Math Answers

Seven students went on a diet in an attempt to lose weight, with two of them losing weight while all the others added weight. Is the diet is an effective way to losing weight α=1% (5mks)

(a) Find the derivative of the function 𝑦 = 2𝑥^2+12/x^2, when 𝑥 = 2.

(b) Let 𝑓(𝑥) = −3/𝑥−7. Find the inverse of the function.

The proportion of eligible voters in the next corporation election (in tumkur) who will vote 

for the incumbent is assumed to be 55%. What is the probability that in a random sample of 

500 voters less than 49% say they will vote for the incumbent? Write your conclusion. 

The diameter , Say X , of a electric cable , is assumed to be continuous random variable with p.d.f : f(x)= 6x(1-x) , 0<=x<=1.

(1) Check that the above is a P.D.F.

(2) Obtain an expression for the c. d. f. of X.

(3) Compute P(X<=1/2| 1/3<=X<=2/3), and

(4) Determine the value of k such that P(X<k)=P(X>k).

Question 6 [2]

State the mean Value Theorem.

Question 5 [2;2]

Investigate whether the following functions are odd or even.

(a) 𝑓(𝑥) = 𝑥^

3

(b) 𝑓(𝑥) = cos 𝑥

A mainframe computer has 4 ports. At any given time each port is either in use or not in use. How many possibilities are therefore overall port usage of this computer? Determine possible outcomes of at least two ports

Question 4 [7]

Prove that 𝑓(𝑥) = 𝑥^2 + 2𝑥 is not injective.

Question 2 [7]

Use sign table to determine the values of 𝑥 for which

x^2 + 9𝑥 + 20 ≤ 0.

Consider the relation 𝑃 = {(1,7), (−1,7), (3,9), (1,3)}. Is 𝑃 a function? Justify

your answer