1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna11 [10]
3 years ago
6

The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is cl

osest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 741,000,000 km at perihelion and 817,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis. Use the following as necessary: x, y.)
Mathematics
1 answer:
gladu [14]3 years ago
7 0

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

  • from perihelion to the sun in terms of ellipse is a-c;
  • from aphelion to the sun in terms of ellipse is a+c.

Then

\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.

Add these two equations:

2a=1,558,000,000 \\ \\a=779,000,000

and subtract first equation from the second:

2c=76,000,000 \\ \\c=38,000,000.

Note that b=\sqrt{a^2-c^2}, thus

b=\sqrt{779,000,000^2-38,000,000^2}=\sqrt{605,397,000,000,000,000}.

The equation for the planet's orbit is

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.

You might be interested in
X<br>+ 3 + 5x =<br>I dont know<br>understand<br>this help me​
spin [16.1K]

Answer:

6x + 3

Step-by-step explanation:

Just add the X's (5x + x)=6x, since there is only one whole number without any variables you dont have to do anything to it. So 6x + 3 is your answer.

4 0
4 years ago
Read 2 more answers
Which of the following rectangular prisms has a base area of 40 cm2 and a volume of 160 cm3?
Anon25 [30]
The base is 4 x 10. which means that you can divide 160 by 40 to get the hieght. (The height is 4)
4 0
3 years ago
Write an equation of a line parallel to y = 5x + 4 that passes through (-1, 2)
nikitadnepr [17]

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Step-by-step explanation:

The parallel lines have:

  • Same slopes
  • Different y-intercepts

The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y = 5x + 4

∴ m = 5 and b = 4

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = 5

- Substitute the value of the slope in the form of the equation

∴ y = 5x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The parallel line passes through point (-1 , 2)

∴ x = -1 and y = 2

∵ 2 = 5(-1) + b

∴ 2 = -5 + b

- Add 5 to both sides

∴ 7 = b

- Substitute the value of b in the equation

∴ y = 5x + 7

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Learn more:

You can learn more about the equations of the parallel lines in brainly.com/question/9527422

#LearnwithBrainly

5 0
3 years ago
Please help me find y
sertanlavr [38]

Answer:

5

Step-by-step explanation:

cos 60° = y / 10

y = 10 * 1/2 = 5

3 0
3 years ago
To determine whether the means of two populations are equal,
worty [1.4K]

Answer:

The correct option is C. either a t test or an analysis of variance can be performed.

Step-by-step explanation:

Consider the provided information.

  • The t-test, is used for whether the means of two groups are equal or not. The assumption for the test is that both groups are sampled from normal distributions with equal variances.
  • Analysis of Variance (ANOVA) is a statistical method evaluating variations between two or more methods. ANOVA is used in a study to analyze the gaps between group methods.
  • ANOVA is used not for specific differences between means, but for general testing.
  • The chi-squared test is often used to evaluate whether there was a significant difference in one or more groups between the predicted frequencies and the observed frequencies.

Hence, Either a t test or an analysis of variance can be performed to determine whether the means of two population are equal.

Therefore, the correct option is C. either a t test or an analysis of variance can be performed.

4 0
3 years ago
Other questions:
  • The water level in the aquarium's shark tank is always greater than 25 feet. If the water level decreased by 6 feet during clean
    7·1 answer
  • 14x+21y+7z distribute property. Pls help. First will be awrared
    7·1 answer
  • Tim Worker expects Social Security benefits of $937 per month. His wife, Mary, is eligible for a wife's benefit of 50 percent of
    14·1 answer
  • What is 7/11 equivalent to
    9·1 answer
  • I don’t know how to solve these can someone help me
    14·1 answer
  • Suponga que le piden averiguar cuán alto es un poste de luz, su mejor
    9·1 answer
  • 2. (-x + 3) - (4x - 10)
    15·1 answer
  • Question 3<br> Write the rational number as a decimal.
    9·2 answers
  • I need equations from the graphs written in slope intercept form.
    5·2 answers
  • Can SOMEONE PLEASE HELP ME I NEED HELP!!!! :( PLEASEE
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!