The bast x of the right triangie in the figure, increases at a rate of 5 cm/s, while the nei ght remains constant at h=20. How fast iŞ the angle o changing when x=20? Fig. 20

Q: 1. Aman 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1).…

A: Given that dxdt=3 ft/slet height of streetlight = AB=18 ftheight of man DE =6 ft b.  dydtin ∆ABC…

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: Length of ladder is l= 10ft X=8 ft, dx/dt= 18ft/sec From the fig l =[ x2 + y2 ]0.5= 10 a) from…

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

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: 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 spherical snowball melts at a rate of 16 in / sec. when the radius is 2 in, then the radius of the…

A: The formula for  volume of sphere is: V=43πr3 Given that dVdt=16 in3/secr=2

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

A: .

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: A kite 100 ft above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle…

A: Let's solve given rate of change problem.

Q: A 13 ft ladder is leaning against a house. The ladder slides down the wall at a rate of 3ft/min. a)…

A: We have to use differentiation to solve the problem

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

A: topic - trigonometric ratios and application of derivatives

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A: Given that

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:

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: 4.A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: This question is based on application of Derivative.

Q: A ladder 25 ft long rests against a vertical wall. If the bottom of the ladder is sliding away at a…

A:

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

A:

Q: O H.W3: A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing…

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 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: 20. If a point R on the unit circle moves along the circle at the rate of 1 unit per second, then…

A: Given: A point R on the unit circle moves along the circle at the rate of 1 unit per second. To find…

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

A:

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

A: Given that,

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

A:

Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume 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: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: topic - application of derivatives

Q: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: The given data is: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is…

Q: 33. The base x of the right triangle in Figure 14 increases at a rate of 5 cm/s, while the height…

A:

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: ce of a circle is increasing at a rate of 2 cm/s. rea increasing when r= 6 cm?

A: We have to choose the correct answer from the given options according to the given information

Q: and passes directly over a tracking telescope on the ground. When the angle of elevation is ?/4,…

A:

Q: The edge length of a cube is 12 cm and increasing at a rate of 2 m. How fast is the Surface Area of…

A: Given dx/dt=2cm/hr X=12cm

Q: s. How fast (in knots) is the distance between the ships changing at 4 PM? (Note

A:

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 13-foot long ladder is leaning against the side of a house when its base starts to slide away. By…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off…

A:

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: The velocity of an object moving along a line is given by v1t2= 20 cos pt (in ft>s). What is the…

A: Consider the given velocity function as vt=20cospt

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 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying…

A: Let the distance of the base from the wall is x ftAnd the top of the ladder is y ft high. Then x and…

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) A 5-ft ladder is leaning against a house when the base starts to slide away. by the time the…

A: First we use Pythagoras theorem and then we calculate dA/dt and solve it .

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