Q5.  (i) Find the rate of change of the function f(x) = x + 2                                                                                               1 − 8xwith respect to x when x = 1. (ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3.

Q: 2. A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a…

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Q: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by P (…

A: The given function is Pt=0.009t2-0.7t+3.43. Compute the average rate of change of P ( t ) over the…

Q: 1. Use the Difference Quotient to find the instantaneous rate of change of 2. f(x) = -5x2 - x at x…

A: We have to find the instantaneous rate of change using difference quotient we have  f(x)=-5x2-xat…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: 2. Find the average rate of change of g (x) =x*-3x¯+2x from x=1 to x=3.

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Q: for #16

A: Average rate of change of a function f(x) over an interval [a, b] can be found using the formula…

Q: Suppose that the profit (In dollars) from the sale of Kisses and Kreams is given by P(x, y) = 15x +…

A: Sale of Kisses Kreams is given by P(x, y)=15x+6.5y-0.004x2-0.015y2 where, x is the number of pounds…

Q: 13. a) Determine the average rate of change over the interval x = [1, 5] of the function y = 3x + 1.…

A: To solve the following

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

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Q: Suppose that a companys sales volume, y (in thousands of units) is related to its auvertising…

A:

Q: If the marginal revenue (in dollars per unit) for a month is given by MR = 0.3x + 450, what is the…

A:

Q: 6. Suppose the radius of hemispherical container is 10 cm. It contains water and it is placed under…

A: Given query is to find the rate of change of area.

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

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Q: The rate of growth of the bacterial population is proportional to the number of bacteria present at…

A: Introduction: Differential Equation applications are useful in both the classroom and in real life.…

Q: 6) The marginal revenue from the sale of x units of certain commodity is given by R'(x) = 4x-1.2x…

A: Since, the marginal revenue from the sale of x units of certain commodityis given by…

Q: Suppose x and y are functions of third variable t. In the equation x2+y²=45, what are the values of…

A: This question is related to application of derivatives.

Q: A company is increasing the production of a product at the rate of 20 units per week. The demand and…

A: Given: Demand function is:  p=60-0.03x   Cost function is:  C(x)=4000+30x-0.04x2

Q: The rate of growth of profit (in millions) from an invention is approximated by P'(x) = x e -X,…

A:

Q: 3. A mixture is transferred into a cylindrical container through a conical filter. If the filter is…

A: The volume of a cone: V=13πr2h Where, r  is the radius of the cone. h is the vertical height of the…

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: Given that a company can produce 12,000 units when the number of hours of skilled labor y and…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: 4) Determine the instantaneous rate of change at x = 2 for f(x) = 2x2 + 4x

A: We have to find instantaneous rate of change

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Suppose total cost in dollar from the production of x printers is given byC(x) =…

Q: Supposed that the yearly rate of consumption of oil (in millions of barrels) is given by C'(t) =…

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Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

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Q: If the average rate of change of a function between x = a and x = b is negative, then is the…

A: The rate of change of function between two points of a curve represents the slope of the curve.   If…

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: The line with the rule y = 3x + 4 intersects the curve with equation ¦(x) = x2 at the points (-1, 1)…

A: Given:- The line with the rule y = 3x + 4 intersects the curve with equation f(x) = x2 at the points…

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given,  f(x)=x3+4x2-11x-30, x=1

Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

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Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

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Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60) where x…

A: Given that the monthly output is Qx=15,000+2x2 units, where x is the number of workers. Find Q'52.

Q: In Example 6 in this section, we were given fx) = 3x? + 2x + 11 and found rx) = 6x + 2. (a) Find the…

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Q: Suppose that the profit (in dollars) from the sale of Kisses and Kreams is given by P(x, y) = 10x +…

A: Px,y=10x+6.2y-0.008x2-0.02y2

Q: find the function that gives the value of the investment as a function of t. (Round your value of k…

A:

Q: 2. For a certain rectangle the length of one side is always three times the length of the other…

A: Let length of the rectangle be "x"       breadth of the rectangle be "y"     let "x" be the longer…

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

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Q: When the price of a certain commpdity is p dollars per unit, the manufacturer is willing to supply x…

A: Given  5p2 - 2x2 = 27 where p is the price of a certain commodity in dollars per unit x is the…

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A:

Q: 2. The instantaneous rate of change of g(x) is the same for every real value of x. What conclusion…

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Q: z = x2 + y2, where x and y are increasing at the constant rates of 2 units per second and 3 units…

A: