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

Solve for xxx. Enter the solutions from least to greatest. x^2 +7=43x 2 +7=43x, squared, plus, 7, equals, 43 \text{lesser }x =le

vaieri [72.5K]

Answer:

Step-by-step explanation:

x²+7=43x

x²-43x+7=0

$x=\frac{43 \pm \sqrt{(43)^2-4(1)(7)} }{2(1)} \\=\frac{43 \pm \sqrt{1849-28} }{2} \\=\frac{43 \pm \sqrt{1821} }{2} \\\approx \frac{43 \pm 42.673}{2}\\\approx 0.1635,42.8365$