At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 700 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by A(n) = (700 + n)(10 − 0.01n) where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.

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Q: B1(b): Solve the initial value problem : f'(x) = x° + 12x + 13 and f(0) = 3.

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Q: Solve for g'(x).

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Q: 3.) The revenue for a company producing widgets is given by y =- 25x widget. The cost for the…

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A: Given DE is  tx'-3x=t3+2t .......(1) We find the general solution of (1).

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Q: 2x - 10 K x+ 1

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Q: If f(x) = 2x3 + Ax2 + 4x - 5 and f(2) = 5, what is thevalue of A ?

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Q: 8) A soft-drink vendor at a popular beach analyzes his sale records and finds that if he sells x…

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Q: Find the consumer's and producer's surplus if for a product D(x) = 43 – 5x and S(x) 20 + 2x . Round…

A: Topic:- consumer and product surplus

Q: The constant term of f(x)=x2+4x3+1 is 1. How can you say that 1 is the constant term?

A: fx=x2+4x3+1

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Q: 2. How many, and what type, of solutions exist for the function f(x) = x - 3x- 27x + 19x² +114x-72?

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Q: 2. For what values of x is y = 150x - 2x3 an increasing function?

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 160 and a revenue function R(x) = 6x.…

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Q: A company involved in the export of trucks has estimated that the profit (U) in millions of dollars…

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Q: x°-x°+4x* -6x°+2n²- 8x t8=0 Solue for x,

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A: Given  Demand function is Dx=25-0.009x2 and supply function is Sx=0.007x2

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Q: f(x)=43^2x+4x^4−44x3−864+72x^2 What is the end behaivoir of this?

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Q: Find the number of units x that produces a maximum revenue R in the given equation. R = 108x2/3 −…

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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.