if given ..,. y=4x^-4 if x triples what happens to y?
y = 4/x^4
y' = 4/(3x)^4
y' = 4/81x^4
divide original y by 81
To determine what happens to y when x triples in the equation y = 4x^-4, we substitute the new value of x (which is tripled) into the equation.
Let's first calculate the value of y when x triples:
x triples = 3x (new value of x when tripled)
Substituting this into the equation:
y = 4 * (3x)^-4
To simplify this, we need to apply the Power Rule for negative exponents. The Power Rule states that for any non-zero number a, (a^m)^n = a^(m * n).
Using the Power Rule, we can rewrite (3x)^-4 as (3^-4 * x^-4):
y = 4 * (3^-4 * x^-4)
Next, we apply the rule for multiplying variables with negative exponents, which states that for any non-zero number a, a^m * a^n = a^(m + n):
y = 4 * (3^-4 * x^-4) = 4 * 3^-4 * x^-4
Since 3^-4 is a constant, we can simplify this further:
y = 4 * 3^-4 * x^-4 = (4 * 3^-4) * x^-4
Next, we calculate the value of 4 * 3^-4:
4 * 3^-4 = 4 * (1/3^4) = 4/81
So, substituting back into the equation, we have:
y = (4/81) * x^-4
In summary, when x triples, the new value of y is (4/81) times x raised to the power of -4.
To find out what happens to y when x triples, we need to substitute the new value of x (three times the original value) into the equation y = 4x^(-4) and evaluate the resulting y.
1. Start with the original equation: y = 4x^(-4)
2. Substitute the value of x tripled: x_tripled = 3x
3. Replace x in the equation with 3x: y = 4(3x)^(-4)
4. Simplify the equation: y = 4/(3x)^4
5. Expand the power: y = 4/81x^4
6. Simplify further: y = 4/(81x^4)
Therefore, if x triples, the new value of y is given by y = 4/(81x^4).