Math Answers

A small business enterprise makes dresses and trousers. To make a dress

requires 1

2

hour of cutting and 20 minutes of stitching. To make a trouser

requires 15 minutes of cutting and 1

2

hours of stitching. The profit on a dress is

P40 and on a pair of trousers is P50. The business operates for a maximum of

8 hours per day. Determine how many dresses and trousers should be made to

maximize profit and what the maximum profit is.

Evaluate the following functions in differential operator form.

1. D2((x+1)2/x-1) Answer: 8/(x-1)³
2. D(ln(x²+2x+1) Answer: 2/x-1

Evaluate the following functions in differential operator form.

1. D(x²+2x-3) Ans. (2x+2)
2. D²(xe^3x-e^4x) Ans. 9xe^3x+6e^3x-16e^4x

1.Determine the nature of the stationary value of x= t^3 - 3t + ty^2

2. A rectangle box whose value is 32 is open at the top,if the surface area is 2(L+B)H + LB where LBH are Length,Breadth and Height Respectively

i.Find the Dimension of the box that may require list material

ii.investigate weather the dimension found requires List material.

use Euler’s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for each initial-value problem

8∑(j=1)2^j

∑j=08​(j8​)(j+1)(j+2)

10.             A continuous random variable X having values only between 0 and 4 has density function given by f (x) =  1/2 - ax ; where “a”

is constant. Calculate “a”. Find P(1 < X < 2) 

10. A continuous random variable X having values only between 0 and 4 has density function given by f (x) = 1/2 - ax ; where “a”

is constant. Calculate “a”. Find P(1<X<2)

∑ (2 𝑗+1 − 2 𝑗 ) 8 𝑗=0