6. The hypotenuse of a right triangle is increasing at a constant rate of 3 ft per second and one leg (first leg) is decreasing at a constant rate of 2 ft per second. How fast is the acute angle between the hypotenuse and the second leg is changing if the first and second legs are 10 ft and 24 ft, respectively? Is the angle increasing or decreasing?

Q: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: If the first line has the form Ax + By + C = 0 the second line has the form Dx + Ey + F = 0 the…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second,…

A:

Q: A ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the…

A: Follow the procedure given below.

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing…

A:

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

A:

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A:

Q: Two cars are at an intersection. One goes east at a speed of 40 feet per second; the other goes…

A: Given The first car is 240 feet away from the intersection and the other is 360 feet away from the…

Q: A certain escalator travels at a rate of 13.4 meters per minute, and its angle of inclination is…

A: So from the triangle we have: Answer(a): Vertical component of the velocity is 6.1667 meters per…

Q: area given by the following.   A = 1/2xy   If the rate of change of x is 2 units per minute and the…

A:

Q: fast is the distance between the two cars changing?

A:

Q: Two people on bikes are separated by 350 meters. Person A starts riding north at a rate of 5 m/sec…

A: Let x be the distance travelled by Person A at a speed of 5 meter per second, after 25 minutes. Use…

Q: One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knats.…

A: Let the time at 2:00 Pm be t  The two ships will form a right angled triangle, with horizontal side…

Q: A kite 30 m above the ground moves horizontally at a speed of 10 m/min. At what rate is the angle…

A:

Q: 19. A 6 foot ladder is sliding down a vertical wall at a rate of 1 foot per second. What is the rate…

A:

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

A:

Q: At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: Given that  At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B…

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

A:

Q: "A Kite 65 feet above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle…

A: Given a kite 65 feet above the ground moves horizontally at a speed of 6 ft/s.

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second,…

A:

Q: A baseball diamond has equal sides of 90 ft in length and each pair of adjacent sides are…

A: We will use vector projection and project the velocity vectors of B and C along the line joining…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second…

A: Given that, a man flying in a hot air balloons in a straight line with constant rate 5 feet per…

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

A:

Q: A plane flies horizontally at an altitude of 6km and passes directly over a tracking teles cope on…

A:

Q: A triangle has two sides a = 8 cm and b = 12 cm. How fast is the third side c increasing when the…

A: Since two sides and one angle opposite to the third side are given; cosine law has to be applied.…

Q: One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots.…

A: Given that at time 2 p.m the second ship is at the place occupied by the first ship one hour before.…

Q: 2.) A ladder 5 feet long rests against a vertical wall. If the bottom of the ladder (on level…

A: A ladder is 5 feet long. The speed at which the ladder slides away from the wall is 1 foot per…

Q: Car A is 40 km east of Car B and begins moving west at 40 km/h. At the same moment, Car B begins to…

A: Answer is in below steps.

Q: 9. At noon, ship A is 160 km north of ship B. Ship A is sailing south at 40km/h and ship B is…

A: Given Ship A is 160 km north of ship B Ship A is sailing south at 40Km/h and ship B is sailing east…

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: 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: At noon, ship A is 180 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: In this question we have to find how fast is the distance between the ships is changing at 4:00 PM.

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: A baseball diamond has equal sides of 90ft in length and each pair of adjacent sides are…

A:

Q: The slope of the tangent at a point (x0, y0) of x3 + y3−6x2y = 0, is indicated as 4x0y0 −…

A:

Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

A:

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A:

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

A:

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: 8. If a plan is moving horizontally at 100 mi and is falling at 10 mi how fast must an observers eye…

A: Solution

Q: An airplane is flying on a horizontal path at the height of 3,800 feet. At what rate is the distance…

A: We need to find rate of distance changing.   ddθ(cscθ)=-csc(θ)cot(θ)

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

A:

Q: A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 16 ft high. At what rate is…

A: Given: Height of the man, h=6 ft Height of the post, H=15 ft Walking rate, dxdt=5 ft/sec

Q: A baseball diamond has equal sides of 90ft in length and each pair of adjacent sides are…

A:

Q: A baseball diamond has the shape of a square with sides 90 feet long.  Suppose that player A is the…

A: Use Pythagoras theorem

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: OH NO!! CERTAIN DOOM: Car A is traveling west at 50 mi/hr and car B is traveling north at 60 mi/hr.…

A:

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

A:

Q: Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and moving…

A: Given data: The speed of  A is dxdt=-20 mph. The speed of  B is dydt=15 mph. Position of A is xA=15…

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.