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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.m2 = 14m
Using the variable x, write each interval as an inequality. 0 8 00
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.y2 – 4yz – 21z2
Write each rational expression in lowest terms.(6y2 + 11y + 4)/(3y2 + 7y + 4)
Perform the indicated operations.(6m + 5)(6m – 5)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.2k2 –
Using the variable x, write each interval as an inequality. -4 0 4
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.3x2 + 4x – 7
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.12x2 –
Using the variable x, write each interval as an inequality. 0 3
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.3a2 + 10a + 7
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.m(m –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.15y2 + y – 2
Perform the indicated operations.(3p – 1) (9p2 + 3p + 1)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.4x2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.21m2 + 13mn + 2n2
Solve each inequality and graph the solution.6k – 4 < 3k – 1
Perform the indicated operations.(3p + 2) (5p2 + p – 4)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.z(2z +
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.6a2 – 48a – 120
Solve each inequality and graph the solution.m – (3m – 2) + 6 < 7m – 19
Perform the indicated operations.(2m + 1)(4m2 – 2m + 1)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.12y2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.3m3 + 12m2 + 9m
Solve each inequality and graph the solution.–2(3y – 8) ≥ 5(4y – 2)
Perform the indicated operations.(k + 2)(12k3 – 3k2 + k + 1)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.3x2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.4a2 + 10a + 6
Perform the indicated operations.(x + y + z)(3x – 2y – z)
Solve each inequality and graph the solution.3p – 1 < 6p + 2(p – 1)
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.2m2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.24a4 + 10a3b – 4a2b2
Perform the indicated operations.(r + 2s – 3t)(2r – 2s + t)
Solve each inequality and graph the solution.x + 5(x + 1) > 4(2 – x) + x
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.p2 + p
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.24x4 + 36x3y – 60x2y2
Perform the indicated operations.(x + 1)(x + 2)(x + 3)
Solve each inequality and graph the solution.–11 < y – 7 < –1
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.k2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.x2 – 64
Perform the indicated operations.(x – 1)(x + 2)(x – 3)
Solve each inequality and graph the solution.8 ≤ 3r + 1 ≤ 13
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.5x2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.9m2 – 25
Perform the indicated operations.(x + 2)2
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.2r2 –
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.10x2 – 160
Perform the indicated operations.(2a – 4b)2
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.9x2 + 64
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.2x2 –
Perform the indicated operations.(x – 2y)3
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.z2 + 14zy + 49y2
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.3k2 + k
Perform the indicated operations.(3x + y)3
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.s2 – 10st + 25t2
Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.5m2 + 5m
Solve each quadratic inequality. Graph each solution.(m – 3)(m + 5) < 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.9p2 – 24p + 16
Solve each quadratic inequality. Graph each solution.(t + 6)(t – 1) ≥ 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.a3 – 216
Solve each quadratic inequality. Graph each solution.y2 – 3y + 2 < 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.27r3 – 64s3
Solve each quadratic inequality. Graph each solution.2k2 + 7k – 4 > 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.3m3 + 375
Solve each quadratic inequality. Graph each solution.x2 – 16 > 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.x4 – y4
Solve each quadratic inequality. Graph each solution.2k2 – 7k – 15 ≤ 0
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.16a4 – 81b4
Solve each quadratic inequality. Graph each solution.x2 – 4x ≥ 5
Solve each quadratic inequality. Graph each solution.10r2 + r ≤ 2
Solve each quadratic inequality. Graph each solution.3x2 + 2x > 1
Solve each quadratic inequality. Graph each solution.3a2 + a > 10
Solve each quadratic inequality. Graph each solution.9 – x2 ≤ 0
Solve each quadratic inequality. Graph each solution.p2 – 16p > 0
Solve each quadratic inequality. Graph each solution.x3 – 4x ≥ 0
Solve each quadratic inequality. Graph each solution.x3 + 7x2 + 12x ≤ 0
Solve each quadratic inequality. Graph each solution.2x3 – 14x2 + 12x < 0
Solve each quadratic inequality. Graph each solution.3x3 – 9x2 – 12x > 0
Solve each inequality.(m – 3)/(m + 5) ≤ 0
Solve each inequality.(k – 1)/(k + 2) > 1
Solve each inequality.(a – 5)/(a + 2) < –1
Solve each inequality.(2y + 3)/(y – 5) ≤ 1
Solve each inequality.(a + 2)/(3 + 2a) ≤ 5
A manufacturer is planning to sell a new product at the price of $350 per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, consumers
A study conducted at a waste disposal site reveals soil contamination over a region that may be described roughly as the interior of the ellipsewhere x and y are in miles. The manager of the site
Exercises 36 through 39 require the extreme value property.In this exercise, you are asked to re-examine Exercise 29 as an optimization problem over a closed, bounded region.a. In Exercise 29,
Exercises 36 through 39 require the extreme value property.In this exercise, you are asked to re-examine Example 7.3.4 as an optimization problem over a closed, bounded region.a. In Example 7.3.4,
In Exercises 29 through 35, assume that the required extreme value is a relative extremum.A manufacturer is planning to sell a new product at the price of $210 per unit and estimates that if x
Exercises 36 through 39 require the extreme value property.McKinley Martin is the business manager of an electronics store. He determines that when he charges x dollars per unit for the standard
Exercises 36 through 39 require the extreme value property.Carmen Ramos, a colleague of the salesman in Example 7.3.7, has a territory that can be described in terms of a rectangular grid as the
In Exercises 25 through 36, evaluate the given double integral for the specified region R.where R is the region in the first quadrant bounded by y = x3 and y = x. R 12x²e³²³ dA, ܒܐ
Recall from Exercise 47 of Section 7.1 that an empirical formula for the surface area of a person’s body is S(W, H) = 0.0072W0.425 H0.725 where W (kg) is the person’s weight and H(cm) is his or
In Exercises 37 and 38, you will need to know that a closed cylinder of radius R and length L has volume V = πR2L and surface area S = 2πRL + 2πR2. The volume of a hemisphere of radius R is V =
In Exercises 25 through 36, evaluate the given double integral for the specified region R.where R is the region bounded by y = ln x, y = 0, and x = e. SSx R y dA,
There are F hundred foxes and R hundred rabbits on a large island. An ecologist determines that the populations F and R are related by the formulaWhat is the largest total number F + R of foxes and
In Exercises 37 through 44, sketch the region of integration for the given integral and set up an equivalent integral with the order of integration reversed. C.S. (4-x2² lo Jo f(x, y) dy dx
At a certain factory, the marginal cost is 6(q − 5)2 dollars per unit when the level of production is q units. By how much will the total manufacturing cost increase if the level of production is
At a certain factory, the daily output is approximately 40K1/3L1/2 units, where K denotes the capital investment measured in units of $1,000 and L denotes the size of the labor force measured in
A manufacturer receives N units of a certain raw material that are initially placed in storage and then withdrawn and used at a constant rate until the supply is exhausted 1 year later. Suppose
In Exercises 17 through 24, find all critical points of the given function and use the second partials test to classify each as a relative maximum, a relative minimum, or a saddle point.f(x, y) = x2

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