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Quadratic Variation

If f(x) varies directly with x2, and f(x) = 75 when x = 5, find the value of f(4).
  A.100  B.50  C.48  D.25

Find the constant of variation for the quadratic variation.    
 6y = 9x2  A.4/9  B.2/3  C.3/2  D.

Write a quadratic variation equation if g(x) varies directly with x2, and g(x) = 108 when x = 6.  A.  B.  C.  D.

Quadratic VariationIf fx varies directly with x2 and fx 75 when x 5 find the value of f4 A100 B50 C48 D25Find the constant of variation for the quadratic variat class=


Answer :

kate200468
[tex](1)\\f(x)=a\cdot x^2\ \ \ and\ \ \ f(5)=75\\\\75=a\cdot 5^2\ \ \ \Leftrightarrow\ \ \ a= \frac{75}{25}=3\\\\ \ \ \Rightarrow\ \ \ f(x)=3x^2\ \ \ \Rightarrow\ \ \ f(4)=3\cdot4^2=3\cdot16=48\ \ \ \Rightarrow\ \ \ Ans.\ C.\\\\(2)\\6y=9x^2 \ \ \ \ \Leftrightarrow\ \ \ \ \ \frac{y}{x^2}= \frac{9}{6}= \frac{3}{2} \ \ \Rightarrow\ \ \ Ans.\ C. \\\\(3)\\g(x)=a\cdot x^2\ \ \ and\ \ \ g(6)=108\\\\108=a\cdot 6^2\ \ \ \Leftrightarrow\ \ \ a= \frac{108}{36} =3\ \Rightarrow\ \ \ g(x)=3x^2\ \Rightarrow\ \ \ Ans.\ B.[/tex]

[tex](4)\\f(x)=ax^2\ \ \ and\ \ \ f(5)=75\\\\75=a\cdot5^2\ \ \ \ \Leftrightarrow\ \ \ \ a= \frac{75}{25} =3\ \ \ \Rightarrow\ \ \ f(x)=3x^2\ \ \Rightarrow\ \ \ Ans.\ C.[/tex]

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