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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find the roots of the given equation by inspection.x(2x + 5)2 (x2 − 64) = 0
Determine each of the following as being either true or false. If it is false, explain why.Without solving, it can be determined that there is no more than one possible negative root of the equation
Use the factor theorem and synthetic division to determine whether or not 2x + 1 is a factor of 2x4 + 15x3 + 23x2 − 16.
Solve the given equation without using a calculator.2x3 + 5x2 − x + 6 = 0
Find the roots of the given equation by inspection.(x − 5)(x2 + 9)
Find the remainder of the indicated division by the remainder theorem.(2x3 − 4x2 − x + 7) ÷ (x − 1)
Use the remainder theorem to find the remainder of the division (x3 + 4x2 + 7x − 9) ÷ (x + 4).
Find the remainder by long division.(x3 + 2x − 8) ÷ (x − 2)
Solve the given equation without using a calculator.x3 + 2x2 − 5x − 6 = 0
Find the roots of the given equation by inspection.(4y2 + 9)(25y2 − 10y + 1) = 0
Find the remainder of the indicated division by the remainder theorem.(x3 − 2x2 + 9) ÷ (x + 2)
Find the remainder by long division.(x4 − 4x3 − x2 + x − 100) ÷ (x + 3)
Solve for x: 2x4 − x3 + 5x2 − 4x − 12 = 0.
Solve the given equation without using a calculator.t3 − 12t − 16 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.x³ − 5x² + 2x + 8 = 0 (r1 = 2)
Find the remainder of the indicated division by the remainder theorem.(3n3 + n + 4) ÷ (n + 3)
Find the remainder by long division.(2x5 − x2 + 8x + 44) ÷ (x + 1)
The ends of a 10-ft beam are supported at different levels. The deflection y of the beam is given by y = kx2 (x3 + 436x − 4000), where x is the horizontal distance from one end and k is a constant.
Solve the given equation without using a calculator.3x4 − x2 − 2x = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.R³ + 1 = 0 (r1 = − 1)
Find the remainder of the indicated division by the remainder theorem.(x4 − 5x3 + 8x2 + 15x − 2) ÷ (x − 3)
Find the remainder by long division.(4s3 − 9s2 − 24s − 17) ÷ (s − 5)
Solve the given equation without using a calculator.21t3 + 56t2 − 7 = 0
A cubical metal block is heated such that its edge increases by 1.0 mm and its volume is doubled. Find the edge of the cube to the nearest tenth. Solve graphically using a calculator.
Find the remaining roots of the given equations using synthetic division, given the roots indicated.2x3 + 11x² + 20x + 12 = 0 (r1 = −3/2)
Use the factor theorem to determine whether or not the second expression is a factor of the first.x4 + x3 + x2 − 2x − 3; x + 1
Find the remainder by long division.(2x4 − 3x3 − 2x2 − 15x − 16) ÷ (2x − 3)
Solve the given equation without using a calculator.2x3 − 3x2 − 3x + 2 = 0
In Example 3, change the −4 in the top equation to −2 and then solve the system of equations.Data from Example 3Use matrices to solve the system of equationsSetting up matrices A, C, and X, we
Find the remaining roots of the given equation using synthetic division, given the roots indicated.4x³ + 6x² − 2x − 1 = 0 (r1 = 1/2)
Use the factor theorem to determine whether or not the second expression is a factor of the first.2s3 − 6s − 4; s − 2
In Example 3(a), change the 2 in the first row to a 3 and then find the determinant.Data from Example 3(a) 2 18 0 -5 9 0 0-6 = 2(-5)(-6)= 60 property 1
Find the remainder by long division.(2x4 − 11x2 − 15x − 17) ÷ (2x + 1)
In Example 6, find the matrix −2A.Data from Example 6For the matrix A, whereBy combining the definitions for the addition of matrices and for the scalar multiplication of a matrix, we can define
Perform the indicated multiplication. 12 -47 43 -18 36 -22 12 -1 1
Solve the given equations without using a calculator.4x3 − 16x2 + 21x − 9 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.5x3 − 2x² + 5x − 2 = 0 (r1 = j)
For matrix C of Problem 3, find C−1.Data from Problem 3 C = 10 04 2 -2 1 -1 32 D = 2-2 4-5 6 1
Use the factor theorem to determine whether or not the second expression is a factor of the first.2t4 − 10t3 − t2 − 3t + 10; t + 5
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 9x - 3y + 6z = 9 4x - 2y + z = 3 6x + 6y + 3z = 4
Find the remainder using the remainder theorem. Do not use synthetic division.(R4 + R3 − 9R2 + 3) ÷ (R − 3)
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal
Use the given value of the determinant at the right and the properties of this section to evaluate the following determinants. 2-3 1 1 -3 -4 1 3 -2 40
Perform the indicated multiplication. [54 4 -5 -4 5
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. X x + y || 20 4 -3
Determine the values of the literal numbers. sin x + y x - y COS TT x y a b
Solve the system of equations in Problem 6 by Gaussian elimination.Data from Problem 62z − 3y = 11x + 2y = 2
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Solve the given systems of equations by using the inverse of the coefficient matrix.x + 2y = 33x + 4y = 11
Fifty shares of stock A and 30 shares of stock B cost $2600. Thirty shares of stock A and 40 shares of stock B cost $2000. What is the price per share of each stock? Solve by setting up the
Use a graphing calculator to perform the indicated multiplications. | ² 2-3 8-1 3 7 -5 نیا 0-1 6
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. w + 2xy + 3z = 12 2w2yz = 3 3x y z = -1 -w + 2x + y + 2z = 3
Evaluate the given determinants by expansion by minors. 224 2 -2 00 14 4-2 3
Find the indicated sums of matrices. 6 3 -5 -4 + - 1 7 5-2
Use a graphing calculator to perform the indicated multiplications. -7 8 50 -90 100 10 40
Solve the given systems of equations by using the inverse of the coefficient matrix.2.5x + 2.8y = −3.03.5x − 1.6y= 9.6
Determine the values of the literal numbers. Ine log100 b² a² 2 1-[ a+b a-b X y
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 3x - 2y = 5x + y = -11 1 2x + 3y = 10 x - 5y = -21
Evaluate the given determinants by expansion by minors. 10 0 -3 -2 -4 30 1 2
Find the indicated sums of matrices. | []+[ 109 3-5-2 4 -1 20-3 7
Solve the given systems of equations by using the inverse of the coefficient matrix.24x − 10y = −800 31x + 25y = 180
Use the given matrices and perform the indicated operations.A + B A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Evaluate the given determinants by expansion by minors. 31 0 -2 3-1 4 2 5
Find the indicated sums of matrices. 50 -34 -15 -82 57 62 + -55 30 26 82 14 -70
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Use a graphing calculator to perform the indicated multiplications. -7.1 2.3 0.5 -3.8 -2.4 4.9 6.5 -5.2 4.9 1.7 -1.8 6.9
Use the given matrices and perform the indicated operations.2C A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Use a graphing calculator to perform the indicated multiplications. 1 2 -6 0 -24 -6 -6 1 12 1 - 1 0 -5 2
Solve the given systems of equations by using the inverse of the coefficient matrix. x + 2y + 2z = −44x + 9y + 10z = −18−x + 3y + 7z = −7
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Evaluate the given determinants by expansion by minors. 30 -20 -40 -8 8 16 -15 75 -45
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.x – 4y + z = 52x – y + 3z = 4
Use the given matrices and perform the indicated operations.B − A A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Solve the given systems of equations by using the inverse of the coefficient matrix. x − 4y − 2z = −7−x + 5y + 5z = 183x − 7y + 10z = 38
Find the indicated sums of matrices. 4.7 2.1 -6.8 4.8 -1.9 0.7 9.6 7.4 5.9 + -4.9 -9.6 -2.1 3.4 0.7 0.0 5.6 10.1 -1.6
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.4x + z = 62x – y – 2z = – 2
Find, if possible, AB and BA. If it is not possible, explain why. A = [138] B = 5 7
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 2x = y + z = 5 3x + 2y 2z = 4 5x + 8y8z = 5
Evaluate the given determinants by expansion by minors. 4 360 3004 5012 2117
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.A + B A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Find, if possible, AB and BA. If it is not possible, explain why. A -3 20 1-4 5 B = -2 0 4-6 5 -1
Solve the given systems of equations by using the inverse of the coefficient matrix.2x + 4y + z = 5−2x - 2y − z = −6 −x + 2y + z = 0
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 3u + 6v+2w = -2 u +3v 4w = 2 2u3v2w = -2
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Use the given matrices and perform the indicated operations.2A − B A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Use the given matrices and perform the indicated operations.2A − 3B A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Find, if possible, AB and BA. If it is not possible, explain why. A -10 25 40 42 -5 0 1 B = = 6 -15 12
Evaluate the given determinants by expansion by minors. 6 -3 -2 1 18 7 -6 3 2 -1 5 10 -1 -1 0-1 10
Solve the given systems of equations by using the inverse of the coefficient matrix.4x + y = 2−2x − y + 3z = −182x + y − z = 8
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.A + C A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. x + 3y + z = 4 2x 6y3z = 10 - 4x9y+ 3z = 4
Use the given matrices and perform the indicated operations.2(A − B) A= 2-3 4 1 -5 0 2-3 B = - 1 0 4-6 -2 -7 -3 1 с 5-6 2 8 0-2
Evaluate the given determinants by expansion by minors. 530 42 1 3 2-2 0 1 2 -1 522 2
Find, if possible, AB and BA. If it is not possible, explain why. A = || -2 17 0 3 -1 02 2-1 B = [4 -15]
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 30x + 20y - 10z - 10z = 30 4x - 2y 6z = 4 -5x + 20y - 25z = -5

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