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Question: Consider a rectangular corral with two partitions,

Consider a rectangular corral with two partitions, as in Fig. 15. Assign letters to the outside dimensions of the corral. Write an equation expressing the fact that the corral has a total area of 2500 square feet. Write an expression for the amount of fencing needed to construct the corral (including both partitions).
Consider a rectangular corral with two partitions, as in Fig. 15. Assign letters to the outside dimensions of the corral. Write an equation expressing the fact that the corral has a total area of 2500 square feet. Write an expression for the amount of fencing needed to construct the corral (including both partitions).





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Derivative of Linear Function If f(x) = mx + b, then we have f'(x) = m. (1)


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> A college student earns income by typing term papers on a computer, which she leases (along with a printer). The student charges $4 per page for her work, and she estimates that her monthly cost when typing x pages is C(x) = .10x + 75 dollars. (a) What

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> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. h(f (x))

> What is meant by “the value of a function at x”?

> What is a function?

> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f(1 / t)

> A specialty shop prints custom slogans and designs on T-shirts. The shop’s total cost at a daily sales level of x T-shirts is C(x) = 73 + 4x dollars. (a) At what sales level will the cost be $225? (b) If the sales level is at 40 T-shirts, how much will t

> Assign variables to the dimensions of the geometric object. y = f(x) f(a + h)): (a + h, f(a + h)) + + a + h a

> Assign variables to the dimensions of the geometric object. 1 f (x) = ² → s"(x)= - -3/2 7/1- = f'(x): When x = 1, f (x)= =1. The slope of the 1 tangent at x = 1 is ƒ'(1 = -÷(1)-*2 2 Thus, the equation of the tangent at (1,1) in point-slope form is y

> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x)g(x)

> Assign variables to the dimensions of the geometric object. f (x) = \x = xV? = f" (x) =² 1 f (x) = Vx = x2 = f" (x): -1/2 2Vx When x-. S(x)= = 1 ) = : 1 The slope of 3 9 1 the tangent at x =- is 1 1(1 -1/2 1 (9)'2 3 Thus, the 2 equation of the tange

> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. f (h(x))

> A store estimates that the total revenue (in dollars) from the sale of x bicycles per year is given by the function R(x) = 250x - .2x2. (a) Graph R(x) in the window [200, 500] by [42000, 75000]. (b) What sales level produces a revenue of $63,000? (c) Wha

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> The daily cost (in dollars) of producing x units of a certain product is given by the function C(x) = 225 + 36.5x - .9x2 + .01x3. (a) Graph C(x) in the window [0, 70] by [ -400, 2000]. (b) What is the cost of producing 50 units of goods? (c) Consider the

> A ball thrown straight up into the air has height -16x2 + 80x feet after x seconds. (a) Graph the function in the window [0, 6] by [ -30, 120]. (b) What is the height of the ball after 3 seconds? (c) At what times will the height be 64 feet? (d) At what

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. h(s) / f (s)

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. g(x + 5) / f (x + 5)

> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-32y-5)3/5

> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. h(g(x))

> Evaluate each of the functions in Exercises 37–42 at the given value of x. f (x) = |x|, x = -2.5

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = -x - 2; g(x) = -4x2 + x + 1; [-2, 2] by [-5, 2]

> A ball is thrown straight up into the air. The function h(t) gives the height of the ball (in feet) after t seconds. In Exercises 45–50, translate the task into both a statement involving the function and a statement involving the graph of the function.

> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = √(x + 2) - x + 2; [-2, 7] by [-2, 4]

> Refer to the profit function in Fig. 19. The point (1500, 42,500) is on the graph of the function. Restate this fact in terms of the function P(x). Derivative of Linear Function If f(x) = mx + b, then we have f'(x) = m. (1)

> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. g(h(x))

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> Calculate the compound amount from the given data. principal = $1500, compounded daily,1 year, annual rate = 6%

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> Decide which curves are graphs of functions. 8 7 6 3 2 1 2 3 4 5 6 7 8 4) 1.

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