How do you write a general formula to describe each variation if T varies jointly with the cube root of x and the square of d; T=18 when x=8 and d=3?

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How do you write a general formula to describe each variation if T varies jointly with the cube root of x and the square of d; T=18 when x=8 and d=3?

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Answer 1 · 2017-09-06T13:23:06

$T = d^{2} \sqrt[3]{x}$ $T=d^2root(3)(x)$

Explanation:

$the initial statement can be expressed as$ $"the initial statement can be expressed as"$

$T \propto d^{2} \sqrt[3]{x}$ $Tpropd^2root(3)(x)$

$to convert to an equation multiply by k the constant$ $"to convert to an equation multiply by k the constant"$
$of variation$ $"of variation"$

$\Rightarrow T = k d^{2} \sqrt[3]{x}$ $rArrT=kd^2root(3)(x)$

$to find k use the given condition$ $"to find k use the given condition"$

$T = 18 when x = 8 and d = 3$ $T=18" when "x=8" and "d=3$

$T = k d^{2} \sqrt[3]{x} \Rightarrow k = \frac{T}{d^{2} \sqrt[3]{x}} = \frac{18}{9 \times 2} = 1$ $T=kd^2root(3)(x)rArrk=T/(d^2root(3)(x))=18/(9xx2)=1$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(T=d^2root(3)(x))color(white)(2/2)|)))$

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How do you write a general formula to describe each variation if T varies jointly with the cube root of x and the square of d; T=18 when x=8 and d=3?

1 Answer

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