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.

( 1 ) f ( x ) = a ⋅ x 2 an d f ( 5 ) = 75 75 = a ⋅ 5 2 ⇔ a = 25 75 ​ = 3 ⇒ f ( x ) = 3 x 2 ⇒ f ( 4 ) = 3 ⋅ 4 2 = 3 ⋅ 16 = 48 ⇒ A n s . C . ( 2 ) 6 y = 9 x 2 ⇔ x 2 y ​ = 6 9 ​ = 2 3 ​ ⇒ A n s . C . ( 3 ) g ( x ) = a ⋅ x 2 an d g ( 6 ) = 108 108 = a ⋅ 6 2 ⇔ a = 36 108 ​ = 3 ⇒ g ( x ) = 3 x 2 ⇒ A n s . B .
( 4 ) f ( x ) = a x 2 an d f ( 5 ) = 75 75 = a ⋅ 5 2 ⇔ a = 25 75 ​ = 3 ⇒ f ( x ) = 3 x 2 ⇒ A n s . C .

Answered by kate200468 | 2024-06-10

The value of f(4) is calculated to be 48, making the correct option C. The constant of variation for the equation 6y = 9x² is 2 3 ​ , which corresponds to option C. Additionally, the quadratic variation equation for g(x) is given by 3x², matching option B.
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Answered by kate200468 | 2024-09-03