The volume of a cube decreases at a rate of 0.6 ft° /min. What is the rate of change of the side length when the side lengths are 9 ft? The rate of change of the side length when the side lengths are 9 ft is

Q: A spherical snowball melts at a rate of 36π^2in³/sec. At what rate is the radius of the snowball…

A:

Q: velocity

A: We have : h=12t2+12t We have to find the velocity of the balloon at the end of the 39 sec.

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: A rocket is fired vertically upward from the ground with an initial velocity of 580 ft / sec. How…

A: Given : Initial velocity = 580 ft/sec

Q: The side of a cube is increasing at a rate of 5cm/sec, find the related change in surface area wher…

A:

Q: 16 foot ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

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

A: Shown below

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

Q: A car traveling at 42 ft/sec decelerates at a constant 44 feet per second per second. How many feet…

A: Given,A car traveling at 42 ft/sec decelerates at a constant 4 feet per second.i.e., initial…

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 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A: Solve using increasing & decreasing function.

Q: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

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

A: Given:         Length of ladder =20 ft    dhdt=-2 ft/sec

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: 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: The cone is 12 cm tall and has a radius of 4 cm. If the ice cream fills the cone evenly at a rate of…

A:

Q: A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the…

A:

Q: A bird 150 ft above the ground flies horizontally at a speed of 11 ft/s. At what rate is the angle…

A: Given Data: The height of the bird above the ground is: y=150 ft The speed of the bird is: x'=11…

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: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A: Given: Rate of change of area is increasing at the rate of 4 cm2/sec, that is, dAdt=4 cm2/sec. To…

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

A:

Q: . Betty and Bob take off in an airplane and travel at an angle of 45 degrees to the ground as per…

A: Let dh/dt represent the rate at which altitude is increasing:

Q: A car traveling at 46 ft/sec decelerates at a constant 7 feet per second per second. How many feet…

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

A:

Q: A car traveling at 46 ft/sec decelerates at a constant 8 feet per second per second. How many feet…

A:

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: If the velocity of a moving object is v(t)=t-2/t^2 in meters per second, then what is its…

A: We have to find displacement

Q: A wheel has a diameter of 100 centimeters. If the wheel is supporting a cart moving at 45 kilometers…

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: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area

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

A:

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm4/min, find the rate at…

A: Note that snowball has a shape of sphere.

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 rectangular beam is to be cut from a cylindrical log of diameter 20cm. Express the cross sectional…

A: It is given that the rectangular beam is cut from a cylindrical log of diameter 20cm.Therefore,…

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 kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle…

A: The diagrammatic representation of the problem is shown below.

Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at…

A:

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: 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 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: at a velocity of 3 ft/

A: Given the spring constant is 9 lb/ ft.

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

A:

Q: A balloon ascending at the rate of 12 ft/sec is at a height 80 ft above the ground when a package is…

A: Sol:-v0=12 ft/secHeight = h = 80 ftThen, y-y0=v0t-12gt2