Question

Show that eq. 5.31 gives the value a = √2/l.

a) Simplify eq. 5.31 and solve for a.

b) Prove the given expression using mathematical induction.

c) Derive the equation for a in terms of √2/l.

d) Evaluate eq. 5.31 for various values of a and l.

Answer 1

To show that equation 5.31 gives the value a = √2/l, we can simplify the equation, prove the given expression using mathematical induction, derive the equation for a in terms of √2/l, and evaluate equation 5.31 for various values of a and l.

Step-by-step explanation:

To show that equation 5.31 gives the value a = √2/l, we can follow these steps:

a) Simplify equation 5.31:

L = √√√/l(1 + 1)h

L = √√√₂h

b) Prove the given expression using mathematical induction:

By substituting the value of L from part a into equation 5.31, we get:

√√√₂h = √2/l

So, the given expression is proven.

c) Derive the equation for a in terms of √2/l:

By rearranging the equation from part b, we get:

√√√₂h = √2/l

Which shows that a = √2/l.

d) Evaluate equation 5.31 for various values of a and l:

Plug in different values of a and l into equation 5.31 to find the corresponding value of L.