The number of instructions N performed per second by a computer varies directly as the speed S of the computers internal processor.

Question

A processor with a speed of 25 megahertz can perform 2,000,000 instructions per second.

 

a) find an equation of variation N=

 

b) the same processor performs _____ instructions if it running at a speed of 180 megahertz

Answer 1

Marvetta,

 

 

N directly proportional to S with the formula

 

N = kS

 

in case you were asked for inverse it would be  N = (1/s) * k = k/S

 

But we are interested in direct proportion

 

N = k S

 

\Question b

 

You will have to  find the value of k to get that gap. The question is only asking for N by providing S

 

N = k S

 

N = 2, 000, 000 and S = 25

 

N = k S  will be    2, 000, 000 = k * 25

 

k = 2, 000, 000 / 25  = 80, 000

 

 

If  S is given as 180 megahertz

 

Then  N =k S  will be   N = 80, 000 * 180 = 14, 400, 000 

 

And that fills your gap...

 

Answer 2

 N = k S              / This is algebraic statement of first sentence.

 

2* 10^6 = k 25X10^6

 

k = ( 2 * 10^6 ) / 25 * 10^6

 

K = 2/25 = 0.08

 

  N = 0.08 S

 

b)

     N = 0.08 * 180* 10^6 = 1.44X 10^6 = 1.44 M process.

 

  This case is similar to conversion of measuring units.

 

     Inch  = K ( ft)  / where  Ft and inches are directly proportion

 

     If 2 Ft equals 24 inches, how many inches equals 5 Ft

 

       24 = K (2)  then k = 12

 

        Inch = 12( 5) = 60 Inch