Math Answers

<e> Congratulations! You are hired in a business organization. In this company the market research department that you are the member recommended to manufacture and market a promising new product (x). After extensive surveys, the research department supported the recommendation with the demand function:

Dx = f (p) = 60 – 3 P

Where Dx is quantity demanded at price P during a month. Financial department has brought the cost function and is given by

C(x) = 72 + 6x

Now the team leader of the market research department ordered you to manipulate the following problems.

Express revenue as a function of X

Expresses profit as a function of X

<e> Solve the first order linear inhomogeneous differential equation using the bernoulli method

(2x+1)y^,=4x+2y

<e> Gerry needs a loan of 8000 € for his holiday trip. The loan period is 1 year and the payments are made quarterly. The loan has fixed principal payment and the interest rate is 3.8 % p.a. How much money Gerry needs for the third payment?

<e> Evaluate the integral ∮c= 1 /(z-1)(z-2)(z-4) dz where C is |z| = 3 ?

<e> Show that if P and Q are vector Subspaces of a vector space V then P ∩ Q is also a vector subspace of V.

<e> Solve using the method of separation of variables the pde partial du/dt+du/dx+2e^tu=0

<e> A vending treasury is purchased for RM 2,800 in cash with RM 700 down payment and fourteen monthly payments. If the interest calculated is 10% per annum, using the fixed rate equation calculation find:

1. Total interest charged

2.Secondly. monthly payment

<e> Let f

f be a function such that at each point (x,y)

(x,y) on the graph of f

f, the slope is given by dy

dx

=1

2

x−1

4

y

2

dydx=12x−14y2. The graph of f

f passes through the point (1,−2)

(1,−2) and is concave up on the interval 1<x<1.5

1<x<1.5. Let k

k be the approximation for f(1.3)

f(1.3) found by using the locally linear approximation of f

f at x=1

x=1. Which of the following statements about k

k is true?

<e> Examine the f:R->R defined by

f(x)={1/6(x+1)^3 x is not equal to 0

5/6 x=0}

for continuity on R .If it is not continuous at any of R find the nature of discontinuity there

<e> m is a straight line with a 1 on the right side.

n is a straight line with a number 3 & 2 in the middle but there’s a diagonal line that goes straight through both lines and the numbers 3 & 2 are in between that diagonal line.

Given: Line m is parallel to line n.

Prove: <1 is supplementary to <3

statement: reason:

S1. Line m is parallel to line n. R1. given

S2. <1 =~ <2 R2. ?

S3. m<1 =~ m<2. R3. ?

S4. <2 & <3 for a linear pair. R4. definition of linear pair

S5. <2 is supplementary to <3 R5. ?

S6. m<2 + m<3 = 180° R6. definition of supplementary

S7. ? R7. Substitution Property of Equality

S8. ? R8. Definition of supplementary