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Questions and Answers of College Mathematics For Business

Rationalize the denominators in Problem. 2(х + 3) Vх - 2
In Problem factor completely. If a polynomial cannot be factored, say so.y4 - 3y2 - 4
In Problem factor completely. If a polynomial cannot be factored, say so.15y(x - y)3 + 12x(x - y)2
Rationalize the denominators in Problem. 3 (х + 1) Vx + 4
You have $10,000 to invest, part at 9% and the rest at 12%. If x is the amount invested at 9%, write an algebraic expression that represents the total annual income from both investments. Simplify
Rationalize the denominators in Problem. 7(x - y)? Vx - Vy
Rationalize the numerators in Problem. V5xy 5x²y? ,2
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If m and n are positive integers and m ≠ n, then um - vn is not factorable.
Rationalize the numerators in Problem. V3mn Зтп
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If n is a positive integer greater than 1, then un + vn can be factored.
Rationalize the numerators in Problem. Vi - Vĩ 2 - x?
Rationalize the numerators in Problem. Vx + h - V
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.If k is a positive integer, then u2k + 1 + v2k + 1 can be factored.
Food mix A contains 2% fat, and food mix B contains 6% fat. A 10-kilogram diet mix of foods A and B is formed. If x kilograms of food A are used, write an algebraic expression that represents the
Rationalize the numerators in Problem. V - Vy Vĩ + Vy X.
In Problem express the given standard:(A) In scientific notation(B) In standard decimal notation(C) As a percent9 ppm, the standard for carbon monoxide, when averaged over a period of 8 hours
Problem illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side. 1 (x + y)3 + (x + y)3
In 2015, the United States had a violent crime rate of 373 per 100,000 people and a population of 320 million people. How many violent crimes occurred that year? Compute the answer using scientific
The United States had a 2016 population of 323 million people and a land area of 3,539,000 square miles. What was the population density? Compute the answer using scientific notation and convert the
Problem illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side.(x + y)1/2 ≠ x1/2 + y1/2
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counter example. The fourth roots of 100 are V10 and -V10
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counter example.If r < 0, then r has no cube roots.
In Problem simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. (x- 2) (x + 3)3/2 + (x + 3)-/2 1.
In Problem simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. 2(x-2) -/2 -극(2r (2x + 3) (x 2)-3/2
In Problem simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. (x – 1)/2 – x(}) (x – 1)-1/2 X - 1
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counter example.If r > 0, then r has three cube roots.
In Problem evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)223/2
In Problem evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)155/4
In Problem evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)103-3/4
In Problem evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)37.097/3
In Problem evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)2.8768/5
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. (a) fe (A) (4x + 6y + 5) dx (B) (4x + 6y + 5) dx
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. (A) / 3ye*+* dr 3y²e*+Y°dx (B)
In Problem find the least squares line and use it to estimate y for the indicated value of x. Round answers to two decimal places.Estimate y when x = 25. y 10 5 22 10 31 15 46 20 51
Evaluate each integral in Problem. Vy SoS (2x + y) dx dy
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. In x In x (В) (A) xp- ху ху
For f(x, y) = (x2 + y2)5, find fx and fxy.
In Problem find the indicated values of the functionsg(1, 7) 88 f(x, y) = 2x + 7y – 5 and 8(x, y) x + 3y
Use the method of Lagrange multipliers in Problem.Find the maximum and minimum of f(x, y) = 2xy subject tox2 + y2 = 18.
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. In x dy xy In x dy xy (A) (B)
In Problem find the least squares line and use it to estimate y for the indicated value of x. Round answers to two decimal places.Estimate y when x = 2.5. y 1 3 1. 2. 2. 2. 3.
For f(x, y) = ex2 + 2y, find fx, fy, and fxy.
Let f(a, b) be a local extremum (a local maximum or a local minimum) for the function f. If both fx and fy exist at (a, b), thenfx(a, b) = 0 and fy(a, b) = 0In Problem find fx(x, y) and fy(x, y), and
Evaluate each integral in Problem. S.S (x + y) dy dx
For R = {(x, y) | √y ≤ x ≤ 1, 0 ≤ y ≤ 1}, evaluate (6x + y) dA R
For R = {(x, y) | - 1 ≤ x ≤ 1, 1 ≤ y ≤ 2}, evaluate the following in two ways: (4х + бу) dA R
In Problem find the indicated values of the functionsf(8, 0) 88 f(x, y) = 2x + 7y – 5 and 8(x, y) x + 3y
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. (A) (B) dx Vy + x Vy + x2
Use the least squares line for the data in the following table to estimate y when x = 10. y 2 12 4 10 6. 7 8 3.
In Problem find the least squares line. Graph the data and the least squares line. y 1 3 4 4 6 2. 3.
Let f(a, b) be a local extremum (a local maximum or a local minimum) for the function f. If both fx and fy exist at (a, b), thenfx(a, b) = 0 and fy(a, b) = 0In Problem find fx(x, y) and fy(x, y), and
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. (A) (4 (4х + бу + 5) dy (4х + бу + 5) dy (В)
In Problem find the indicated values of the functionsf(4, -1) 88 f(x, y) = 2x + 7y – 5 and 8(x, y) x + 3y
Use the method of Lagrange multipliers in Problem.Minimize f(x, y) = x2 + y2subject to 3x + 4y = 25
If f(x, y) = x + 3y and g(x, y) = x2 + y2 - 10, find the critical points of F(x, y, λ) = f(x, y) + λg(x, y).
Let f(a, b) be a local extremum (a local maximum or a local minimum) for the function f. If both fx and fy exist at (a, b), thenfx(a, b) = 0 and fy(a, b) = 0In Problem find fx(x, y) and fy(x, y), and
In Problem find the least squares line. Graph the data and the least squares line. y 1 4. 2. 3. 4,
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. (A) 12ry dx 12ry dx (B)
In Problem find the least squares line. Graph the data and the least squares line. y 1 1 3 4 4 3. 3. 2.
For f(x, y) = -4x2 + 4xy - 3y2 + 4x + 10y + 81, find [fxx(2, 3)] [fyy(2, 3)] - [fxy(2, 3)]2.
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = (3x + 1)2
In Problem find each antiderivative. Then use the antiderivative to evaluate the definite integral. | 12ry" dy (A) (B) 12x?y dy
For f(x, y) = 3x2 - 2xy + y2 - 2x + 3y - 7, find f(2, 3) fy(x, y), and fy(2, 3).
In Problem evaluate each iterated integral. (x - y) dydx
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = x3 - x2 + x - 1
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums. k=1 3D1
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Minimize f(x, y) = 10x
In Problem find each antiderivative. In x TTX
For f(x, y) = 6 + 5x - 2y + 3x2 + x3, find fx(x, y), and fy(x, y), and explain why f(x, y) has no local extrema.
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums. k=1 k=1
In Problem evaluate each iterated integral. (x + y) dy dx 0.
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = ex2
In Problem find each antiderivative. ex dx
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Maximize f(x, y) = 2x
Evaluate ∫10 ∫10 4xy dy dx.
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = e-x2
In Problem evaluate each iterated integral. ydxdy -2
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums.
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0. 1 f(x) 1 + x?
In Problem find each antiderivative. (1+ dx TT
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Maximize f(x, y) =
Evaluate ∫(6xy2 + 4y) dx.
In Problem evaluate each iterated integral. x dx dy -2
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums. k=1
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0. 1 f(x) 1 – x?
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Minimize f(x, y) =
In Problem find each antiderivative. (1 + dx
Evaluate ∫(6xy2 + 4y) dy.
In Problem evaluate each iterated integral. 2dx dy
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums. 5 Yk k=1
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Maximize f(x, y) = 64
In Problem evaluate each iterated integral. 4dydx
In Problem find each antiderivative. | (x7? + Tx²) dx
For z = x3y2, find ∂2z/∂x2 and ∂2z/∂x ∂y.
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = 4x3 + 6x2 + 100
Problem refer to the n = 5 data points (x1, y1) = (0, 4), (x2, y2) = (1, 5), (x3, y3) = (2, 7), (x4, y4) = (3, 9), and (x5, y5) = (4, 13). Calculate the indicated sum or product of sums. Σ k=1
In Problem maximize or minimize subject to the constraint without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x, y).Minimize f(x, y) = x2
In Problem find each antiderivative. T + x) dx
For f(x, y) = 2,000 + 40x + 70y, find f(5, 10), fx(x, y), and fy(x, y).
In Problem find f′(0), f″(0), and determine whether f has a local minimum, local maximum, or neither at x = 0.f(x) = 2x3 - 9x2 + 4

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