Two sides of a triangle are 4m and 5m in length and the angle between them is increasing at a rate of .06rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3.

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. Let x be the distance between the bottom…

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: A helicopter takes o from a point 80 m away from an observerlocated on the ground, and rises…

A: Thus when the helicopter is 60 m above the ground the elevation angle of theobserver’s line of sight…

Q: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

A:

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A: Rate of change

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

A:

Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: A vertical cylinder is leaking water at a rate of 3 m/sec. If the cylinder has a height of 10 m and…

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

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: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

A:

Q: A ladder 10 feet long is leaning against the side of a vertical wall. The bottom of the ladder…

A:

Q: The depth of water in a 4m diameter cylindrical tank is increasing at the rate 0.7m/min. Find the…

A:

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

A:

Q: A 25-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 5…

A:

Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

A:

Q: Water flows at the rate of 2000 cibic cm per second into a verical cylindrical tank 120 cm in…

A: Given: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm…

Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

A:

Q: Two sides of a triangle are 15 and 20 ft long, respectively. a) How fast is the third side…

A: Given: Two sides of triangle are 15ft and 20ft. We use cosine rule         C=a2+b2-2abcosθ     where…

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A: Given data:     The given sides of the square is: a=90 feet. The speed of the batter towards the…

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A:

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

A: It is given that,

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

A:

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

A:

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Given: dVdt==55, side length b0=4 and height h0=11. To find: dhdt, when h=2.

Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

Q: A plane flying parallel to the ground at a height of 4 km passes over a radar station R. A short…

A: NOTE: Refresh your page if you can't see any equations. . here we have y=4 when s=5, s'=300 km/h

Q: Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at a rate…

A: Topic:- application of derivatives

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: The volume of a cube increases at a constant rate of 135 ft°/ sec. The rate at which the side of the…

A:

Q: Two sides of a triangle are 15 and 20 ft long, respectively. a) How fast is the third side…

A: Consider the given information:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: . A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A:

Q: A vertical circular cylinder has radius r ft and height h ft. If the height and radius both increase…

A:

Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A:

Q: A 17-ft ladder is leaning against a wall. The foot of this ladder is sliding away at the rate of…

A:

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

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: A triangle has two constant sides of length 6 ft and 2 ft. The angle between these two sides is…

A:

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

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: Two sides of a triangle are 19.2 m and 29 m in length and the angle between them is increasing at a…

A:

Q: Two sides of a triangle are 17.8 m and 27 m in length and the angle between them is increasing at a…

A: In this question we have to use some properties of triangle and differentiation. According to the…

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

A:

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

A: