Question

which distance formula or formulas show(s) d as direct variation with t?
i $d = 50t$
ii $d = 16t^2$
iii $d = r \cdot t$
\bigcirc \\ iii only
\bigcirc \\ i only
\bigcirc \\ ii only
\bigcirc \\ i and iii

Explanation:

Step1: Recall Direct Variation

Direct variation is \( y = kx \) (k constant), so \( d \) and \( t \) must have \( d = kt \) (k constant).

Step2: Analyze Formula I

Formula I: \( d = 50t \). Here, \( k = 50 \) (constant), so \( d \) varies directly with \( t \).

Step3: Analyze Formula II

Formula II: \( d = 16t^2 \). This is quadratic in \( t \), not direct variation (\( y = kx^2 \) is not direct variation).

Step4: Analyze Formula III

Formula III: \( d = r \cdot t \). If \( r \) is constant, then \( d = (r)t \), so \( d \) varies directly with \( t \) (r is the constant of variation).

Answer:

I and III