2/3=x/12
Use cross multiply
2*12=3*x
24=3x
Divided both side by 3
24/3=3x/3
x=8
Check:
2/3=x/12
Substitute x with 8
2/3=8/12
2/3=(8/4)/(12/4)
2/3=2/3. As a result, x=8. Hope it help!

8 0

2 years ago

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X = sin 1/2θ, y = cos 1/2θ, −π ≤ θ ≤ π(a) eliminate the parameter to find a cartesian equation of the curve.

Roman55 [17]

First solve for theta in 'x' equation:
$\theta = 2 sin^{-1} x$

Substitute into 'y' equation:
$y = cos (\frac{2 sin^{-1} x}{2}) = cos (sin^{-1} x)$

Simplify by rewriting cos in terms of sine.
Using pythagorean identity: $sin^2 + cos^2 = 1$

$cos = \sqrt{1-sin^2} \\ \\ y = \sqrt{1-sin^2 (sin^{-1} x)}$
Simplify using inverse function property: $f(f^{-1} (x)) = x$

$y = \sqrt{1 - x^2}$

5 0

3 years ago

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