A car starts from rest at time t = 0 and accelerates at – 0.61 + 4 meters/sec? for 0

Q: A car is merging onto a freeway (beginning at rest), accelerating at a constant rate of 12ft/sec How…

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Q: A population of insects increases at a rate of 200 + l0t + 0.25t 2 insects per day (t in days). Find…

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Q: Water is drained from a swimming pool at a rate given by |(-0.2)t R(t) = 100e' gallons per hour. If…

A: Solution : We have given the rate of water drain form a swimming pool is R(t) = 100e(-0.2)t…

Q: The radius of a circular oil slick expands at a rate of 3 m/min. (a) How fast is the area of the oil…

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Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 2…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A: Find the length of ladder when bottom of the ladder is increasing at the rate of 0.3m/s when bottom…

Q: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

A: Rate at which surface area increases is

Q: The cost of certain piece of machinery is $ 700 and its value is depreciating with time according to…

A: We have to find the value after 6 years.

Q: e skid marks made by an automobile indicated that its brakes were fully applied for a distance of 85…

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Q: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

A: I=VR here V is constant and that is V=6 I=6R take the derivative with respect to t  dIdt=ddt6R…

Q: The radius of a circular oil slick expands at a rate of 8 m/min. (a) How fast is the area of the…

A: Write the expression for the area of the circle and take the derivative of it.

Q: Initially stationary, a train has a constant acceleration of 1.8 m/s2 How far it travel after…

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Q: The radius of a circle is growing at a constant rate of 3 in./sec. (a) What is the area of the…

A: Introduction :

Q: An object is thrown vertically upward with an initial velocity of 16 /sec from the top of a house o6…

A: Calculate the time by using equation of motion in the following way:-

Q: A rock thrown vertically upward fromthe surface of the moon at a velocity of 24 m/sec (about 86…

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Q: 7. A car can accelerate at 4 m./sec.?. How long will it take to reach 90 km./h. from rest ? (ans.:…

A: Givem acceleration 4 m/sec ^2 Initial velocity 0 Find the time

Q: A ball is thrown vertically upward with an initial velocity 15 m/s from an          initial height…

A: Use the kinematics equation to solve the problem and at the highest position the final velocity will…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: let the length of rectangle is l cm and width is w cm area of rectangle is(A) =lxw differentiate…

Q: The radius of a circular oil slick expands at a rate of 2 m/min. (a) How fast is the area of the oil…

A: Given, dr/dt = 2 m/min. (a) r = 29 m A = pi*r^2 dA/dt = (2*pi*r)(dr/dt) = 2*pi*29*2 = 116*pi…

Q: Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Assume that brine containing…

A: Given that Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Let x(t) be the…

Q: Beginning at rest, an automobile drives around a circular trackof radius R = 300 m, accelerating at…

A: Given :           radius R = 300 m           Acceleration = 0.3 ms2           Coefficient of…

Q: A culture of bacteria is growing at a rate of 5e0.bt per hour, with t in hours anc 0sts 20. How many…

A: The growth rate of culture is given as, dNdt=5e0.6t We need to find the new bacteria developed in…

Q: An object is moving so that it's velocity after t hours is v(t)=te^-t^2 mph. How far does it travel…

A: Hey the equation of velocity that you have written is v(t)=t·e-t2mph following is the solution to…

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

A: Given that A rocket is fired vertically upward from the ground with an initial velocity of 580…

Q: A triangle with constant base b and height h is changing with time where h(t) = 2t – 3. What is the…

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Q: The radius of a circular oil slick expands at a rate of 5 m/min. (a) How fast is the area of the oil…

A: Given,  drdt = 5 m/minArea(A) = πr2       dAdt=2πrdrdta) r = 25m    dAdt=2π255          =  785.4…

Q: evaporation As a spherical raindrop falls, it reachesa layer of dry air and begins to evaporate at a…

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Q: A ball is thrown from a height of 880 feet above ground with an initial velocity of 96 feet per…

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Q: The radius of a circle is increasing at a constant rate of 0.2 meters per second What is the rate of…

A: Given that the radius of a circle is increasing at a constant rate of 0.2 meters per second. To find…

Q: What is the period of time ''t'' required for the initial infection rate ''I(t=0)'' to double in…

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Q: A 25-foot ladder is leaning against a house, as shown in the figure below. If the base of the ladder…

A: Using Phthagorous therome, r2 +x2=252  First we find rate of change in r, then we get Dr/dt in terms…

Q: A radio active element (x) has a half-life of 38 hours. Initially, X = X0 %3D . Determine the amount…

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Q: A ball is thrown straight up from the ground. If the ball is to reach a max height of 64 feet, what…

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Q: The edges of a cube increase at a rate of 5 cm/s. How fast is the volume changing when the length of…

A: Solution:- The edge  of the cube increase at a rate of 5cmsec let the edge of the cube =a =10cm⇒da…

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: The surface area is

Q: The area of a circle increases at a rate of 3 cm2 /s. a. How fast is the radius changing when the…

A: Given that: The area of a circle increases at a rate of 3 cm2/s To find: (a) How fast is the radius…

Q: The radius of a circular oil slick expands at a rate of 5 m/min. (a) How fast is the area of the oil…

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Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: Rate of change of radius = 3m/s Find the change in surface area at radius = 6m

Q: A rock thrown vertically upward fromthe surface of the moon at a velocity of 24 m/sec (about 86…

A: Velocity is 24m/sec To calculate the time taken by the rock to reach its highest point.

Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How…

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: A submarine telegraph cable consists of a core of copper wires with a covering made of nonconducting…

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Q: 2. The volume of a cube decreases at a rate of 10m/sec. Find the rate at which the side of the cube…

A: dVdt=10m3/min, side=2mFormula of volumeV= side3

Q: Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and…

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Q: Water flows from the bottom of a storage tank at a rate of r(t) = 4(50 − t)e −0.05t liters per…

A: Given:  rt=450-te-0.05t    , 0≤t≤50    1 We need to find the amount of water that flows from the…

Q: A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held…

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Q: a girl flies a kite at a height of 300ft. the wind carrying the kite horizontally away from her at a…

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Q: ositioned 4 meters higher than the boat. If the rope is being pulled in at a rate of 3m/sec, ow fast…

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

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Q: A particle that moves along a straight line has velocity v(t) meters per second after t seconds. How…

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Q: 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank…

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