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# C2 - Differentiation....HELP!! Watch

1. got a few questions which i did not understand at all, would be grateful for some guidance. Thank you

17. A strip of wire of length 150cm is cut into 2 pieces. one piece is bent to form a square of side x cm, the other piece is bent to form a rectangle which is twice as long as it us wide.
Find an expression in terms of x, for:
a)the width of the rectangle
b)the length of the rectangle
c)the area of the rectangle
Given also that the sum of the two areas enclosed is a minimum
d)calculate the value of x

18. A rectangular enclosure is formed from 100m of fencing. given that each of the two opposite sides of the rectangle has length x metres
a)find in terms of x, the length of the other two sides
Given also that the area enclosed is a minimum
b)find the value of x, and hence calculate the area enclosed.

20. A closed cubodial box of sqaure base has a volume of 8m^3. given that the square base has sides of length x metres, find an expression, in terms of x, for
a)the height of the box
b)the surface area of the box
Given also that the surface area enclosed of the box is a minimum
c)find the value of x

21. An open metal tank of sqaure base has volume of 108m^3. given that the square has sides of length x metres, find an expression in terms of x, for
a)the height of the tank
b)the surface area of the tank
Given also that the surface area is a minimum
c)find the value of x

22. A silver bar of volume 576cm^3 is a cubodial shape, and has a length which is twice its breadth. given that the breadth of the bar is x cm, find expressions, in terms of x, for
a)the length of the bar
b)the height of the bar
Given also that the surface area is a minimum
c)find the value of x

Thank you very much. much appreciated.
2. (Original post by harshdeep_kohli)
got a few questions which i did not understand at all, would be grateful for some guidance. Thank you

17. A strip of wire of length 150cm is cut into 2 pieces. one piece is bent to form a square of side x cm, the other piece is bent to form a rectangle which is twice as long as it us wide.
Find an expression in terms of x, for:
a)the width of the rectangle
b)the length of the rectangle
c)the area of the rectangle
Given also that the sum of the two areas enclosed is a minimum
d)calculate the value of x

18. A rectangular enclosure is formed from 100m of fencing. given that each of the two opposite sides of the rectangle has length x metres
a)find in terms of x, the length of the other two sides
Given also that the area enclosed is a minimum
b)find the value of x, and hence calculate the area enclosed.

20. A closed cubodial box of sqaure base has a volume of 8m^3. given that the square base has sides of length x metres, find an expression, in terms of x, for
a)the height of the box
b)the surface area of the box
Given also that the surface area enclosed of the box is a minimum
c)find the value of x

21. An open metal tank of sqaure base has volume of 108m^3. given that the square has sides of length x metres, find an expression in terms of x, for
a)the height of the tank
b)the surface area of the tank
Given also that the surface area is a minimum
c)find the value of x

22. A silver bar of volume 576cm^3 is a cubodial shape, and has a length which is twice its breadth. given that the breadth of the bar is x cm, find expressions, in terms of x, for
a)the length of the bar
b)the height of the bar
Given also that the surface area is a minimum
c)find the value of x

Thank you very much. much appreciated.
17. THe lengt of the sides of the square is 4x. THe remaining length for
the rectangle is 150-4x. THe half perimeter of rectangle is 75-2x. Divide it
in the ratio of 2:1.
The sum of areas is a function of second degree for x. FImd the minimum with completing the square.

18. THe length of two gives sides is 2x. The others is 100-2x . Area: similarly
to above

19. THe base area x^2. V=x^2*L What will be the L if V=8
and so on
3. unfortunately they are all incorrect. i have the proper mark scheme available.

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Updated: December 6, 2010
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