So, let planet X's orbital period be T and its mean distance from the sun be A. Also let planet Y's orbital period be T_1, so that means if planet Y's mean distance from the sun were double that of planet X:

$Z^2=(2A)^3\\ Z^2=8A^3\implies\\ Z^2=8T^2 \implies\\ Z=2\sqrt{2}T$

Which means that the orbital period in planet Y is increased by a factor of $2\sqrt{2}$

4 0

3 years ago

(X-2) is a factor of x^4+2x^3-7x^2-8x+12. The other factors are ____, ____, and _____

Vika [28.1K]

We have

$\dfrac{x^4+2x^3-7x^2-8x+12}{x-2}=x^3+4x^2+x-6$

The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that $x=-2$ is a root, since $(-2)^3+4(-2)^2+(-2)-6=0$ , so $x+2$ is also a factor and we have

$\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3$

Finally, we can factorize the remaining quotient easily:

$x^2+2x-3=(x+3)(x-1)$

so the other factors are $x+2$ , $x+3$ , and $x-1$ .

5 0

4 years ago