A particle moves in a straight line with velocity 12 – 4t ft/s. Find the total displacement and total distance traveled over the time interval [0, 10]. Displacement: , ft. Distance: , ft.

Q: The volume of a cube decreases at the rate of 84 m /sec. The rate at which the side of т the cube…

A: To find the rate at which the side length of cube changed when side is equal to 8 m/s

Q: hot air ballon is hovering 110 meters above the ground and begins to assend at a rate of 17 meters…

A: This is a question of application of differentiation and integration... We will proceed as follows

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

A:

Q: The volume of a cube decreases at a rate.1 of 15 m/sec. Find the rate at which the side of the cube…

A: It is given that the volume of a cube is decreasing at a rate of 15 m/sec. It is known that volume…

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube…

A: We have to find rate  of change of side of cube .dV/dt  is negative beacuse it is…

Q: A honeybee population starts with 100 bees and increasesat a rate of n'(t) bees per week. What does…

A: Given data: The initial honeybee population is n(0)=100. If n'(t) is the rate at which the…

Q: A particle moves in a straight line with velocity t-² – + ft/s. Find the total displacement and…

A: We need to find displacement and distance.

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: We have to find the rate of change of surface area.

Q: A faucet is filling a hemispherical basin of diameter 60 cmwith water at a rate of 2L/min . Find the…

A:

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A:

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: (b) What is the displacement of the snail over the interval 0 <ts 15 minutes?

A:

Q: Water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours after…

A: Given, water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours…

Q: The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated…

A: Given: The volume V, in liters, of air in the lungs during a five-seconds respiratory cycle is…

Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 50t – 3 m/s over…

A:

Q: One airplane is approaching an airport from the north at 203 km/hr. a second airplane approaches…

A: Let in the below figure P represents the airport, Q represents the southbound plane and R represents…

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

A:

Q: 2. Find the rate of change of a volume V of a cube with respect to (a) the length w of a diagonal of…

A: Consider a cube of a side a , and diagonals z and w  We know that Pythagorean theorem , Hypotenuse 2…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second (a) How fast is the surface…

A: Rate of change of surface area is given by ds/dt = a . dA/dt Where a = edge length dA/dt =rate of…

Q: A 1500-L tank is initially filled with a solution that contains 3000 g of salt. A salt solution with…

A: This question can be solved using the concept of differential equation.

Q: Water is poured at a rate of 10 cubic meters per minute into a conical tank 6 meters across the top…

A:

Q: A car travels along a straight line at a constant speed of E60.0mi/h for a distance d and then…

A:

Q: a ball is free falling from height of 200 mifind 1-the time of the ball wheureach to the ground. 2-…

A: Part(a): Given, Height=200 mg=9.8 m/s2u=0 Velocity for free falling body Let, the time be t and…

Q: spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.

A: Volume of the sphere is V=43πr3where r = radius of the sphere

Q: A tank initially contains 100 gallons of brine whose salt concentration is 3 lb/gal. Freshwater is…

A: We will make a differential equation for amount of salt and then will solve it to get amount of salt…

Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…

A: Remaining capacity of tank is 50-10 = 40 gallons.

Q: The volume of a cube is growing at a rate of 2 in3/min. Determine the rate at which the surface of…

A: Given:The volume of a cube is growing at a rate of 2 in3/min, that is dVdt=2 in3/min, where V is the…

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the- radius of the…

A: The volume of a cylinder is given by the formula V=πr2h. Where, V-volume, r-radius and h is the…

Q: All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the volume…

A: Let , the edges of a cube=a cmall edges of a cube are expanding at a rate of 7 centimetres per…

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A: Solve the given problem

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

A: Explanation of the answer is as follows

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the volume…

A:

Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

A:

Q: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The…

A: Consider the volume of right circular cylinder V. Differentiate it w.r.t time t.…

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

A:

Q: pouring

A: We will find the rate of change of height.

Q: What is the velocity of flow in feet per seconds f

A:

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A: From the given data: The rate of expanding of a cube is 4cm/sec

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A:

Q: A particle moves in a straight line with velocity t-2 – - ft/s. Find the total displacement and…

A: Derivative of displacement is called velocity

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

A:

Q: A tank containing 100 gallons of brine made by dissolving 40 lbs of salt in water. Pure water runs…

A: Pure water in flow rate = 5 galmin

Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

A: