A Conical Cup is 4cm across and 6cm deel. Water leaks cut of the bottom of the cup cit a rate of Zcm?/sec. How fast is the Water level dopping when the height of the water is 3cm?

Q: A 1.6-oz golf ball is driven o¦ the tee at a speed of280 ft/sec (about 191 mph). How many…

A: The mass of the ball is found as: m=Weightg   =1.6 oz32x1 lb16 oz   =1320slugs

Q: Coffee is draining out of a conical filter at a rate of 2.25 in3>min. If the cone is 5 in tall…

A: Given: The change in volume for the filter is -2.25 in3/min The change in volume for the coffee pot…

Q: If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in…

A:

Q: At JCS Construction Plant, cement mixture is falling off a metal conveyor and onto an inverted…

A: Given: Cement mixture is falling off a metal conveyor and onto an inverted conical pile at a rate of…

Q: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

A: Given that the initial velocity of the car is 50 mi/h and the deceleration is 40 ft/s2. The…

Q: An equilateral triangle gutter is 27 ft long, 1 ft wide across the top, and 6 ft deep. If rainwater…

A: Let Vt be the volume of the water at time t. Given that dVdt=12 ft3/min Let h be the height of the…

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: Given that,

Q: The sides of a square increase in length at a rate of am/s. At what rate is the larea of the square…

A: Area of square with side 's' isA=s2Differentiate with respect to xdAdt=2sdsdt Substitute dsdt=2,…

Q: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

A: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

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

A:

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 man on a wharf is pulling a small rope tied at the end of a cable, used in mooring a boat…

A: Let L be the length of the rope out      x be the distance between the boat and the wharf As man on…

Q: Assume gravity is 32 ft/s? and no external forces (ex: wind resistance). If you Jump off a 34 ft…

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: om the tank at a rate of r(t) = 115e liters per minute. How much oil le

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

Q: The sides of an equilateral triangle are increasing at the rate of 3cm/min. Find: a.)the rate of…

A:

Q: Coffee is draining out of a conical filter at a rate of 2.25 in³/min. If the cone is 4 in all and…

A: The volume of cone is given by . The rate of coffee draining is 2.25 cubic inch per minute. This…

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

A:

Q: Coffee drips into a cylindrical coffee pot at a rate of 10 in3/min. How fast is the level inthe pot…

A: For the volume of the coffee on the conical filter F at any given time t, refer to the figure:

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: Topic:- application of derivatives

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: we have to find the rate change in diameter

Q: A bar with a diameter of 2 inches is put under a 7000 pound load. What is the stress in the bar, in…

A: Stress in the bar in psi: The general formula to obtain stress in the bar in psi is given below:

Q: A triangular trough is 10ft long, 6 ft across the top, and 3 ft deep. If water flows in at the rate…

A: Given: A triangular trough is 10 ft. long, 6 ft. across, and 3 ft. deep.If water flows in at the…

Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: We will be using the trigonometric ratios relating the sides of the triangle formed by strings and…

Q: On a day  when the wind is blowing toward the south at 3 m/s, a runner jogs west at 1.9 m/s.what is…

A: Let V1 be the velocity of the air and V2 be the velocity of the runner, then the relative velocity…

Q: The side of a cube increases at a rate of 2.5m/s. Find the rate at which the surface area increases…

A: As we know that; The expression of the surface area of the cube is: As=6a2        ....(1) Where;…

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

A:

Q: The speed of a moving sidewalk at an airport is 2ft/sec. A person can walk 45ft forward on the…

A: Let his speed on a non-moving sidewalk is = x ft/sec Given the speed of the moving sidewalk = 2…

Q: diameter

A:

Q: A rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. If water lows in at rate 2…

A: It is given that rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. Suppose that x…

Q: A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5 ft/sec. i) How…

A: Given problem:- A light hangs 15ft above a horizontal path and a man 6ft tall is walking away at 5…

Q: A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from the…

A: Calculation of rate by which shadows lengthening.

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

A:

Q: The velocity, in feet per second, of a running rodent is modeled by v(t) = 5√t − 2t. What is the…

A:

Q: A rectangle has one side of 6 cm. How fast is the area of the rectangle changing at the instant when…

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: A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope…

A: To find: The speed of the boat approaching the dock when the total length of rope out is 50 feet.…

Q: A car braked with a constant deceleration of 18 ft/s2, producing skid marks measuring 100 ft before…

A:

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

A:

Q: A street light is at the top of a 20 ft pole. A 5 ft tall girl walks along a straight path away from…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given information:

Q: The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the…

A: Consider the given equation: V=43πr3 Where V is the volume and r is the radius. Differentiating the…

Q: The sides of a cube increase at a rate of R cm/s. When the sides have a length of 2 cm, the rate of…

A:

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

A:

Q: The volume of a cube increases at the rate of 59m3/sec The rate at which the side of the cube…

A:

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…

Exponential Growth Model

The relation that represents an exponential function is: