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ss7ja [257]
1 year ago
6

Observations of the center of the Milky Way show the presence of a super massive black hole with a mass of 4.6 x 106 solar masse

s. Compute the Schwarzschild radius of this supermassive black hole. Give your answer in units of astronomical units (AU). At what distance does Mercury orbit from the Sun in AU? If we swapped out the Sun for this super massive black hole, would the event horizon extend beyond the orbit of Mercury? Be sure to show your calculations. 1 AU = 1.5 x 108 km.
Mathematics
1 answer:
natali 33 [55]1 year ago
6 0

The Schwarzschild radius of the black hole depends on its mass

The Schwarzschild radius of this supermassive black holeis 0.091 AU

<h3 /><h3>How to determine the Schwarzschild radius?</h3>

The Schwarzschild radius (r) is calculated using:

r_s = \frac{2GM}{c^2}

Where:

G =  Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2

M = Mass of the object = 4.6 x 10^6 solar masses

c = Speed of light = 299792458 m / s

Express the mass in Kg

M = 4.6 x 10^6 * 9.2 * 10^18 = 9.15 * 10^36 kg

Substitute the above values in the equation

r_s = \frac{2 * 6.67408 * 10^{-11} * 9.15 * 10^36}{299792458 ^2}

Evaluate the expression

r_s = 13589425339.6 m

Express as km

r_s = 13589425.3396 km

Expressas AU

r_s = \frac{13589425.3396}{1.5 * 10^8}

Evaluate the quotient

r_s = 0.09059616893

Approximate

r_s = 0.091\ AU

Hence, the Schwarzschild radius of this supermassive black holeis 0.091 AU

Read more about gravitational radius at:

brainly.com/question/4208016

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3 years ago
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My son, Garrett, is 11 years old and has a piggy bank that he wants to fill. He started with 5 one dollar bills. Every Saturday
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Answer:

1) M(x) = 5 + 3x

2) Dependent variable; 3 dollar bills

Independent variable: chores

3) Range is continuous

Domain is discrete

4) Range: 0 ≤ x ≤ 10

Domain: 5 ≤ M ≤ 35

Step-by-step explanation:

We are told he started with 5 number of $1 dollar bills and that every Saturday, he earns 3 more $1 dollar bill.

Thus, total number of $1 bills earned after x number of Saturdays(weekly) is;

M(x) = 5 + 3x

After 10 weeks, total number is;

M(10) = 5 + 3(10)

M(10) = 35

The dependent variable is the 3 more dollar bills earned each Saturday because it depends on chores he completed. While the independent variable is the chores because it doesn't depend on anything.

After 10 weeks, the range and domain will be;

Range: 0 ≤ x ≤ 10

For the; Domain:

For x = 1, M(0) = 5 + 3(0) = 5

M(10) = 35

Thus;

Domain: 5 ≤ M ≤ 35

The range could be all numbers in the interval from 0 to 10. Thus, it is continuous.

Whereas, the domain doesn't contain all the numbers in the interval from 5 to 35. Thus it is Discrete.

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Answer:

<em>Explanation below</em>

Step-by-step explanation:

<u>Angles in a Triangle</u>

There are two basic relations of angles we need to recall:

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  • Internal angles of a triangle add up to 180°

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

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Step-by-step explanation:

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Answer:

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