Related InterviewSolutions

• Show that among all positive numbers `x`and `y`with `x^2+y^2=r^2,`the sum `x+y`is largest when `x=y=r/(sqrt(2))`.
• The total cost of producing `x`radio sets per day is `R sdot((x^2)/4 35 x+25)`and the price per set at which they may be sold is `R sdot(50-x/2)dot`Find the daily output to maximize the total profit.
• Prove that the semi-vertical angle of the right circular cone of givenvolume and least curved surface is `cot^(-1)(sqrt(2))dot`
• A straight line is drawn through a given point `P(1,4)dot`Determine the least value of the sum of the intercepts on thecoordinate axes.
• The strength of a beam varies as the product of its breadth and squareof its depth. Find the dimensions of the strongest beam which can be cut from a circular log of radius `adot`
• A particle is moving in a straight line such that its distance `s`at any time `t`is given by `s=(t^4)/4-2t^3+4t^2-7.`Find when its velocity is maximum and acceleration minimum.
• Determine the points on the curve `x^2=4y`which are nearest to the point (0,5).
• A rectangle is inscribed in a semi-circle of radius `r`with one of its sides on diameter of semi-circle. Find the dimensionsof the rectangle so that its area is maximum. Find also the area.