Suppose x=4sin(theta, for theta (-pie/2, pie/2). Rewrite(sqrt16-x^2)^3/x^3
(Sorry Im not very good at making symbols. I hope you know what I mean here! if not I can try to rewrite it a different way)
malachi has three tvs of: 25",27",32".
what the average size of malachi tvs?
x = 4sinθ
sinθ = x/4
so, the other side is √(16-x^2)
√(16-x^2)/x = cotθ
[√(16-x^2)/x]^3 = cot^3(θ)
No problem, I understand the expression you want to rewrite. To simplify the expression (sqrt(16 - x^2))^3 / x^3, we can start by substituting the given value x = 4sin(theta).
So, let's substitute x = 4sin(theta) into the expression:
(sqrt(16 - (4sin(theta))^2))^3 / (4sin(theta))^3
Now, let's simplify this expression step by step using the properties of exponents and trigonometric identities.
First, let's simplify the numerator: (sqrt(16 - (4sin(theta))^2))^3
Using the identity sin^2(theta) + cos^2(theta) = 1, we can rewrite 4sin(theta)^2 as 4(1 - cos(theta)^2):
(sqrt(16 - (4(1 - cos(theta)^2))))^3
Simplifying further:
(sqrt(16 - (4 - 4cos(theta)^2)))^3
(sqrt(12 + 4cos(theta)^2))^3
Now, let's simplify the denominator: (4sin(theta))^3
Using the property (ab)^n = a^n * b^n, we can rewrite (4sin(theta))^3 as 4^3 * (sin(theta))^3:
64 * (sin(theta))^3
So, the final expression becomes:
(sqrt(12 + 4cos(theta)^2))^3 / (64 * (sin(theta))^3)
That's the simplified expression for (sqrt(16 - x^2))^3 / x^3 after substituting x = 4sin(theta).