Mathematics`s questions-!-－飛航模式

標題:

Mathematics`s questions?!?

發問:

Given that w partly varies directly as s and partly varies directly as s^3 , and w=56 when s=6 , w=436 when s=12 , find an equation connecting s and w

最佳解答:

let w= ps+ qs^3 , where p,q are constants when s=6, w=56 so, 56= 6p +6^3*q 6p +6^3*q= 56...(1) when s=12, w=436 so, 436= 12p +12^3*q 12p +12^3*q =436 ...(2) (2) -(1)*2 12p +12^3*q -2(6p +6^3*q)=436 -2*56 =>12^3*q - 6^3*2q=324 =>(6*2)^3*q - 6^3*2q=324 =>6^3*8q - 6^3*2q=324 =>6^3*6q =324 =>6^4*q =324 => q =324/6^4 => q = 1/4 sub q into (1) 6p +6^3*(1/4)= 56 => 6p +6^3*(1/4)= 56 => 6p = 2 => p = 1/3

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