. A 13-ft ladder is leaning against a house when its base is being pushed towards the wall. By the…

A:

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

A:

Q: Assume a spring is oscillating and the length of the spring can be described as sin (t) L (t)=- What…

A:

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

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.