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ss7ja [257]
2 years 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]2 years 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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dusya [7]

Answer:

6.1

Step-by-step explanation:

Taking cos function,

Cos C=BC/AC

Cos 35°=5/a

a=5/cos 35°

a=6.1

5 0
3 years ago
The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,020,00
tatyana61 [14]

1. The Year-0 net cash flow is -$1,061,500.

2. The net operating cash flows in Years 1, 2, and 3 are as follows:

Year 1: $288,750 ($386,000 x 1 - 0.25)

Year 2: $288,750 ($386,000 x 1 - 0.25)

Year 3: $288,750 ($386,000 x 1 - 0.25)

3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.

4. The NPV of the project is ($13,139).

5. The machine should not be purchased because it does not yield a positive NPV.

<h3>What is the net present value?</h3>

The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

It is determined by calculating the present values of cash flows using their present value factors as below:

<h3>Data and Calculations:</h3>

Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)

Salvage value = $599,000

Increase in net working capital = $19,500

Annual savings before tax = $386,000

Tax rate = 25%

Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)

<h3>Determination of Net Present Value (NPV):</h3>

Year      Cashflows        PV Factor     Present Value

0          -$1,061,500               1             -$1,061,500

1              $288,750          0.901           $260,164

2             $288,750          0.812          $234,465

3             $288,750          0.731            $211,076

3             $468,750          0.731          $342,656

Net present value                                -$13,139

Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.

Learn more about determining the NPV at brainly.com/question/18848923

#SPJ1

5 0
2 years ago
Help me please I don’t know how to do this !?!?
lesya692 [45]
The answer is 2^27 because the 2 is supposed to stay the same and 9*3=27.

Hope this helped☺☺
7 0
2 years ago
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Cuantas veces cabe el 7 en el 4
SVEN [57.7K]
<span>7 no encaja en 4, por lo que la respuesta sería cero 7 ajustes en 4, cero veces</span>
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aniked [119]

Answer:

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Step-by-step explanation:

3 0
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