Answer:
t = 10
Step-by-step explanation:
Proportions
D is directly proportional to t squared. This can be written as:
[tex]D = kt^2[/tex]
Where k is the proportionality constant. It can be calculated by substituting the given condition in the formula, when t=4, D=8:
[tex]8 = k4^2=16k[/tex]
Solving for k:
[tex]k=\frac{8}{16}=\frac{1}{2}[/tex]
Thus, the proportional relationship is:
[tex]\displaystyle D = \frac{1}{2}t^2[/tex]
When D=50, the value of t can be found by solving for t:
[tex]\displaystyle 50 = \frac{1}{2}t^2[/tex]
Multiplying by 2:
[tex]t^2=100[/tex]
Taking the square root:
[tex]t=\sqrt{100}[/tex]
The positive value of t is:
t = 10
