Answer:
B) x^2+6x+8
Explanation:
x-4 | x^3+2x^2-16x-32
- x^3-4x^2 <-- (x-4)(x^2)
_________________
6x^2-16x-32
- 6x^2-24x <-- (x-4)(6x)
_________________
8x-32
- 8x-32 <- (x-4)(8)
___________________________
0 | x^2+6x+8
This means the answer is B) x^2+6x+8
Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
The mass of the second mass (astronaut) cancels out. We are left with:
We are solving for the radius of the new planet, so we can rearrange the equation:
Substitute in our known values given in the problem (<u><em>G = 6.67 * 10⁻¹¹ </em></u><em> ; </em><u><em>M = 7.5 * 10²³</em></u><em> ; </em><u><em>a = 12</em></u>).
The radius of the new planet is ~2.04 * 10⁶ m.
Answer:
Option d
The minimum angular separation between two objects that the Hubble Space Telescope can resolve is
.
Explanation:
The resulting image in a telescope that will be gotten from an object is a diffraction pattern instead of a perfect point (point spread function (PSF)).
That diffraction pattern is gotten because the light encounters different obstacles on its path inside the telescope (interacts with the walls and edges of the instrument).
The diffraction pattern is composed by a central disk, called Airy disk, and diffraction rings.
The angular resolution is defined as the minimal separation at which two sources can be resolved one for another, or in other words, when the distance between the two diffraction pattern maxima is greater than the radius of the Airy disk.
The angular resolution can be determined in analytical way by means of the Rayleigh criterion.
(1)
Where
is the wavelength and D is the diameter of the telescope.
Notice that it is necessary to express the wavelength in the same units than the diameter.
⇒
Finally, equation 1 can be used.
Hence, the minimum angular separation between two objects that the Hubble Space Telescope can resolve is
.
An element would be the type of substance that only contains one kind of matter.