VARIATION

Question

The number of telephone call N between two cities A and B varies directly as the P_AP_B in A and B respectively and inversely as the square of the distance between A and B which of the following equation represents this relation. (UME 1998 Question 8).

Question

If  varies inversely as y and y varies directly as the square of z and z varies directly as . write down in word how x varies. (UME1980 Question 49)

A         x varies inversely as w²

B          x varies directly as w²

C         x varies directly as w

D         x varies inversely as w

E          x varies directly as square root of w

 

Answer: Option C: x varies directly as w

 

            Question

A variable y is inversely proportional to x². when y =10, x = 2. What is y when x =10

(UME 1982,Question46)

 

Solution

 

Question

if x is jointly proportional to the cube of y and fourth power of  z. In what ratio is x increased or             decreased when y is halved and z is doubled.(UME 1983,Question 6)      

Solution.

 

Question

y varies partly as the square of x and partly as the inverse of the square root of x. write down the expression for y, if y = 2, when x =1 and y = 6,when x = 4 (UME 1983,Question 14)

 

Solution

Question

p varies directly as the square of q and inversely as r. if p = 36,when q = 3 and r = 4.find p when q=     5 and r = 2. (UME 1984,Question 15)

 

Solution

Question

In a restaurant, the cost of providing a particular type of food is partly constant and partly inversely        proportional to the number of people. If the cost per head for 100 people is 30k and the cost for 40 people is 60k. find the cost of 50 people (UME 1985,Question16)

 

Solution

 

Question

if x varies directly as y³ and x = 2,when y =1 find x when y = 5 (UME 1986,Question16)

Solution

           

 

 

Question

If P varies inversely as V and V varies directly as R². find the relationship between P and R given that R = 7 when P = 2 (UME 1987,Question 19)

 

Solution

Question

If x varies inversely as the cube root of y and z =1, when y = 8, find y when x = 3 (UME1988, Question14)

 

Solution

 

 

Question

y varies inversely as x² and x varies directly as z². Find the relationship between y and z if c is    a constant.(UME 1990, Question 13)

 

Solution

           

Question

If w varies inversely as  and is equal to 8 when u = 2 and v = 6.find a relationship between u, v and w (UME1991,Question 15)

 

Solution

 

Question

The length a person can jump is inversely proportional to his weight. If a 20kg person can jump 1.5m. Find the constant proportionality. (UME 2003,Question 6)

 

Solution

 

Question

y is inversely proportional to x and y = 4 when x = ½ , find x when y =10 (UME 2004, Question 14)

Solution

           

Question

The length L of a simple pendulum varies directly as the square of its period T. if a pendulum with a period of 4sec is 64cm long. Find the length of the pendulum whose period is 9sec.         

(UME 2004,Question 15)

 

Solution

 

Question

The weight Wkg of a metal bar varies jointly as its length L metres and the square of its diameter d metres, if W=140, when  and L=54. Find d in term of W and L (UME 2005,Question 16)

 

Question

If x – 3 is directly proportional to the square of y and x = 5 when y =2 , find x when y = 6

(a) 30   (b)  21   (c)  16   (d) 12 (UME 2008 Question 15, Type A Set U03)

  Solution

             

Question

 If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32

(a) ±16  (b)  ±8  (c)  ±4  (d) ±2  (UME 2008 Question 15, Type A Set U03)

 

Solution

Answer: Option D

 

Question

W is directly proportional to U. If W = 5 when U = 3, find U when W =  (UME 2009 Question 15, Type A Set U03)   

 

Solution

Answer: Option B