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Say in(Triangle) ◇ABC ,D,E,F are three points on
BC,CA,AB respectively, such that AE:EC=1:3, DC:DB=2:1, BF:FA=3:2

What is the area of (Triangle) ◇HIG?
COMPUTE THE TORSION OF γ(t) = (cos^3 t,sin^3 t)
COMPUTE THE TORSION OF γ(t) = (1/3 〖(1+t)〗^(3/2),1/3 〖(1-t)〗^(3/2),t/√2 )
the perimeter of a triangle is 45, if the largest side is twice the smallest and the medium side is the smallest increased by 5. find all three sides of the triangle.
Q. Compute the torsion of the following curves
(i) γ(t)=4/5cos t, 1-sin⁡t,(-3)/5cos t
(ii) γ(t)=(t, cosht)
(iii) γ(t)=4/5 (〖cos〗^3t,〖sin〗^3t)
For the astroid in (iii), show that the curvature tends to ∞ as we approach one of the points (±1,0), (0,±1)
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Q. Show that if curvature K(t) of a regular curve γ(t) is >0 every where, then k(t) is a smooth function of t. Give an example to show that this may not be the case without the assumption that k>0.
A room is 10m long and 6m breadth it has one door measuring 2mx1m and two windows each measuring 1.5mx1m. Find the cost of painting the walls of the room at the rate of Rs. 15.50 per m. Sq
Two points D and E are taken inside the triangle ABC such as <ABD = <EBC
From the point D two perpendicular lines DF and DG are drawn to AB and BC
respectively . From the point E two perpendicular lines EH and EI are drawn to
AB and BC respectively . DF=7,DG=8,EI=15, EH=?