# Misc 11

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 11 A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening. Let Length of rectangle be x & breadth of rectangle be y Diameter of semicircle = x Radius of semicircle = 2 Given , Perimeter of window = 10 m Length + 2 Breadth + circumference of semicircle = 10 +2 + 2 =10 2 =10 2 =5 2 2 =5 1 2 + 4 We need to maximize area of window Area of window = Area of rectangle + Area of Semicircle A = + 1 2 2 2 A = 5 1 2 + 4 + 2 8 A = 5 5 2 2 2 4 + 2 8 A = 5 5 2 2 2 8 Finding = 5 5 2 2 2 8 =5 5 4 Putting =0 0 = 5 5 4 5 4 =5 = 5 5 4 = 20 + 4 Now, calculating 2 2 at = 20 + 4 2 2 = 5 5 4 2 2 = 5 4 <0 So, 2 2 <0 at = 20 + 4 Hence, = 20 + 4 maxima Hence, A is maximum when = 20 + 4 Now, Finding value of y =5 1 2 + 4 =5 20 + 4 1 2 + 4 =5 20 + 4 4 + 2 2 =5 5 2 4 + 2 + 4 =5 5 2 + + 4 =5 + 4 2 + + 4 = 5 2 + 4 = 10 + 4 Hence, for maximum area, Length = = + m & Breadth = = + m

Chapter 6 Class 12 Application of Derivatives

Ex 6.3,5
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Ex 6.3,7 Important

Ex 6.3,12 Important

Ex 6.3,15 Important

Ex 6.3,26 Important

Example 35 Important

Example 37 Important

Example 38 Important

Example 40 Important

Ex 6.5,1 Important

Ex 6.5,5 Important

Ex 6.5,7 Important

Ex 6.5,11 Important

Ex 6.5,18 Important

Ex 6.5,20 Important

Ex 6.5,23 Important

Ex 6.5,26 Important

Ex 6.5,28 Important

Example 46 Important

Example 47 Important

Misc 6 Important

Misc 11 Important You are here

Misc 13 Important

Misc 17 Important

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Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.