The productivity of a worker after t hours on the job can be modeled by the function, P(t) = 9t + 3t2 – t³. After how many hours will productivity be maximized? %3D

Q: The value of a timber forest after t years is V(t) = 434Vt - 31t (for 0 sts 50). Find when its value…

A: Given,  V(t)=434t-31t

Q: The average cost per hour in dollars of producing x riding lawn mowers is given by the following.…

A: We have to find - the number of riding lawn mowers to produce in order to minimize average cost,…

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function 1 x +…

A: To find the maximum revenue and items to be sold to obtain maximum revenue.

Q: The supply for a particular item is given by the function S(x) = 15 + 13x . Find the producer's…

A: Given, S(x)=15+13x           And the equilibrium price =$ 236

Q: The energy expended by a bird per day, E, depends on the time spent foraging for food per day, F…

A: To find the foraging time

Q: Consider the following. 1 y = 3 – 3x2 + 8x + 1 Find the relative maxima, relative minima, and points…

A:

Q: A case of vintage wine appreciates in value each year, but there is also an annual storage charge.…

A: Answer

Q: Find the maximum sustainable harvest of the given function. f(S) = 24S025, where S is measured in…

A: Consider the given function fS=24S0.25 , where S is measured in thousands Suppose HS be the harvest…

Q: At a certain vineyard it is found that each grape vine produces about 10 lbs of grapes in a season…

A: To find the number of vines that should be planted to maximize grape production.

Q: Estimate f(3.2)by using the following Data obtain from the f(x) = x? + 1by use Quadratic…

A: NDDP stands for Newtown Divided Difference Polynomial. The quadratic interpolation is the same as…

Q: Suppose the amount of a certain drug in the bloodstream is modeled by C(t)=8te-0.2t ,then the…

A:

Q: Investigate for maxima and minima the function $(x)=[{2(--1)(t–2) +(»-1°(r-2)"}at |

A:

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02g? + 3q – 22, where q…

A:

Q: For Exercise, identify the location and value of any relative maxima or minima of the function. 2 y…

A: A relative maximum is a point where a curve goes from increasing to decreasing.  A relative minimum…

Q: Consider the following. P = -0.1s3 + 6s2 + 400 Find the amount s of advertising (in thousands of…

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Q: What values of a and b maximize the value of ! (7x-x) dx? a

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Q: The cube root parent function y = Vx has been transformed a) 2.

A: given graph

Q: Estimate f(3.2)by using the following Data obtain from the f(x) = x? + 1by use Quadratic…

A: First we see a formulaFormula:Newtons divide difference interpolation formulafx=fx0+x-x0 f…

Q: Antonio has $5.00 to spend on a lunch consisting of hamburgers($1.50 each) and french fries ($1.00…

A: Antonio has $5.00 to spend on a lunch consisting of hamburgers ($1.50 each) and french fries ($1.00…

Q: Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist,…

A: Given function, y=Fx=13x3-x2-3x+8 Used formulas, ddxxn=nxn-1ddxConstant=0ddxKf(x)=Kddxfx…

Q: Consider the following total revenue function for a hammer. R = 20x – 0.01x² (a) The sale of how…

A: The revenue function of the hammer is R = 20x-0.01x2.

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Q: For the function y= -1+6cos what is the maximum value? Answer here

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Q: Consider the following total revenue function for a hammer. R = 24x – 0.01x2 (a) The sale of how…

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Q: Suppose that the selling price pp of an item for the quantity xx sold is given by the function…

A:

Q: Consider the following. P = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

A:

Q: Find the points on the graph of the function f that are closest to the point (a, b) by minimizing…

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Q: If a baseball is projected upward from ground level with an initial velocity of 32 feet per​…

A: When we throw a ball upwards, that ball goes and goes up, at a certain level of height, the thing is…

Q: A particie moves along the X-axis so that at time t > 0 its position is given by x(t)= 2t3 +…

A: Given that xt=2t3+3t2-36t+50t≥0To find the total distance in the interval 0≤t≤5

Q: | (1 – a*)dæ (1 — а?) а

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Q: Suppose that a company's daily sales volume attributed to an advertising campaign is given by 56…

A: Given the sales volumes S(t)=8t+7-56t+72+6 the sales volume will be maximized when S'(t)=0…

Q: Consider the following total revenue function for a hammer. R = 36x – 0.01x² (a) The sale of how…

A:

Q: The total-cost, C(x), and total-revenue, R(x), functions for producing x items are shown below,…

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Q: A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by cutting…

A: Given:- A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by…

Q: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a…

A: Given model of the equation is simplified by expanding the brackets:

Q: The value of a timber forest after t years is V(t) = 444 t - 37t (for 0 sts 50). Find when its value…

A:

Q: If a projectile is fired straight upward from the ground with an initial speed of 128 feet per​…

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Q: Consider the following total revenue function for a hammer. R = 48x – 0.01lx² (a) The sale of how…

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Q: Find the relative maxima and relative minima, if a does not exist, enter DNE.) f(x) = 3x - 10x³ + 10…

A:

Q: Consider the following total revenue function for a hammer. R = 60x − 0.01x2 (a) The sale of how…

A: a) Consider the given revenue function:

Q: For some positive constant , a patient's temperature change, T , due to a dose, D , of a drug is…

A: Given: For some positive constant c and D=Drug Dose  T=Patient's temperature change T=C2-D3D2

Q: A printed poster is to have a total area of 567 square inches with top and bottom margins of 6…

A: Given: In the printed poster is to have a Total area = 567 square inches  The top and bottom margins…

Q: Consider the following total revenue function for a hammer. R = 28x − 0.01x2 (a) The sale of how…

A: The given revenue function is Rx=28x-0.01x2. (a) It is known that the maximum value occurs at the…

Q: Consider the following total revenue function for a hammer. R = 44x – 0.01x²2 (a) The sale of how…

A: We have given the total revenue function for a hammer.              R = 44x - 0.01x2  We have to…

Q: The number of mosquitos, M(x), in millions, in a certain area of Florida depends on the June…

A:

Q: Consider the following total revenue function for a hammer. R = 36x – 0.01x² %3! (a) The sale of how…

A: Given Data: The total revenue function is: R=36x-0.01x2 (a) At maximum revenue, the derivative of…

Q: Consider the following total revenue function for a hammer. R = 20x - 0.01x2 (a) The sale of how…

A:

Q: Consider the following total revenue function for a hammer. R = 32x – 0.01x² (a) The sale of how…

A: a) R= 32x-0.01x^2 Differentiate with respect to x dR/dx = 32 -0.02x dR/dx=0 => x= 1600

Q: An inferior product with a large advertising budget sells well when it is introduced, but sales fall…

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Q: A time study showed that, on average, the productivity of a worker after t hours on the job can be…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.