7. Five marks exercise problems II

1. An open box is to be made from a square piece of material, \(24 \ cm\) on a side, by cutting equal squares from the corners and turning up the sides as shown in the below figure. Express the volume \(V\) of the box as a function of \(x\).

 

 

Volume of the box \(=\) \(4x^3 + 96x^2 + 576x\)\(4x^2 - 96x - 576\)\(4x^2 - 96x + 576\)\(4x^3 + 96x^2 - 576x\)\(4x^3 - 96x^2 + 576x\) \(cm^3\).

 

 

2. A function \(f\) is defined by \(f(x) = 3 - 2x\). Find \(x\) such that \(f(x^2) = (f(x))^2\).

 

The value of \(x\) \(=\)

 

 

3. The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height \((y)\) and the forehand length \((x)\) as \(y\) \(=\) \(ax\) \(+\) \(b\), where \(a\), \(b\) are constants.

 

 

(i) Check if this relation is a function.

 

The given relation is not a functiona function.

 

 

(ii) Find \(a\) and \(b\).

 

\(a\) \(=\) 

 

\(b\) \(=\)

 

 

(ii) Find the height of the woman whose forehand length is 35 \(cm\).

 

The height of the woman is  inches.

 

 

(iv) Find the length of the forehand of the woman if her height is 62.08 inches.

 

The length of the forehand \(=\)  \(cm\)

 

[Note: Round off the answer to one decimal place.]