Let s(t) = 4t represent the distance in meters from its starting point. %3D Round the answer to two decimal places.

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

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Q: Q4. A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the…

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Q: (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of…

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Q: y= f(x) y = f(x) 2- b) Find new estimates using ten rectangles in each case. (Round your answers to…

A: Given:    only using this two diagram because number of rectangles are 10 in both the diagram.

Q: At what rate is the distance between the planes changing? mph (b) How much time does the controller…

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Q: If a snowball melts so that its surface area decreases at a rate of 2 cm²/min, find the decreasing…

A: To find- Radius is decreasing at the rate of

Q: The intensity of a light from a light bulb varies inversely as the square of thedistance from the…

A: Let y=intensity of light from a light bulb x=the distance from the bulb.  So, according to the…

Q: If a ball is thrown into the air with a velocity of 34 ft/s, its height (in feet) after t seconds is…

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Q: The length of a rectangle is given by 4t + 9 and its height is √t, where t is time in seconds and…

A: Given:

Q: The displacement, in meters, of an object moving in a straight line is given by s(t) = 3+ 4t +t2,…

A: The displacement is given by

Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

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Q: What is the rate of change of f (t) at t = 7.5?

A: The rate of change is calculated using differentiation. The derivative of f(t) at t=7.5 gives the…

Q: The displacement (in meters) of a particle moving in a straight line is given by = 9t3 + 4t – 18, |…

A: Given,         The displacement in meters of a particle moving in a straight line is given by…

Q: The velocity of a moving object is v(t)=2t +/t in meters per second. What is its displacement, in…

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Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from vertical…

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Q: t 2 If the velocity of a moving object is y(t) = --- 2 12 in meters per second, then what is its…

A: The veloctiy of a moving objcet is v(t)=t2-2t2 in meters per second.

Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

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

Q: If a ball is thrown with a velocity 48 ft/s, its height in feet t seconds later is given by y = 48t…

A: Given that if a ball is thrown with a velocity 48ft/sec, its height in feet t seconds later is given…

Q: At t sec after liftoff, the height of a rocket is4t2 ft. How fast is the rocket climbing 7 sec after…

A: We have the height of the rocket as a function of time after liftoff as h(t)=4t2 Now h'(t)=4·2t=8t

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

A: Given  Decreasing rate of surface area = 3cm2/min To find: the rate of decreasing of diameter when…

Q: The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and…

A: Formula:  Area=length times height A(t)=t(6t+5)

Q: The acceleration after t seconds of a hawk flying along a straight path is a(t) = 0.7 + 0.16t ft/s2.…

A:

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

A:

Q: the radius r, of a circle is decreasing at a rate of 2cm per minute. Find the rate of change of  the…

A: givenradius (r)=5 cmdrdt=2 cm/minwe knoww circumference of the circle (C)=2πrdiffrentiatedCdt=2πdrdt

Q: Evaluate the rate of change of the Area if the area of the circle is given by A= 6 r² when dr 7 and…

A: Given, the area of circle A=6r2

Q: On a morning of a day when the sun will pass directly overhead, the shadow of a 60-ft building on…

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Q: The displacement (in feet) of a particle moving in a straight line is given by s= - 9t + 19, where t…

A:

Q: Find E(X) and if students pay $500 per course plus a $100 per-semester registration  fee., What is…

A: Amount paid for course fee=$500 Amount paid for per-semester registration fee=$100 The objective is…

Q: pproximately ft. ed to the nearest thousandth as need

A: Parabola: In figure height of the parabola is 29ft. width of the parabola is 30ft. We need to find…

Q: An analysis of the daily output of a factory assembly line shows that about 50t+t²- 1 tunits are…

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Q: from the edge of a cliff into described by the function ht rate of change in the height - 4.9t² +…

A: Formula average height change=(h(b)-h(a))/(b-a) Where a=4second b=5second

Q: Give the procedure to fit the following exponential curves, (ii) y =abx.

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Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

A: The given function is: y=3t-8t2-t3, 0≤t≤4 where y is the number of frames painted in t hours. Here,…

Q: The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute.  Find the rate of…

A:

Q: The velocity of a moving object is V (t)=2t +/t in meters per second. What is its displacement, in…

A: We have to find displacement

Q: The velocity, v m/s of a ball thrown directly up in the air is given by ? = 20 − 10?, where t is the…

A: Soln :-         V = 20-10t            The time (t) when V is between 5 and 15 m/s.…

Q: The distance (in feet) of an object from a point is given by s(t) = t2, where time t is in…

A: Given the distance of an object from an point at time t is given by equation s(t) = t2, where t in…

Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

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Q: The resale value R​ (in dollars) of a company car after t years is estimated to be given by…

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Q: If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does (see picture)…

A: solution is given below

Q: D. Now that you know the equation of the line of best fit, use the equation to estimate the BMI of a…

A: Use EXCEL to determine the regression equation.   EXCEL procedure:   Go to EXCEL Go to Data>Data…

Q: If a ball thrown into the air with a velocity of 41 ft/s, its heigh (in feet) after t seconds is…

A: Given that a ball thrown into the air with a velocity of 41 ft/s, its height (in feet) after t…

Q: The displacement (in feet) of a particle moving in a straight line is given by  s = (1/2)t2 − 9t +…

A: Use instantaneous velocity concept

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing…

A: topic - application of derivatives

Q: If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is…

A: Given, The height of the ball is given by : y = 42t -16t2 ;  Where y is in feet and t is in seconds…

Q: a drug concentration curve is given by C(t)= 20te^-0.2t, which C in mg/ml and t in minutes. What is…

A: A drug cocentration curve isC(t)=20te-0.2tTo find the rate of concentration. We have to…

Q: The displacement, s in feet, of a particle moving in a straight line is given by s = 5t2 – 6t + 14,…

A:

Q: Suppose that a turtle is moving along a straight line, and its displacement s(t) at any given time t…

A: Given data: The expression for the displacement is s(t)=(t-√(t2+3)+√3). The given interval is [a,…

Q: The displacement, 8 in feet, of a particle moving in a straight line is given by 8 = 5t2 6t + 14,…

A:

Q: If a ball is thrown into the air with a velocity of 40ft/s, its height (in feet) after t seconds is…

A: Consider the given question,The distance(y) equation is given as,