A particle moves in a straight line with velocity 12 – 2t ft/s. Find the total displacement and total distance traveled over the time interval [0, 10). Displacement: ft. Distance: A ft.

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

A: Surface area of cube = 6x2Where x is the edge of the cube

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: B. How rapidly will the water level inside a vertical cylindrical tank if we pump the water out at…

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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 surface…

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

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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: 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: 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: 10. Gas is escaping from a spherical balloon at a rate of 2 cubic feet per minute. How fast is the…

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Q: Calculate the rate of change of escape velocity vesc = (2.82 × 107)r −1/2 m/s with respect to…

A: Given, vesc=2.82×107r-12 m/s where r is a distance from the center of the earth.

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

A:

Q: 5. A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows…

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Q: 10 inches 6 inches 18 inches Using the dimensions from the previous item, find the rate of change in…

A: Given total surface area formula of rectangular solid SA=2lw+2lh+2wh   ......(1) where l,w,h are the…

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…

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

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

A:

Q: ht h(t), in feet, of an airborne tee-shirt t seconds after being la ld a tee-shirt be airborne if it…

A: The height h(t) in feet, of an airborne tee-shirt t seconds after being launched is approximately…

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

A:

Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

A:

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: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 2 centimeters per second.

Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

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

A:

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

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Q: v(t) = 90 − 32·t.

A:

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

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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: The heat transfer rate of the rocket engine is given by:

A: Part (a) - Given equation - Q = -kAdTdx        ..........(1)Given that - T(x) = tanxsecx + sinx2k =…

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: 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: Show that the period of motion of an undamped vibration of a mass hunging from a vertical spring is…

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Q: The radius of the sphere increases at a rate of 4 cm/sec . Find the rate at which the volume…

A: we have given the rate change in radius of a sphere.  We have to find the rate of change of volume…

Q: pouring

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

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 the sqhere is increasing at a rate of 10cm^3/sec. Find the rate of change of its…

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: A spherical balloon is inflated at a rate of 21 cm's1. Find the rate of change of the surface when…

A: Volume (V) of the sphere = (4/3) pi r3 Surface area (S) of the sphere = 4 pi r2 where r is the…

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

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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