Let a_1 , a_2 , a_3 ,..., a_n be real numbers such that:
(√a_1 ) + (√(a_2 −1 )) +(√(a_3 −2 )) +...+(√(a_n −(n−1) ))=(1/2)(a_1 +a_2 +a_3 +...+a_n )−((n(n−3))/4)
Then find the value of [ Σ_(i=1) ^(100) (a_i )].
A bullet with a velocity of 30 ms^(−1) after
pentrating a 6 cm whole tree the velocity is
reduced by one−third and then the bullet
travels for 1s more.
Will the bullet penetratee
th tree? Analyze mathematically.
If θ be the acute angle between two regression
line in the case of two variables x and y
Show that
tan θ=((1−r)/r).((σ_x σ_y )/(σ_x ^2 +σ_y ^2 ))
where r,σ_x ,σ_y have their usual meanings.
Explain the significance where r=0 and r=±r
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