The gravitational force that Earth exerts on an object is inversely proportional to the square of the distance between the center of the Earth and the object. When Bill is on the surface of Earth, 4,000 miles from the center, the gravitational force is 600 Newtons. What is the gravitational force (in Newtons) that the Earth exerts on him when he's standing on the moon, 240,000 miles from the center of the earth? Express your answer as a fraction.

Answers

Answer 1

In Einstein's theory of general relativity, gravity is treated as a phenomenon resulting from the curvature of spacetime. This curvature is caused by the presence of mass. Generally, the more mass that is contained within a given volume of space, the greater the curvature of spacetime will be at the boundary of its volume. As objects with mass move around in spacetime, the curvature changes to reflect the changed locations of those objects. In certain circumstances, accelerating objects generate changes in this curvature, which propagate outwards at the speed of light in a wave-like manner. These propagating phenomena are known as gravitational waves.

As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain. Distances between objects increase and decrease rhythmically as the wave passes, at a frequency corresponding to that of the wave. This occurs despite such free objects never being subjected to an unbalanced force. The magnitude of this effect decreases proportional to the inverse distance from the source. Inspiraling binary neutron stars are predicted to be a powerful source of gravitational waves as they coalesce, due to the very large acceleration of their masses as they orbit close to one another. However, due to the astronomical distances to these sources, the effects when measured on Earth are predicted to be very small, having strains of less than 1 part in 1020. Scientists have demonstrated the existence of these waves with ever more sensitive detectors. The most sensitive detector accomplished the task possessing a sensitivity measurement of about one part in 5×1022 (as of 2012) provided by the LIGO and VIRGO observatories.[20] A space based observatory, the Laser Interferometer Space Antenna, is currently under development by ESA.

Linearly polarised gravitational wave

Gravitational waves can penetrate regions of space that electromagnetic waves cannot. They are able to allow the observation of the merger of black holes and possibly other exotic objects in the distant Universe. Such systems cannot be observed with more traditional means such as optical telescopes or radio telescopes, and so gravitational-wave astronomy gives new insights into the working of the Universe. In particular, gravitational waves could be of interest to cosmologists as they offer a possible way of observing the very early Universe. This is not possible with conventional astronomy, since before recombination the Universe was opaque to electromagnetic radiation. Precise measurements of gravitational waves will also allow scientists to test more thoroughly the general theory of relativity.

In principle, gravitational waves could exist at any frequency. However, very low frequency waves would be impossible to detect and there is no credible source for detectable waves of very high frequency. Stephen Hawking and Werner Israel list different frequency bands for gravitational waves that could plausibly be detected, ranging from 10−7 Hz up to 1011 Hz

Hope this helped...

Now my fingers are tired.

Answer 2

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Let d be the distance from Bill to the center of the Earth and f be the gravitational force that the Earth exerts on him. Since f is inversely proportional to [tex]d^{2}[/tex], [tex]f\cdot d^2=k[/tex] for some constant k. Since the force when Bill is on the surface of Earth is 600 Newtons, [tex]k=600\cdot4000^2=960,000,000[/tex]. Therefore, if we let x be the force that the Earth acts on Bill with when he is on the Moon, [tex]x\cdot240,\!000^2=960,\!000,\!000[/tex] [tex]$x=\boxed{\dfrac{1}{6}}$[/tex]

Related Questions

3Q + 11 + 8q less than 99

Answers

The solution of the inequality 3q + 11 + 8q < 99 is q < 8.

How to solve inequalities?

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. Therefore, the inequalities can be solved as follows:

3q + 11 + 8q < 99

combine like terms

3q + 11 + 8q < 99

3q + 8q + 11 < 99

11q + 11 < 99

subtract 11 from both sides of the inequalities

11q + 11 < 99

11q + 11 - 11 < 99 - 11

11q < 88

divide both sides of the inequalities by 11

11q / 11 < 88 / 11

q < 8

Therefore,

q < 88

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what is 7 x 1,829 in expanded form

Answers

The answer: 7 * 1,829 = " 12,803 " .
______________
The following is the explanation—"in expanded form" — (as per the specfic instructions— within this very question—as to how to get the answer:
____________________
Given: 7 * 1,829 = ? ; Find the solution; using "expanded form" :
____________
(7 * 9 = 63 ) ; +

(7 *20 = 140) ; +

(7 * 800 = 5,600) ; +
___________________________________________
(7 * 1,000 = 7,000) ;
___________________________________________
Now, add the the values together to solve the problem:
___________________________________________
→ 7 * 1,829 = 63 + 140 + 5,600 + 7,000 ;
     { = 203 + 5,600 + 7,000 } ;
       { = 5,803 + 7,000 }  ;
     = 12,803 ; which is the answer.
________________________________________________
Alternately, write out the steps as follows—using "expanded form":
________________________________________________
→ 7 * 1,829 = ?
________________________________________________
     →  7 * 1,829 = (7*9) + (7*20) + (7*800) + (1,000) ;
________________________________________________
→   7 * 1,829 = 63 + 140 + 5,600 + 1,000 ;
   { = 203 + 5,600 + 7,000 } ;
      { = 5,803 + 7,000 } ;
     = 12,803 ; which is the answer.
____
→ {Now, is our obtained answer: "12,803" ; the "correct answer"—to the problem: " 7 * 1,829 " ;} ??

→ Let us check:   {Note: " 7 * 1,829 " ; is the same as: ↔ " 1,829 * 7 " .}.

→ Using a calculator, does: "7 * 1829 = ? 12,803" ?? ; Yes! ;
→  &, for that matter; does: " 1829 * 7 =? 12,803" ?? ; Yes! .
_______
Furthermore, let us check, using the "traditional format" ;
→  Does: "1,829 * 7 =? 12,803 ?? " ;
________
{NB: We are multiplying 2 (TWO) numbers together; & 1 (ONE) of these 2 [TWO] numbers is a "1-digit" ["single-digit"] number; & the "OTHER" multiplicand is a "multiple-digit" [specifically, a"4-digit"] number.}.
______
NB: Yes; using a calculator is sufficient. Below, I simply provide an alternate method to confirm whether our "obtained value" is correct.
_____
  → Does: "7 * 1,289 = ? 12,803" ?? ;
→  Using the "traditional method"; let us check; as follows:
_____
₅ ₂ ₆
   → 1, 829
*    7
12 8 03 ;
_____
So; does: "12,803 =? 12,803" ?? ; YES!
  → This "traditional method" shows that: "7 * 1,829" ;  does, in fact, equal: "12,803".
_____
{NB: Explanation of the steps used in solving the aforementioned problem using the "traditional method"—just for clarification and confirmation} :
_____
→Start with: "7*9= 63" ; Write down the "3" & 'carry over' the "6" ; {Note the small-sized digit, "6"; written on top of the "2"; {commonly done—to keep track);

→Then; "7*2 = 14" ; then add the "small digit 6"; to the "14" ; →"14+6 =20" ;
Write down the "0" ; & 'carry over' the "2" ; {Note the "small-sized digit, "2"; written over the "8"; (commonly done—to keep track);

→ Then; "7*8 = 56" ; then add the "small digit 2"; to the "56"; → "56+2 = 58" ; Write down the "8" ; & 'carry over' the "5" ; {Note the "small-sized digit", "5" ; written over the "1" ; (commonly done—to keep track);

→Then; "7*1 = 7" ; then add the "small digit 5"; to the "7" ; → "7+5 = 12" ; Write down the "12" ; in its entirety—since are no digits left [in the multiplicand, "1,829"] ; to "carry over".
____
We get: "12,803" ; which =? "12,803" ?? ;→Yes!
____
I hope my explanation of how to solve "7 * 1,829" ; using the "expanded form" is helpful.  Also, i hope my explanation—albeit lengthy— of confirming that [our]  "correctly obtained value"—which is: "12,803"— is of some help.
__

Since 43 is a 2 digit odd number is it a composite and why

Answers

the answer is it is also prime

It is not composite because nothing times itself equals 43. It is prime though which means that nothing times itself equals it. So that means that it is not composite it is prime.

A store sells grapes for $1.99 per pound. You buy 2.34 lbs. of grapes. How much do you pay? Please help!

Answers

2.34 lbs at 1.99 per lb..

2.34 * 1.99 = 4.6566 rounds to 4.66 <=

4.6566 would be the exact answer but since it’s money write Down 4.65

PLEASE HELP ME you measured 6 cups of water and 5 cups of lemon juice to make how many in total quarts of lemonade

Answers

2.75 quarts of lemonade :) I hope this helps

Total cups of lemonade:

6 cups + 5 cups = 11 cups

Total quarts and cups of lemonade:

11 cups ÷ 4 cups = 2 quarts 3 cups

When 605,000 is written in scientific notation, what will be the value of the exponent?

Answers

6.05 x 10^5 would be your answer.

I hope this helps!

Answer:1

10x2

Step-by-step explanation:

for f(x) =24-2x, find f(2) and find x such that f(x) =10

Answers

f(2) = 20
f(10)= 4

for each f(x) when it says find f of a number like f(2) just plug that number into the x that is in the regular equation.

example- f(x) = 24-2x find f(2) --- 24-2(2)= 20

The value of the function for x = 2 is 20 and the value of x for which function equal to 10 is 7

What is function?

A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.

Given is a function, f(x) =24-2x, we need to find f(2) and value of x for which function's value is 10,

For f(2), put x = 2

f(2) = 24-2(2)

= 24-4

= 20

Therefore,

f(2) = 20

For f(x) =10

Set the function equal to 10,

24-2x = 10

-2x = -14

2x = 14

x = 7

Hence, the value of the function for x = 2 is 20 and the value of x for which function equal to 10 is 7

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Factor each of the following. Remember: It is the reverse of the distributive property and your first step is to find the greatest common factor of all terms.

Answers

To factor using the reverse of the distributive property, find what common factor the numbers have and what common factor the variables have.

10.

-8x - 16

8 is a factor of both -8 and 16.
The first term has x, but the second term does not, so there is no common variable. The only common factor is 8, or -8.

Factor out a -8:

-8x - 16 = -8(x + 2)

To see if the factorization is correct, multiply the answer using the distributive property. If you get the original expression, then the factorization is correct.

11.

w^2 - 4w

The first term only has a factor of 1. The second term has a 4. There is no common factor between 1 and 4 except for 1, so there is no number you can factor out. The first term has w^2. The second term has w. Both terms have a common factor of w. We can factor out w from both terms.

w^2 - 4w = w(w - 4)

12.

4s + 10rs

4 and 10 have a common factor of 2.
s and rs have a common factor of s.
2 times s is 2s, so the common factor is 2s.
We now factor out 2s

4s + 10rs = 2s(2 + 5r)

Help:42÷7+1/5 order of operations:basic

Answers

42÷7+1/5
6 +1/5
7 1/5

seven and one fifth is the answer

42 divided by 8= 5.25+.20=5.45

If you estimate 342÷7 by using 350÷7 = 50 is 50 greater than or less than the exact answer? How did you decide? It’s 50 and overestimate or an under estimate

Answers

The answer will be greater then that because you are increasing by estimating so ur answer will be larger

4(5n+7)-3n=3(4n-9) Solve. Its supposed to equal -11
I have no idea how it got to -11 mine is always -6.5...
HELP??

Answers

Here are the steps to solve the equation. Good luck!

If it is 4:40 now, what time was it 5 hours and 15 minutes ago?

Answers

the answer is that it would be 11:25

11:25 is the answer.

Determine if the side lengths 6, 11, and 19 form a triangle. If it is a triangle, classify it by its sides.

Answers

It is not triangle because the one side of triangle should be smaller than the other two sides
Let's check
6+11=17
17<19
Or
11+19=31
9<31

-10-5x in standard form

Answers

-10 - 5x in standard form.

Standard form is when everything is in order.

Variables go before numerical values, so simply rearrange this expression.

-5x - 10

~Hope I helped!~

-5x-10 should be the answer

30% of what number is 21

Answers

The correct answer is 70
21 divided by 30% is 70.

What is the part of a line with two endpoints?

Answers

the part of a line with two end points is called a line segment.
hope this helps!

A Line Segment, because it is usually defined as part of a line that has two endpoints or just ask google why

What does the A stand for in the R.A.C.E. Strategy

Answers

The A means Answer.

lol

Your answer is answer if your doing this strategy
R= restate
A=answer
C=cite
E=explain
HOPE IT HELPS:)

What's the largest 3-digit base 14 integer?

Answers

Base 10 has the ten digits: {0, 1, 2, 3, 4, 5, 6,7, 8, 9}

Base 11 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A} where A is treated as a single digit number

Base 12 has the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}

Base 13 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C}

Base 14 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D}

The digit D is the largest single digit of that last set. So the largest 3-digit base 14 integer is DDD which is the final answer

Note: It is similar to how 999 is the largest 3-digit base 10 integer

which of the following will solve Ohm's law, V=IR for R

Answers

V=IR

to solve for R divide both sides by I

so you get R=V/I

The vet says that we nice puppy will grow to be at least 27 inches tall. Lena’s puppy is currently 1 foot tall. How many more inches will the puppy grow? The puppy will grow a.) at least 2.) at most ? Inches

Answers

1 ft = 12 in.
The puppy is now 1 ft tall, so it is now 12 in. tall.
The puppy will grow to 27 in. tall

27 in. - 12 in. = 15 in.

The puppy will grow at least 15 in.

The rectangular backboard of a basketball court needs to be assembled. Its area is given as 18,900 cm2 and the width as 1.8 m.

What is the backboard’s length in metres?

Answers

Answer:
1.05

Explanation:
The formula for area is:
A = l • w
So to find the length, you would rearrange to make:
l = A ÷ w
1.8 m = 180 cm
So:
l = 18,900 ÷ 180
l = 105 cm
105 cm = 1.05 m

Answer:

1.05 m

Step-by-step explanation:

The area of the rectangular backboard is A = 18900 cm²

And the width is w = 1.8 m = 1.8 ×100 = 180 cm

The area of the rectangle is given by

[tex]A=l\cdot w[/tex]

Substituting the known values

[tex]18900=l\cdot 180\\\\l=\frac{18900}{180}\\\\l=105\text{ cm}[/tex]

Thus, the length of the backboard's is 105 cm = 1.05 m

Use compatible numbers to find two estimates

Answers

Use compatible numbers to find two estimates that the quotient is between. For example:

1,624 divided by 3
1500 / 3 = 500

1800 / 3 = 600

2000 / 500 = 4

4000 / 800 = 5

It took John 3 minutes to drive 18 laps. How many laps per minute did he run?

Answers

He ran 6 laps per minute. 18/3=6

Divide 18 by 3.
He ran 6 laps every minute.

Veronica is shopping for school clothes. She wants to buy pants and shirts. The cost of her clothes can be found using the expression 30x + 25y where x is the number of pants and y is the number of shirts. She will also have to pay 8% tax. If Veronica buys two pants and eight shirts, what expression could be used to determine the total cost of the bill including 8% tax?

Answers

Hey there.

I'll list the variables so we're clear.

x = 2, y = 8

So far the expression looks like this: (i'll come back to the 8%)

30(2) + 25(8)

60 + 200 = 260

Cool, now we have the price before tax. We can add the sales tax by multiplying $260 by 8% as a decimal.

260 · 0.08 = 20.80

260 + 20.80 + 280.80

The total cost of Veronica's bill is $280.80

Cheers!

Final answer:

To find the total cost of Veronica's school clothes including 8% tax, first calculate the cost before tax with her specific quantities of pants and shirts, and then add the tax. The final expression shows a total cost of $280.8.

Explanation:

Veronica is shopping for school clothes, and the cost of her clothes can be found using the expression 30x + 25y, where x is the number of pants and y is the number of shirts. She will also have to pay 8% tax. If Veronica buys two pants and eight shirts, the expression to determine the total cost of the bill including 8% tax would be:

First, substitute x = 2 (pants) and y = 8 (shirts) into the expression to find the total before tax: 30(2) + 25(8).Calculate the cost before tax: 60 + 200 = 260.Calculate the total with 8% tax: 260 + (0.08 × 260).The final expression to determine the total bill is: 260 + 20.8 = 280.8.

Compute the requested average. Tim Worker receives the following income monthly from a second job. Jan. Feb. Mar. Apr. May June $200 $150 $250 $260 $285 $380 What is his average pay? (To the nearest hundredth.)
254.17255.37257.83259.85

Answers

To find the average, simply add up the values of the money that Tim earned and divide it by the six months that he worked. In this case, it would be (200 + 150 + 250 + 260 + 285 + 380) = (1525 / 6 = 254.166). This gives a closest value of choice (A), which is $254.17 per month.

If you add up all the monthly incomes, you get 1590. If you divide 1590 by 6 (the number of the months), then you get the answer: $265.

Edit: my bad, I read the question wrong, the answer is $254.17

What is 12x3 – 9x2 – 4x + 3 in factored form?

Answers

The factors of the given polynomial 12x^3-9x^2-4x+3 are

(4x-3) (3x^2-1).

Given: Polynomial 12x^3-9x^2-4x+3

We have factorized the given polynomial.

What is the meaning of factors?

The factor means a number that can be multiplied or divided to produce a given number.

Consider the given polynomial 12x^3-9x^2-4x+3.

We will factorize using a grouping of terms,

Taking 3x^2 common from the first two terms and -1 common from the last two terms, we have,

3x^2(4x-3)-1(4x-3)

Now, again taking (4x-3) common, we have,

(4x-3)(3x^2-1)

Thus, The factors of the given polynomial are (4x-3)(3x^2-1).

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Final answer:

The factored form of 12x3 - 9x2 - 4x + 3 is (3x2 - 1)(4x - 3).

Explanation:

The expression 12x3 - 9x2 - 4x + 3 can be factored as follows:

First, identify any common factors among the terms. In this case, the greatest common factor (GCF) is 1.

Next, group the terms:

12x3 - 9x2 - 4x + 3 = (12x3 - 9x2) + (-4x + 3)

Factor out the GCF from each group:

12x3 - 9x2 = 3x2(4x - 3)

-4x + 3 = -1(4x - 3)

Combine the factored terms:

(3x2 - 1)(4x - 3)

Therefore, the factored form of 12x3 - 9x2 - 4x + 3 is (3x2 - 1)(4x - 3).

Neptunes average distance from the sun is 4.503x10^9 km. Mercurys average distance from the sun is 5.791x10^7 km. About how many times farther from the sun is Neptune than mercury? Write your answer in scientific notation

Answers

Neptune is 77.76 times farther from the Sun than Mercury is.

In Louisiana, the highest point of elevation is Driskill Mountain at 535 feet above sea level and the lowest point of elevation in New Orleans at 8 feet below sea level write an expression that represents the difference between these two measures that determine the interpret the difference

Answers

535 + 8

The elevation difference is a total of 543 feet between Driskill Mountain and New Orleans.

The expression that represents the difference between these two measures will be 535 - (-8) and the result is 543 feet.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

In Louisiana, the highest point of elevation is Driskill Mountain at 535 feet above sea level, and the lowest point of elevation in New Orleans at 8 feet below sea level.

The expression that represents the difference between these two measures will be given as,

⇒ 535 - (-8)

⇒ 535 + 8

⇒ 543 feet

The expression that represents the difference between these two measures will be 535 - (-8) and the result is 543 feet.

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Determine if (-2, 10) is a solution of 5x+3y=20

Answers

plug in the -2 into "x", and plug in 10 into "y", because (x,y)

5(-2) + 3(10) = 20

-10 + 30 = 20

20 = 20

True

(-2,10) is a solution

hope this helps

To determine if (-2,10), all we have to do is plug in the appropriate values for x and y into the equation given to us, 5x + 3y = 20. When we use x = -2 and y = 10, we get 5(-2) + 3(10) = 20. When we simplify down, we get -10 + 30 = 20 => 20 = 20. Therefore, the coordinate point (-2, 10) is a solution of 5x + 3y = 20. Hope this helped and have a great day!

Convert 232°F to Celsius.

55°C
95°C
100°C
110°C

Answers

232- 449.6
55- 135
95- 203
100- 212
110- 230

Answer:

the answer is 100"C

Step-by-step explanation:

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