Математика15 мин

Two Types of Variations

Direct, inverse, joint, and combined variation — set up the constant from one data point, then answer any question.

Direct vs inverse

y = kx \quad (\text{direct})

y = \dfrac{k}{x} \quad (\text{inverse})

y = kxz \quad (\text{joint})

Step 1: substitute the given values to find $k$ . Step 2: use $k$ with the new values.

Inverse variation

$y$ varies inversely as $x$ . When $x = 4$ , $y = 9$ . Find $y$ when $x = 6$ .

Жауап: $y = 6$

Жаттығу

$y$ varies directly with $x^2$ . If $y = 12$ when $x = 2$ , find $y$ when $x = 5$ .

Жауап пен түсініктемені көру

Жауап: 75

$y = kx^2 \Rightarrow 12 = 4k \Rightarrow k = 3$ . Then $y = 3 \cdot 25 = 75$ .