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

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

7 0

3 years ago

Find the volume of the cone use pi=3.14 Round to the nearest hundredth?

xenn [34]

Answer:

Volume=2616.67

Step-by-step explanation:

V=1/3pi r squared height

V=1/3(3.14)(10)squ.(25)

V=1/3(3.14)(100)(25)

V=2616.66667

V=2616.67

6 0

3 years ago

at a clothing store, levi's jeans are on sale for 40% off. sales tax is 7%. which expression will calculate the total cost of le

aleksandrvk [35]

Given:

Discount = 40%

Sales tax = 7%

To find:

The total cost of levi jeans with an original price of x.

Solution:

Let x be the original price of the jeans. Then the price after 40% discount is

$Price=x-40\%\text{ of }x$

$Price=x-\dfrac{40}{100}x$

$Price=x-0.4x$

$Price=0.6x$

The price after 7% of sales tax.

$Price=0.6x+7\%\text{ of }0.6x$

$Price=0.6x+\dfrac{7}{100}\times 0.6x$

$Price=0.6x+0.042x$

$Price=0.642x$

Therefore, the total cost of the levi jeans with an original price of x is represented by the expression 0.642x.

4 0

3 years ago