Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, drepresents the distance from a star to the Sun. Using a technique called "stellar parallax," astronomers determined 0 is 0.00001389 degrees.
write an expression to calculate d for any star

Astronomers Often Measure Large Distances Using Astronomical Units (AU) Where 1 AU Is The Average Distance

Answers

Answer 1

By calculating the distance of a star to the Sun, astronomers can calculate the distance from Earth to the star.

[tex]\displaystyle \mathrm{The \ \mathbf{expression} \ to \ calculate \ \mathit{d} \ for \ any \ \mathbf{star} \ is; \ \underline{d \ is \ \frac{1 \, AU}{tan(\theta)}}}[/tex]

Reasons

The given parameters are;

The distance from the star to the Sun = d

The angle formed by the ray to the Sun and the ray to Earth from the star, θ = 0.00001389 degrees

The average distance from Earth to the Sun = 1 AU

By trigonometric ratios, we have;

[tex]\displaystyle tan(\theta) = \mathbf{\frac{Opposite}{Adjacent}}[/tex]

Therefore;

[tex]\displaystyle tan(\theta) = \frac{1}{d}[/tex]

The expression to calculate for d for any star is therefore;

[tex]\displaystyle \underline{ d \ is \ \frac{1 \, AU}{tan(\theta) }}[/tex]

The angle given for θ for the referenced star is θ = 0.00001389

Therefore;

[tex]\displaystyle d = \frac{1 \, AU}{tan(0.00001389^{\circ}) } \approx 4,124,966.13 \, AU[/tex]

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Related Questions

l= prt is an example of.

Answers

Answer:

intrest=principle*rate* time

Step-by-step explanation:

Base formula, written as I = Prt or I = P × r × t where rate r and time t should be in the same time units such as months or years. Time conversions that are based on day count of 365 days/year have 30.4167 days/month and 91.2501 days/quarter.

guys please (number 3)

Answers

Answer:

500 < c < 1,700

Step-by-step explanation:

Which geometric series converges? StartFraction 1 Over 81 EndFraction StartFraction 1 Over 27 EndFraction one-ninth one-third ellipsis 1 one-half one-fourth one-eighth ellipsis Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1.

Answers

The geometric series that converges from the listed option is [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex] Option B is correct.

The nth term of a geometric sequence is expressed as;

[tex]a_n=ar^{n-1}[/tex]

a is the first term of the sequencer is the common ration is the number of terms.

For a geometric sequence to converge, the modulus of its common ratio must be less than 1 (|r| < 1), otherwise, it diverges.

For the first series given as [tex]\frac{1}{81} + \frac{1}{27} +\frac{1}{9} +\frac{1}{3}+ ,...[/tex]

[tex]r = \frac{1}{27} \div \frac{1}{81}\\r=\frac{1}{27} \times 81\\r=\frac{81}{27} \\r=3 > 1[/tex]

Since the common ratio of the sequence is greater than 1, hence the series diverges.

For the series [tex]1+\frac{1}{2} + \frac{1}{4} +\frac{1}{8} ,...[/tex]

[tex]r=\frac{1/2}{1} =\frac{1/4}{1/2} = \frac{1}{2}[/tex]

Since the common ratio of the sequence is less than 1, hence the series converges.

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an auto dealership got a new shipment of 33 cars. Of these, two are red , 6-cylinder 4 door sedans; one is a red 4-door, but not a 6-cylinder sedan. There are four 6-cylinder 4-door sedans that are not red, and three red 6-cylinder sedans that are not 4-door sedans. Altogether, 19 of the 33 cars are 6-cylinder sedans and 12 of the 33 are 4-door sedans. How many of the 33 cars are red but neither 6-cylinder nor 4-door sedans?

Answers

Answer:

2

Step-by-step explanation:

If you take 19 6-cylinder sedans and add 12 4-door sedans you get 31, therefore making 2 red and neither 6-cylinder nor 4-door sedans. Hope this helps!


Solve the system of equations 4x – 5y = –6 and -6x + 7y = 12 by
combining the equations.

Answers

Answer:

x=-9, y=-6. (-9, -6).

Step-by-step explanation:

4x-5y=-6

-6x+7y=12

----------------

6(4x-5y)=6(-6)

4(-6x+7y)=4(12)

-----------------------

24x-30y=-36

-24x+28y=48

-----------------------

-2y=12

y=12/-2

y=-6

4x-5(-6)=-6

4x+30=-6

4x=-6-30

4x=-36

x=-36/4

x=-9

One of the two solutions to the equation $5x^2 - 11x - 36 = 0$ is $x = 4$. What is the other solution?

Answers

the other solution is[tex]\frac{-9}{5}[/tex]

Answer:

Solution given:

[tex]5x^2 -11x-36=0[/tex]

doing middle term factorization

we need to get 11 by subtracting product of 5 and 36.

5*36=180=2*2*3*3*5

we get 11 by subtracting 5*2*2-3*3=20-9

substituting value of 11 as (20-9)

now

[tex]5x^2 -(20-9)x-36=0[/tex]open bracket

[tex]5x^2 -20x+9x-36=0[/tex]

taking common from each two terms

5x(x-4)+9(x-4)=0

again taking common

(x-4)(5x+9)=0

either

x-4=0

x=4

or

5x+9=0

5x=-9

x=[tex]\frac{-9}{5}[/tex]

Step-by-step explanation:

Following are the calculation to the given equation:

Given:

[tex]\to 5x^2 - 11x - 36 = 0[/tex]

one solution:

[tex]x=4[/tex]

To find:

other solution=?

Solution:

[tex]\to 5x^2 - 11x - 36 = 0\\\\\to 5x^2 - (20-9)x - 36 = 0\\\\\to 5x^2 - 20x+9x - 36 = 0\\\\\to 5x(x - 4)+9(x - 4) = 0\\\\\to (x - 4) (5x+9) = 0\\\\\to x - 4=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x+9 = 0\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x = -9\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{-9}{5}\\[/tex]

Therefore, another solution is "[tex]-\frac{9}{5}[/tex]".

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Please help guys this is just domain and range

Answers

Answer:

domain: x>=0

range: y>=1

Step-by-step explanation:

domain: x>=0

range: y>=1

Foster needs to divide a plot of land covering 538 acres into plots covering 34 acre each. How many whole plots can he make?

Answers

Given that the total amount of land in acres is 538

The problem statements requires us to divide the total amount of land into 34 places, the number of whole parts is 15 acres

Mathematically we have

538/34 = 15.823

But we are required to return the whole parts, therefore, let us ignore the values that comes after the decimal point. we have 15

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what is 18 1/5 -7 3/5 as a mixed number in simplest form

Answers

Answer:

53/5

Step-by-step explanation:

I hope this helps u.

Mark me as brainliest.

The neon lights on the dance club sign blink 240 times in 2 minutes. How many times does the neon sign blink in 10 minutes?

Answers

Answer:

1200 times in 10 minutes.

Step-by-step explanation:

There's 5 amounts of 2 minutes in 10.

Therefore multiply 240 by 5.

24 x 5 = 120 x 10 = 1200 times.

Answer:

If it blinks 240 times in 2 minutes, then you need to multiply 240 and 5. My work is shown below...

2 = 240

2 x 5 = 10

5 x 240 = 1200

This means the neon sign blinks 1200 times every 10 minutes.

Step-by-step explanation:

Have a great day and please mark brainliest!

A cable is 40 decimeters long how long is the cable in meters and be sure to include the correct unit

Answers

Answer:

4 m

Step-by-step explanation:

1 m = 10 dm

1 dm = 0.1m

(pls brainliest)

Find the value of x.

Answers

Answer:

Value of [tex]x=-12[/tex]

Step-by-step explanation:

The given triangle is isosceles

Here

[tex]m\angle2+m\angle2+36^0=180^0\\\\2m\angle2=144^0\\\\m\angle2=72^0\\\\x+84=72\\\\x=72-84\\\\=-12[/tex]

[tex]m∠2+m∠2+36⁰= 180°[/tex]

[tex]2m∠2 = 144°[/tex]

[tex]m∠2 = 72⁰[/tex]

[tex]x +84 = 72[/tex]

[tex]x = 72 - 84[/tex]

[tex]x= -12[/tex]

find the value of 40% of 1KM (in m)​

Answers

Answer:

400m

Step-by-step explanation:

40% of some quantity = 0.4 times the quantity

We also know 1 km = 1000 m, therefore: 40% of 1000m = 0.4 * 1000m = 400m.

40% of 1 km in meters is 400 meters

What is percentage :

Percentage simply means per 100. Percentage can be express as decimal or fraction.

For example 25% of 80 can be found as follows:

25 / 100 × 80 = 2000 / 100 = 20

From the example, 25% of 80 is 20 .

Therefore, 40% of 1 km(m) can be found as follows:

Let's convert km to metres.

1000m = 1km

40% of 1000

40 / 100 × 1000 = 40000 / 100 = 400metres

Therefore, 40% of 1 km in meters is 400 meters

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Please help I’ll give brainliest ASAP

Answers

Answer:

x = 10, theta = 30 degrees

Step-by-step explanation:

i. 6^2 + 8^2 = x^2

36 + 64 = x^2

100 = x^2

10 = x

ii. the angle is 30 degrees, because the opposite side is 1/2 of the hypotenuse.

You could also solve it with the law of sines:

sin(90)/12 = sin(x)/6

Multiply each side by 6

6 * sin(90)/12 = sin(x)

0.5 = sin(x)

x = 30 degrees

Please help me Find the slope please no links or bots please and thank you please actually help me please

Answers

I got C

To find slope, you have to use Rise over run
For this example, you would go down One and Run 2 so it’s -1/2

Determine the intercepts of the line.

Answers

Step-by-step explanation:

The x-intercept is the value of x when y is 0

So you need to substitute:

0 = 4x + 7

-7 = 4x

-7/4 = x

(-7/4,0)

Similarly, the y-intercept is the value of y when x is 0

So:

y = 4x + 7

y = 4(0) + 7

y = 7

(0,7)

Find the roots of the equation
x^2 +7= 2x
express your answer in simplest a +bi form

Answers

[tex]x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= \dfrac{-(-2) \pm \sqrt{(-2)^2 -4\cdot 1 \cdot 7}}{2\cdot 1}\\\\\\\implies x =\dfrac{2 \pm \sqrt{-24}}{2}\\\\\\\implies x = \dfrac{2 \pm i\sqrt{24}}2\\\\\implies x =\dfrac{2 \pm i2\sqrt{6}}2\\\\\implies x = \dfrac{2\left(1 \pm i \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\[/tex]

[tex]\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6[/tex]

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean
A. Each member visits the fitness center 3 or 4 days per week.
B. The average number of days that each member visits the fitness center is 3.12 days per week.
C. Half the members visit the fitness center 3 days per week or less, and the other half 4 days per week or more.
D. The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
E. For a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.

Answers

Answer: D

Step-by-step explanation:

The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. Option D is correct.

What is mean?

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
Let the random variable X represent the number of days per week that a member visits.
The mean of X is 3.12.
This mean describes that on an average 3.12 day in a week members visit the fitness center, it implies that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

Thus, the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. Option D is correct.

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The 20th term of the number sequence is 50
Write down the 21st term of the number sequence.

Answers

I hope this help too.

Answer:-

The linear sequence 27, 25, 23, 21, 19... is an arithmetic progression with (-2) as the common difference.

The nth term of an arithmetic progression is an=a1+(n−1)da_n=a_1+(n-1)dan​=a1​+(n−1)d, where ana_nan​ is the nth term, a1a_1a1​ is the first term, d is the common difference.

In our case, n=50,a1=27,d=−2n=50, a_1=27, d=-2n=50,a1​=27,d=−2 , hence, we get

a50=27+49⋅(−2);a50=27−98=−71.a_{50}=27+49\cdot(-2);\\ a_{50}= 27-98=-71. a50​=27+49⋅(−2);a50​=27−98=−71.

The 50th term of this sequence is (-71).

In May, Ali was charging
$20 for individual
basketball lessons and in
August started charging
$25. What percent did
she increase her prices?

Answers

Answer:

25%

Step-by-step explanation:

25 - 20 = 5

20/4 = 5

100 / 4 = 25

Answer:

20+25%=25% Ali Has increased 25%

One number exceed another by 11, the sum of the two numbers is 5. What are the numbers?​

Answers

Answer:

The first number is -3, the second number is 8

Step-by-step explanation

Let x = the first number

exceeded means add, so the second number is x+11

sum means add, so the equation is x+x+11=5

combine like terms to get 2x+11=5

subtract 11 on both sides, 2x=-6

divide by 2 on both sides, x= -3

second number was x+11, so -3+11 = 8

✺༒Question༒✺

Refer to attachment

Nonsense answer will get report​

Answers

Answer:

REFER TO ATTACHMENT.

I HOPE IT IS HELPFUL

What is the value of x + y for the system of equations y= 2x - 2 and y= 4x + 6?

Answers

Answer:

x= -1

y= 2

Step-by-step explanation:

Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2

 y-intercept = 2/1  =  2

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x= -1

 x-intercept = 2/-2 = 1/-1  = -1

HELP PLZZ!! ill give brainlist

Answers

Answer:

Step-by-step explanation:

The spinner should land on whatever color 25% of the time.

25% of 20 = 25/100 * 20 = 500/100 = 5

So the correct answer is the number of times the spinner lands on a color 5 times. Only white does that. All the other colors either go above 5 or below it.

Answer:

White

Step-by-step explanation:

to find the theoretical probability, you just divide the number of times you spin it, which is 20, by how many equal sides the spinner has which is 4.

So therefore you'll do:

20 ÷ 4 = 5

So since that is the same probability as white, the answer is white.

Choose the angle which is represented by the name.

R

Answers

Answer:

Option B

Step-by-step explanation:

Angles can be named by only the middle point's name. Option B would be correct in this case, because the point in the center of the angle is point R.

Solve the system of equations by graphing.
y = 3x - 2
x + y = 6

Answers

x+3x-2=6
4x-2=6
4x+8
x=2

Hope this helps

Solve for C: 20 (greater than or equal too sign) C-11

Answers

Answer:

C (is greater than it equal to) 31

Step-by-step explanation:

Isolate the c by adding 11 to both sides (cancels out the 11 and turns 20 into 31). Keep the sign the same!! Hope this helped! <33

the graph of linear function g is shown on the grid

what is the zero of g

-6
-9
0
-5

Answers

Answer:

Option A, - 6

Step-by-step explanation:

The zero of a function is the value on the x-axis when y is 0

Answer:

the answer is -9

Step-by-step explanation:

the answer is -9 becaise

Four students, Adrian, Claire, Jackson, and Wyatt, line up one behind the other. How many different ways can they stand in line?

Answers

Answer:

8

Step-by-step explanation:

4*3*2*1 i had the same problem

The number of different ways the students can stand in line is A = 24 ways

What are Permutations?

A permutation is an ordered arrangement.

The number of ordered arrangements of r objects taken from n unlike objects is:

Permutation ⁿPr = n! / ( n - r )!

Given data ,

Let the number of different ways the students can stand in line be A

Now , There are 4 students to choose from for the first position in the line, then 3 remaining students for the second position, 2 remaining students for the third position, and only 1 student left for the last position.

Therefore, there are

4 × 3 × 2 × 1 = 24 different ways for the students to stand in line

Therefore , the value of A = 24 ways

Hence , the students have 24 ways to stand in line

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Trevor is fishing from a small boat. His fishing hook is 8 meters below him, and a fish is swimming at the same depth as the hook, 5 meters away. How far away is Trevor from the fish? If necessary, round to the nearest tenth.

Answers

A ray from Trevor to the fish is the hypotenuse side of a right triangle  with

vertices at Trevor's position, the hook and the fish.

The distance from Trevor to the fish is approximately 9.4 meters.

Reasons:

The distance of the hook below Trevor, y = 8 meters

The horizontal distance of the fish from the hook, x = 5 meters

Required:

The distance of the fish from Trevor

Solution:

A line drawn from Trevor's position to the fish, h, then to the hook, x, and

then to Trevor, y, forms a right triangle with the distance from Trevor to the

fish being the hypotenuse side, h.

Therefore, by Pythagorean theorem, we have;

h² = y² + x²

Which gives;

h² = 8² + 5²

h = √(8² + 5²) = √(89 ≈ 9.4

The distance from Trevor to the fish given to the nearest tenth , d ≈ 9.4 meters

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Other Questions
Read the excerpt from President Dwight D. Eisenhower's citation in Jonas Salk's honor, and answer the question that follows.Citation from President Dwight D. Eisenhower to Jonas SalkImmediate Release: April 22,1955James C. Hagerty, Press Secretary to the PresidentThe White HouseFollowing are the Citations given today bythe President to Dr. Jonas E. Salk and theNational Foundation for Infantile ParalysisThe Citation for Dr. Salk is as follows:Because of a signal and historic contribution to human welfare by Dr. Jonas E. Salk in his development of a vaccine to prevent paralytic poliomyelitis, I, Dwight D. Eisenhower, President of the United States, present to him this citation for his extraordinary achievement.The work of Dr. Salk is in the highest tradition of selfless and dedicated medical research. He has provided a means for the control of a dread disease. By helping scientists in other countries with technical information; by offering to them the strains of seed virus and professional aid so that the production of vaccine can be started by them everywhere; by welcoming them to his laboratory that they may gain a fuller knowledge, Dr. Salk is a benefactor of mankind.His achievement, a credit to our entire scientific community, does honor to all the people of the United States.Answer the following question based on the President Dwight D. Eisenhower's citation:President Eisenhower refers to Jonas Salk's work as an "historic contribution to human welfare" and an "extraordinary achievement." President Eisenhower also calls Dr. Salk a "benefactor of mankind." What do these words and phrases express about the president's beliefs? (10 points) aThe president believes that Dr. Salk has impressed other scientists. bThe president believes that Dr. Salk has made an impact on the entire world. cThe president believes that Dr. Salk has proven to be a dedicated doctor. dThe president believes that Dr. Salk has successfully achieved his goal. how many pearl harbor survivors are still alive in 2021? are 6/12 and 12/24 equavilent Find the percent change from the first value to the second. Tell if it a decrease orincrease.36: 63______;_______ 4. What is the message of the German cartoon? DO U KNOW? if so comment what the answer is Point Q is plotted on the coordinate grid. Point P is at (20, 30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?Point R is at (40, 30), a distance of 60 units from point QPoint R is at (40, 10), a distance of 20 units from point QPoint R is at (40, 30), a distance of 60 units from point QPoint R is at (40, 10), a distance of 20 units from point Q Anna and Sam each want to run for president of their school's student body council. In orderto do so, they must collect a certain number of signatures and get a nomination. So far, Annahas 20 signatures, and Sam has 25. Anna is collecting signatures at an average rate of 6 perday, whereas Sam is averaging 5 signatures every day. Assuming that their rate of collectionstays the same, eventually the two will have collected the same number of signatures. Howlong will that take?TimeelapsedWrite a system of equations, graph them, and type the solution. Simplify the expression. Write your answer as a power. 7^57^3/7^2 50 POINTS PLEASE HELPP Circle the compound that has the higher boiling point and explain why we see the differences we do Which of the following does not describe the role of dialogue in a story?Dialogue provides realism.Dialogue slows down the pace of a story.Dialogue advances the story.Dialogue develops the characters.pls help Mir. White has a beach lot that is 60 feet wide.What is the width of his lot in yards? Suppose a normal distribution has a mean of 79 and a standard deviation of 7. What is P(x 72)?A. 0.84B. 0.975C. 0.025D. 0.16 The sum of the angles of a triangle is 180 degrees. The second angle is 40 degrees more than the firstangle and the third angle is 5 times the measure of the first angle. What is the measure of the largestangle? During the last 100 feet prior to an unmarked intersection, a vehicle should slow to ______ miles per hour. Help help help help math What is the equation of the line that passes through the point (5, 6) and has a slopeof 2 If hamlet was my friend what advise would you give him ? 1. When is it best to solve a system of equations using graphing?2. When is it best to solve a system of equations using substitution?3. When it is best to solve a system of equations using elimination? When it is What is la bouche in English