S varies directly to the square of t. Given that S = 100, when t = 4, calculate the value of:
a) k, the constant of proportionality
b) S when t = 8
c) t when S = 1
a)i don't know what it means
b)s=200
c)t=25
To find the value of 'k', the constant of proportionality, we can use the given information that 'S' varies directly with the square of 't'.
The direct variation equation is represented as S = kt^2, where 'k' is the constant of proportionality.
a) To find 'k', we can use the given information that 'S' is 100 when 't' is 4. Plugging these values into the equation:
100 = k * 4^2
100 = k * 16
Dividing both sides of the equation by 16:
k = 100/16
k = 6.25
Therefore, the constant of proportionality 'k' is 6.25.
b) To find 'S' when 't' is 8, we can substitute the values into the equation:
S = k * t^2
S = 6.25 * 8^2
S = 6.25 * 64
S = 400
Therefore, when 't' is 8, 'S' is 400.
c) To find 't' when 'S' is 1, we can rearrange the equation to solve for 't':
S = k * t^2
1 = 6.25 * t^2
Dividing both sides of the equation by 6.25:
1/6.25 = t^2
0.16 = t^2
Taking the square root of both sides:
t = √0.16
t ≈ 0.4 or -0.4
Therefore, when 'S' is 1, 't' is approximately 0.4 or -0.4.