A poster is to be printed on a rectangular sh | vedclass

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

Question

(B) Let height and breadth of the sheet be $y \ m$ and $x \ m$ respectively. Since the area is $18 \ m^2$,we have $x y = 18$. Converting to $cm$,$x y

Vedclass · Accepted Answer

$3 \sqrt{3} \ m, 2 \sqrt{3} \ m$

Vedclass · Answer

(B) Let height and breadth of the sheet be $y \ m$ and $x \ m$ respectively. Since the area is $18 \ m^2$,we have $x y = 18$. Converting to $cm$,$x y = 180000 \ cm^2$,so $y = \frac{180000}{x}$. The margins are $75 \ cm$ at top and bottom (total $150 \ cm = 1.5 \ m$) and $50 \ cm$ at each side (total $100 \ cm = 1 \ m$). The area available for printing is $A = (y - 1.5)(x - 1)$. Substituting $y = \frac{18}{x}$,we get $A = (\frac{18}{x} - 1.5)(x - 1) = 18 - \frac{18}{x} - 1.5x + 1.5 = 19.5 - 1.5x - \frac{18}{x}$. To maximize $A$,find $\frac{dA}{dx} = -1.5 + \frac{18}{x^2} = 0$. $\frac{18}{x^2} = 1.5 \Rightarrow x^2 = \frac{18}{1.5} = 12$. $x = \sqrt{12} = 2 \sqrt{3} \ m$. Then $y = \frac{18}{2 \sqrt{3}} = \frac{9}{\sqrt{3}} = 3 \sqrt{3} \ m$. Thus,the dimensions are height $3 \sqrt{3} \ m$ and breadth $2 \sqrt{3} \ m$.

Similar Questions

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is .... $m$

The $pH$ of $0.01 \ M$ solution of acetic acid is $5.0$. What are the values of $[H^{+}]$ and $K_a$ respectively?

Ferredoxin is a structural component of which of the following?

An inductive circuit contains a resistance of $10 \, \Omega$ and an inductance of $2.0 \, H$. If an $AC$ voltage of $120 \, V$ and frequency of $60 \, Hz$ is applied to this circuit,the current in the circuit would be nearly......$A$.

Which of the following bacteria is associated with bio-insecticides?

Vedclass Test Series

Exam Paper Generator

Online Exam Module