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Solve 6x'. V2x - 2 = 0 by factorization.A natural number, when increased by 12, equal 160 times its reciprocal. Find the number.Find 11 term of AP-5, -5/2, 0, 5/2 ---Find common difference of an AP in which a s-au = 32.Find the sum of numbers from 1 to 100 which are divisible by 2 and 9.If angle between two radii of a circle is 130°, find the angle between the tangents at the end of radii.In an isosceles ABC, AB = AC = 6cm. is inscribed in a circle of radius 9 cm. Find the area of the triangleFind the volume of largest right circular cone that can be cut out from a cube of edge 4.2cm.Volume of two spheres are in the ratio 64:27. Find the ratio of their surface areas.From a solid cube of side 7cm, a conical cavity of height 7cm and radius 3cm is hollowed out. Find thevolume of remaining solid.

Answer»

1.6x²-√2x-2=06x²-3√2x+2√2x-2=03x(2x-√2)+√2(2x-√2)=0(2x-√2)(3x+√2)=02x-√2=0 or 3x+√2=0x=√2/2 or x=-√2/3

let the number be 'x'According to questionx+12=160 of 1/xx²+12x=160(multiply both sides by x)x²+12x-160=0x²+20x-8x-160=0x(x+20)-8(x+20)=0(x+20)(x-8)=0x+20=0 or x-8=0x=-20 or x=8

2.let the no be xincreased by 12=x+12160 times its reciprocal=160(1/x);160/xby equalling,x+12=160/x x*2+12x=160x*2+12x-160=0by factorizing,(x+20)(x-8)=0(x+20)=0 and (x-8)=0x=-20 and x=8

The general form of AP is a+(n-1)d11th term is a+10dwe need a and d a(first term)=-5d=t2-t1=(-5/2)-(-5)=(-5/2+5)d=5/211th term=a+10d=-5+10(5/2)=-5+(5)(5)=-5+25=20


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