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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Regarding 20 :-

*Radius and slant height of a solid right circular cone are in the ratio 3:5. If the curved surface area, square centimeters, then find the total surface area.*

Logically, the total surface area is greater that the curved surface area.

I get

square centimeters, or approximatly 302 square centimeters.22. If

are the roots of the equation , find the value of .23. If the area of the triangle ABC is 12 square units and the vertices are A(a,-3), B(3,a) and C(-1,5) taken in order, find the value of 'a'.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi,

24. Find the sum of all odd natural numbers between 6 and 40.

25. Find the curved surface area of a cone whose volume and height are

cubic centimeters and 10 centimeters respectively.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solutions 22, 23, and 24 are correct. Brilliant!

26. Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solution 26 is correct. Good work!

27. If

is a perfect square, find the values of a and b.(28 Optional)

28. Find the equation of a straight line which passes through the point of intersection of the straight lines

and and the midpont of the straight line joining the points .Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi,

The solutions 27 and 28 are correct. Magnificent!

29 and 30 :-

29. The total surface area of a solid right circular cylinder is 231 square centimeters. Its curved surface area is two thirds of the total surface area. Find the radius and the height of the cylinder.

30. A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total height of the tent is 49 meters. Diameter of the base is 42 meters and height of the cylinder is 21 meters. Find the cost of canvas needed to make the tent if the cost of canvas is $12.50 per square meter.

(30 optional).

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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31. Solve : 3(2x + y) = 7xy and 3(x + 3y) = 11xy.

32. Find the area of the quadrilateral formed by the points

(-4,-2), (-3,-5), (3,-2) and (2,3).

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solutions 31 and 32 are correct. Neat work!

33. Find the equations of the straight lines eah passing through the point (6,-2) and whose sum of interepts is 5.

34. A cylinderial shaped well of depth 20 meters and diameter 14 meters is dug. The dug out soil is evenly spread to form a cuboid platform with base dimension 20 meters x 14 meters. Find the height of the platform.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi,

35. Find the square root of

.36. Find the equation of the straight line whose angle of inclination is 60° and y-intercept is

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

[hide=Solution 36]math]3x + \sqrt{3}y + 1 = 0[/math] is correct. Good work!

37. Solve :

38. Find the equation of the straight line passing through the point (5,-3) and whose intercepts on the axes are equal in magnitude but opposite in sign.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solutions 37 and 38 are correct. Brilliant!

39. If A and B are two events such that

, then find .40. Find the equation of the straight line passing through (1,2) and perpendicular to 3x + 4y + 5 = 0.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solutions 39 and 40 are correct. Brilliant!

41. Find the angular elevation (angle of elevation from the ground level) of the Sun when the length of the shadow of a 30 peter long pole is

meters.42. The Standard Deviation of 20 observations is

. If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solutions 41 and 42 are correct. Brilliant!

43. A retangular sheet of metal foil with dimension 66 centimeters x 12 centimeters rolled to form a cylinder of height 12 centimeters. Find the volume of the cylinder.

44. A mansion has 12 right cylindrical pillars each having radius 50 centimeters and height 3.5 meters. Find the cost to paint the lateral surface area of the pillars at the rate of $20 per square meter.

43 and 44 :-

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi,

45. If

are the roots of the equation , form a quadratic equation whose roots are .46. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son's age. Find their present ages.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solution 46 is correct. Excellent!

47. Find

for the geometri series described :- a = 2400, r = -3, n = 5.48. If the sun and product of one of the quadratic equation ax² - 5x + c = 0 are both equal to 0, find the values of 'a' and 'c'.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,355

Hi bobbym,

The solution 47 is correct. Excellent!

48. (Yet another omission). Regretted.

Find the sum and product of the roots of the quadratic equation

are both equal to 10, find the values of 'a' and 'c'.49. Find the equation of the line which makes equal intercepts on the axes and passing through the point (4,5).

50. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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