2-heptyne

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Which is the correct structure of 5,6,6- trimethyl 3- heptyne ?

Write the structural formulas for the products formed when 3-heptyne reacts with KMnO_(4) under ? (i) neutral condition at room temp. (ii) alkaline or acidic condition at higher temp.

Using the given pattern, find the missing numbers. 1^2+2^2+2^2=3^2 2^2+3^2+6^2=7^2 3^2+4^2+12^2=13^2 4^2+5^2+[\_?]^2=21^2 5^2+[\_?]^2+30^2=32^2 6^2+7^2+[\_?]^2=[\_?]^2=[\_?][\_?]^2

Using the given pattern,find the missing numbers: 1^(2)+2^(2)+2^(2)=3^(2)2^(2)+3^(2)+6^(2)=7^(2)3^(2)+4^(2)+12^(2)=13^(2)4^(2)+5^(2)+()^(2)=21^(2)5^(2)+()^(2)+30^(2)=31^(2)6^(2)+7^(2)+()^(2)=()^(2)

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

Area of the quadrilateral formed with the foci of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1( a) 4(a^(2)+b^(2))( b) 2(a^(2)+b^(2))( c) (a^(2)+b^(2))(d)(1)/(2)(a^(2)+b^(2))

The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2),4^(2),5^(2)),(3^(2),4^(2),5^(2),6^(2)),(4^(2),5^(2),6^(2),7^(2)):}| is