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A window of perimeter P (including the b...

A window of perimeter `P` (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

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A DAS GUPTA-Maxima and Minima-EXERCISE
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  4. Show that f(x) = sqrt(e^(x^(2))-1) has its extremum at x = 0. Also me...

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  5. Using examples, prove that the conditiondy/dx = 0 is neither a necessa...

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  6. Let f(x) = x ^3 - 12x. Prove that the equation x^3 - 12x - k = 0 has a...

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  7. If y=a log x +bx^(2)+x has its exteme values at x=-1 and x=2, then fin...

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  8. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,-1), find the value ...

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  9. Find the shortest distance of the point (0, c) from the parabola y=x^...

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  10. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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  11. Given an interior point A on the axis of the parabola y ^2 = 2px, (p >...

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  12. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

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  13. The parametric equations of the curve are x=2t(t^2+3)-3t^2, y=2t(t^2+3...

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  14. A function is defined parametrically as follows :x=t^5-5t^3-20 t+7y=4t...

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  15. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

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  16. A 12-cm-long wire is bent to form a triangle with one of the angles as...

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  17. The largest area of a rectangle which has one side on the x-axis and t...

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  18. Three sides of a trapezium are each equal to k cm. Find the greatest p...

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  19. A statue 4 meters high sits on a column 5.6 meters high . How far f...

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  20. A wire of length l is cut into two parts. One part is bent into a circ...

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  21. A point P is given on the circumference of a circle of radius rdot Cho...

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