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Question 187. Solve the following system of equations mx - ny = m2 + n2 and x + y = 2m by Supriya Dubey, convent of Gagan Bharti, Uttam Nagar. Answered on 30 Oct 2009 at 11:56 p.m.
Answer 187. mx - ny = m2 + n2 ...... (i) x + y = 2m .........(ii) (i) × 1 + (ii) ×2 mx - ny = m2 + n2 ...... (i) mx + ny = 2mn .........(ii) ______________________________ (m + n)x = (m + n)2 x = m + n Substituting in ( i i) m + n + y = 2m y = m - n |

Question 188. Name the type of quadrilateral formed, if any, by the points A(-3,5), B(3,1), C(0,3), D(-1,-4),

by Harkirat Singh, GHPS Delhi. Answered on 29 Nov. 2009 at 1:35 a.m.

Answer 188. In triangle ABC, AB = 2 squareroot 13, BC = squareroot 13, CA = squareroot 13.

BC + AC = squareroot 13 + squareroot 13

= 2 squareroot 13

AB = 2 squareroot 13

Therefore AB = BC + CA

Triangle ABC cannot be constructed.

Hence quadrilateral ABCD cannot be constructed.

Question 189.The CSA of the cone is
814 sq. cm and and the TSA of the cone is 1584 sq.cm.find its volume, by
Priya S, Chennai. Answered on 29 Nov. 2009 at 5:05 p.m.

Answer 189. CSA = 814 cm^2

pie r l = 814 ........... (i)

WSA = 1584 cm2

pie r2 + pie r l = 1584 cm^2

pie r2 + 814 = 1584

pie r2 = 770 cm^2

r = 7 squareroot5 ........ (ii)

Substituting in ........(i)

l = 37/sqaurerrot5 cm

h2 = l2 - r2

putting values of l and h we get

h = 12/ squareroot5

Therefore Volume of cone = pie h r2/3

= 616 squareroot 5 cm^2