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Forming Math Expressions

Before we start attempting the questions on Java Math class, lets do a quick revision on Java libraries and Math class in particular.

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Lets Start!

  1. Write a Java expression for the following:

5/10+ x5  + 4/ bx3

Ans.

5.0/10.0 + Math.pow(x,5)  + 4.0/ b * Math.pow(x, 3)

  1. Write the Java expression for

ax5 + bx3 + c

Ans.

a * Math.pow(x, 5) + b * Math.pow(x, 3) + c

  1. Write down java expression for :

T = square root (A2 + B2 + C2)

Ans.

    double T = Math.sqrt(Math.pow(A, 2) + Math.pow(B, 2) + Math.pow(C, 2));

  1. Write the Java expression for:

(A2 + B2 )/ 2ab 

Ans.

(Math.pow(a, 2) + Math.pow(b, 2)) / (2 * a * b)

  1. Write the java expressions for each of the following: 

(i)  x = e|2x – 4x|
(ii) s=√(sin(a) + tan(a) – e2x)

Ans:

(i) x = Math.exp(Math.abs(2*x-4*x))
(ii) s = Math.sqrt(Math.sin(a)+Math.tan(a)-Math.exp(2*x))

  1. Write an expression for:
 Ans.

(x + Math.pow (y, 2)) / (Math.cbrt(3)+y)

  1. Write Java expression for following.
 Ans.

x= a*b+(1.0/2.0)*c*Math.pow(b,2);

  1. Write an expression in java for:
 Ans.

A= ( Math.pow((a+b),2 ) * Math.pow((a-b),3)) / 2*a*b

  1. Write an expression in java for:
Ans.

X=Math.abs(A)+ Math.abs(B) +(Math.pow(A,3)+ Math.pow(B,4))

  1. Write an expression in java for:
Ans.

x=Math.sqrt ((2 * Math.pow(x,3) + 3*Math.pow(y,2) ) / (x+y)

  1. Write an expression in java for:
Ans.

A= Math.sqrt(Math.pow(p,x) + Math.pow(q,2));

  1. Write equivalent Java expressions for the following:
Ans.
    1. Math.sqrt(a+b)
    2. 1/3.0*Math.pow(a,3)+1/3.0*Math.pow(b,3)
  1. Write equivalent Java expressions for the following:
Ans.
    1. s=u*t+1/2.0*a*Math.pow(t,2)
    2. d=Math.sqrt(l*l+b*b);
  1. Write equivalent Java expressions for the following:
Ans.
  1. (-b+Math.sqrt(b*b-4*a*c))/(2*a) and (-b-Math.sqrt(b*b-4*a*c))/(2*a)
  2. (Math.pow(a,3)+Math.pow(b,3))/ (Math.pow(a,3)-Math.pow(b,3))
  1. Write equivalent Java expressions for the following:
Ans.
    1. Math.abs((a*a*a+b*b*b)/(a*a*a-b*b*b))
    2. Math.cbrt((a+b)/(a*b))
  1. Write equivalent Java expressions for the following:
Ans.
    1. Math.pow(a+b,n)/Math.sqrt(3+b)
    2. Z=(5*x*x*x+2*y)/(x+y);
  1. Write equivalent Java expressions for the following:
Ans.
    1. (a*a+b*b)/(a+b)
    2. T=Math.sqrt(A*A+B*B+C*C);
  1. Write equivalent Java expressions for the following:

ax5+bx3+c

Ans.

a*Math.pow(x,5)+b*Math.pow(x,3)+c

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