Math Answers

For which values of A , B , C and k is the function yp(x) = x 2 (A x2 + B x + C) a particular solution of the equation 16 y 000 + 9 y 00 = 1458 x k−1 (2x − 1) ? (a) A = 27 , B = 165 , C = −880 , k = 2 (b) A = 27 , B = −219 , C = 1168 , k = 2 (c) A = 27 , B = −219 , C = 1168 , k = 4 (d) A = 54 , B = −411 , C = 2192 , k = 3 (e) A = 54 , B = −411 , C = 2192 , k = 4 

Which of the following is the solution of the initial value problem y (5) + 4y (4) + 4y (3) = 0 , y(0)= 0 , y0 (0)= − 1 2 , y(2)(0)= 5 , y(3)(0)=−14 , y (4)(0)= 36 ? (a) y = −1 − t 4 + t 2 2 + e −2t (b) y = 1 4 − t + t 2 4 − 1 4 e −2t − te−2t (c) y = − 1 4 + t + 1 4 e −2t − te−2t (d) y = −1 + t 2 − t 2 4 + (1 + t 2 )e 2t (e) y = 1 2 + t − 1 2 e 2t + t 2 e 2t

Which of the following is the appropriate form for a particular solution of the differential equation y (4) + 3y 00 − 4y = 2x + cos2 x − cosh x ? (a) yp = (A + Bx)e x + (C + Dx) cos(2x) + (E + F x) sin(2x) (b) yp = (Ax + B)e −x + (C + Dx) cos(−x) + (E + F x) sin(−x) (c) yp = Ax + Bx2 + (C + Dx) cos x + (E + F x) sin(−x) + Ge2x (d) yp = Ax + Bx2 + (C + Dx) cos(2x) + (E + F x) sin(−2x) + Ge−x (e) yp = A + Bx + Cx sin(−2x) + Dx cos(2x) + Exex + F xe−x

A rectangular billboard 6 feet in height stands in a field so that its bottom is 13 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x

x

 feet from the billboard. Express θ

θ

, the vertical angle subtended by the billboard at her eye, in terms of x

x

. Then find the distance x

x

 the cow must stand from the billboard to maximize θ

θ

.

Find the derivatives of all orders of the functions in Exercises 29 - 32 . 29. y = (x ^ 4)/2 - 3/2 * x ^ 2 - x 30. y = (x ^ 5)/120 30. y = (x - 1)(x + 2) * (x + 3) 32. y = (4x ^ 2 + 3)(2 - x) * x

A bus arrives every 10 minutes at a bus stop. It

is assumed that the waiting time for a particular individual is a random variable with a continuous uniform

distribution.(a) What is the probability that the individual waits

more than 7 minutes?

(b) What is the probability that the individual waits

between 2 and 7 minutes?

Describe how you will make the transition from the real life context above to the algorithm of subtraction of fractions.

Three misconceptions that learners might have about the subtraction of fractions

Formulate three questions to establish learners prior under of fraction concepts that will be needed when they do subtraction of fractions.Focus specifically on their understanding of the lowest common denominator between fractions.

At 1% level of significance, can he conclude that the mean daily expenses of the sales staffs are greater than the audit staffs. State the null and alternative hypothesis