i need help with my math problem: x varies directly as the square of s and inversely as t. how does x change when s is doubled? when both x and t are doubled?
x = A s^2/t
A is a constant
If s doubles and t stays the same, x increases by a factor of 4.
In your last question, do you mean s and t are doubled, or x and t ?
In either case, use the formula.
To understand how x changes when s is doubled and when both x and t are doubled, let's start by translating the given information into a mathematical formula.
"X varies directly as the square of s" can be written as:
x ∝ s^2
"x varies inversely as t" can be written as:
x ∝ 1/t
By combining these two equations, we can write the following proportional relationship between x, s, and t:
x = k * (s^2) / t
where k is the constant of proportionality.
Now, let's address the two scenarios:
1. How does x change when s is doubled?
If we double s, we have s' = 2s.
Substituting this into our equation, we get:
x' = k * (2s)^2 / t
= k * 4s^2 / t
= 4 * (k * s^2) / t
= 4 * x
Therefore, when s is doubled, x is quadrupled.
2. How does x change when both x and t are doubled?
If we double x, we have x' = 2x, and if we double t, we have t' = 2t.
Substituting these values into our equation, we get:
x' = k * (s^2) / (2t)
= (1/2) * (k * s^2) / t
= (1/2) * x
Therefore, when both x and t are doubled, x is halved.
In summary:
- When s is doubled, x is quadrupled.
- When both x and t are doubled, x is halved.