2.1 Suppose that f (t) = 3t + 2 – 12t. а. What is the average rate of change of f(t) over the interval 2 to 3? b. What is the (instantaneous) rate of change of f(t) when t = 2?

Q: Suppose that f(t) = 3t + 2 – 12t. а. What is the average rate of change of f (t) over the interval 2…

A: We are given the function f(t) = 3t+2-12t => f(t) = 2-9t. For (a), The average rate of change of…

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [4, 16].…

A: Given:  fx=1x  To Find:  The average rate of change of the function over the interval 4, 16=?…

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: 3. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: We are allow to solve only one question at a time  Thank you for your question

Q: 5. If a ball is thrown into the air with a velocity of 40 ft/s, its - 401- 16r. height in feet…

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Q: If a ball is thrown straight up into the air with an initial velocity of 50 ft/s, it height in feet…

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Q: 2. If f(t) is the rate of change of some quantity, then what does f (t) dt represent?

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Q: Suppose the velocity function of a particle is given by y = 2 – t - t2 at any time t ( time is in…

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Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

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Q: 2. What is the average rate of change between x = 2 and x = 3 for the function g(x) = 4(x + 1)² -5…

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

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V…

A: Given as : P=10TV By differentiating it with respect to t: dPdt=10VdTdt-TdVdtV2 ......1 1). If T is…

Q: Suppose that f(t)=t2+t−3.What is the average rate of change of f(t) over the interval 3 to 4​?

A: f(t)=t2+t−3To find average rate of change of over the interval 3 to 4

Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: suppose that g(s)=s^2+3s+4 . find a value c in the interval [0,2] such that g'(c) equals the average…

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

A: Given, A ball is thrown into the air with an initial velocity of 42 ft/s, its height in feet after t…

Q: t=a,t=ath

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Q: 1. Determine the value of so that the average rate of change of the function h(x) = x + 3x+2 on the…

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Q: You are a process control engineer in a water purification plant. In a certain subprocess, water…

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: If a ball is thrown into the air with an initial velocity of 52 ft/s, its height in feet after t…

A: Given that: An initial velocity of the ball is is 52 ft/s, and height after t seconds is given by…

Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

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Q: Let F(s) = 5s² + 2s + 4. Find a value of d greater than 0 such that the average rate of change of…

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Q: 3. Assume that the level of nitrogen dioxide present in the atmosphere on a certain June day in city…

A: The level of nitrogen dioxideN(t)=0.05t3t-64+53  0≤t≤8

Q: Suppose that f(t) =t+4t-4. W.at is the average rate of change of f(t) over the interval 3 to 4? %3D…

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Q: 8. The following table gives the velocity of a car in meters per second. time (seconds) 05 10 15 20…

A: Given the table which shows the velocity of car in meter per second

Q: An efficiency study of the morning shift at a certain factory indicates that an average worker who…

A: Given, Qt=-t3+6t2+24t a. Compute the worker's rate of production at 11:00 A.M. Here t=3 ( Difference…

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V…

A:

Q: Suppose that f(t) =t +t-5. What is the average rate of change of f(t) over the interval 4 to 5? The…

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Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

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Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

Q: 9. Suppose an object is moving along a path described by; f(t) = t° – 6t, where f (t) is measured in…

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Q: 2 Refer to the graph above and without making any computa- tions find: The average rate of change…

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Q: Find the average rate of change of the function over the given interval. f(t) = 4t2 – 1, [1, 1.1]

A: Given data: The expression for the function is f(t)=4t2-1. The given limit of t is [a, b]=[1, 1.1].…

Q: A pump allows water to flow into a pool at the rate of r (t) = 2t liters per minute, where t is the…

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Q: Let g(x) = 6x + 7 and h(x) = x² + 8. What is the average rate of change of g on the interva 2 < x <…

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Q: Suppose h(t) = t² + 11t + 7. Find the instantaneous rate of change of h(t) with respect to t at t =…

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Q: (a) Calculate the average rate of change of R with respect to q over the intervals 1 < q< 2 and 2 <…

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Q: -4 to x = 1 Find the average rate of change of g(x) = 3x° - 1 from z =

A: Average is (g(1) -g(-4)) /5

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [1, 4]. Ду…

A: Solve the function

Q: 12 6. Suppose that f (t) = 3t + 2 a. What is the average rate of change of f(t) over the interval 2…

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Q: 5. Consider the function f(x) = Vx + 16 a) Estimate the average rate of change of f(x) from x = 0 to…

A: Given, f(x)=x+16

Q: 3. If f (t) = -t² + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: Given : The function ,ft=-t2+5t+3 describes  the distance travelled by the ball in meters. To find:…

Q: A rectangle is growing such that the length of a rectangle is 5t + 4 and its height is t, where t is…

A: Given:- A rectangle is growing such that the length of a rectangle is 5t + 4 and its height is t4 ,…

Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

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Q: suppose s(t) is the position of an object moving along a line at time t&gt;0. What is the average…

A: Given: The position of a moving object moving along a line is s(t) for time, t&gt;0.

Q: 4. Suppose that the population of a certain collection of rare Brazilian ants is given by P(t) = (t…

A: Recall: Rate of change of P(t) is dP(t)dt. d(tn)dt=n.tn-1 d(u.v)dt=u.dvdt+dudt.v

Q: 1) Let h(x)=x2−6x. (a) Find the average rate of change from 4 to 7. (b) Find an equation of the…

A: a Let , hx=x2-6x    we have to find average rate of change from 4 to 7     Now , at x=4 ,…

Q: Consider the following function. 1 f(x) = Find its average rate of change over the interval [4, 9].…

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Q: Consider the function E(x)=x2+6x-5. Compute the average rate of change of E(x) over the interval [a,…

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Q: 1. Determine the average rate of change of y in the function y = 2x³ + 7x² + 2x - 3 over the…

A: We can use the concept of calculus in order to solve the given problem.