The equation 7^2=a^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?

Answers

Answer 1
Answer:

Answer:

The period of Y increases by a factor of k^ {3/2} with respect to the period of X

Step-by-step explanation:

The equation T ^ 2 = a ^ 3 shows the relationship between the orbital period of a planet, T, and the average distance from the planet to the sun, A, in astronomical units, AU. If planet Y is k times the average distance from the sun as planet X, at what factor does the orbital period increase?



For the planet Y:


T_y ^ 2 = a_y ^ 3


For planet X:


T_x ^ 2 = a_x ^ 3


To know the factor of aumeto we compared T_x with T_y


We know that the distance "a" from planet Y is k times larger than the distance from planet X to the sun. So:



a_y ^ 3 = (a_xk) ^ 3


(T_y ^ 2)/(T_x ^ 2)=(a_y ^ 3)/(a_x^ 3)\n\n(T_y ^ 2)/(T_x ^ 2)=((a_xk)^3)/(a_x ^ 3)\n\n(T_y^ 2)/(T_x^ 2)=\frac{k ^ {3}a_(x)^ 3}{a_(x)^ 3}\n\n(T_(y)^ 2)/(T_(x)^ 2)=k ^ 3\n\nT_(y)^ 2 = T_(x)^(2)k^(3)\n\nT_(y) =k^{(3)/(2)}T_x

Finally the period of Y increases by a factor of k^ {3/2} with respect to the period of X


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A teaspoon of common table salt contains about 2,000 mg of sodium. how many grams of sodium is this?

Answers

Answer:

2 grams

Step-by-step explanation:

multiply by 1000

What times what equals 45

Answers

The number 15 times 3 is equals 45.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, We know that;

⇒ 15 × 3

⇒ 45

Hence, 15 times 3 is equals 45.

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The answer is 5 and 9

Please help me with #6

Answers

I guess the answer would be either 3d+12d or 3 times d times(d+4)
hope I help.

the answer is d+4...

What are all the powers of 3 through 1000

Answers

3 to the 1st is 3
3 to the 2nd is 9
3 to the 3rd is 27
3 to the 4th is 81
3 to the 5th is 243
3 to the 6th is 729

jacobs family bought 4 adult tickets and 2 student tickets to the school play for $64. tatiannas family bought 3 adult tickets and 3 student tickets for $60. how much did each ticket cost?

Answers

Answer:10

Step-by-step explanation:

Final answer:

The cost of each adult ticket is $28, but there is no solution for the cost of each student ticket in this case.

Explanation:

To solve this problem, we can set up a system of equations using the given information. Let's represent the cost of an adult ticket as 'a' and the cost of a student ticket as 's'. From the first equation, we know that 4a + 2s = 64. From the second equation, we know that 3a + 3s = 60. Now we can solve this system of equations.

Multiplying both sides of the second equation by 2 gives us 6a + 6s = 120. We can subtract the first equation from this equation to eliminate 's'.

6a + 6s - (4a + 2s) = 120 - 64

Expanding and simplifying the equation gives us 2a = 56. Dividing both sides by 2, we find that a = 28. Now we can substitute this value into either of the original equations to find 's'.

Using the first equation: 4(28) + 2s = 64

Simplifying the equation gives us 112 + 2s = 64

Subtracting 112 from both sides gives us 2s = -48. Dividing both sides by 2, we find that s = -24.

However, since we're talking about the cost of tickets, we can't have a negative value. Therefore, there is no solution for 's' in this case.

The cost of each adult ticket is $28, but there is no solution for the cost of each student ticket in this case.

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There are 18 solarpanels on a house. The solar panels are
arranged in 3 equal columns. How many
rows of solar panels are on this house?
Explain how to solve the problem.​

Answers

Answer:

There are 6 rows of solar panels on this house.

Step-by-step explanation:

18/3=6

Answer:

6

Step-by-step explanation:

18 divided equally into 3 columns should give you 6 rows.

18 ÷ 3 = 6