The lower corner of a leaf in a book is folde | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the width of the page be $w$ and the length of the fold along the bottom edge be $x$. When the corner is folded to reach the inner edge,we for

Vedclass · Accepted Answer

$2/3$

Vedclass · Answer

(B) Let the width of the page be $w$ and the length of the fold along the bottom edge be $x$. When the corner is folded to reach the inner edge,we form a right-angled triangle with the fold as the hypotenuse.Let the length of the fold be $L$. By geometry,the area of the folded triangle is $A = \frac{1}{2} x y$,where $x$ is the base and $y$ is the height.Using the properties of the fold,the area $A$ can be expressed as a function of the width $x$ as $A(x) = \frac{x^3}{2(x-w)}$ or similar geometric constraints.For the area to be minimum,we differentiate the area function with respect to $x$ and set it to zero.Solving $\frac{dA}{dx} = 0$ leads to the optimal ratio of the folded width to the total width.The calculation yields the fraction of the width folded over as $x = \frac{2}{3}$ of the total width.

The lower corner of a leaf in a book is folded over so as to just reach the inner edge of the page. The fraction of width folded over if the area of the folded part is minimum is

Similar Questions

The slant height of a right circular cone is $3 \text{ cm}$. The height of the cone for maximum volume is

The minimum value of $2x^2 + x - 1$ is

Statement-$I$: $e^{\pi} > \pi^e$.
Statement-$II$: The function $f(x) = x^{1/x}$ attains its global maximum at $x = e$.

If $f(x) = 1 + 2x^2 + 2^2 x^4 + \dots + 2^{10} x^{20}$,then $f(x)$ has:

Find the semi-vertical angle of a right circular cone of a given slant height,if the volume of the cone is maximum.

Vedclass Test Series

Exam Paper Generator

Online Exam Module