The planets in our solar system do not travel in circular paths. rather, their orbits are elliptical. the sun is located at a focus of the ellipse.
the perihelion is the point in a planet’s orbit that is closest to the sun. so, it is the endpoint of the major axis that is closest to the sun.
the aphelion is the point in the planet’s orbit that is furthest from the sun. so, it is the endpoint of the major axis that is furthest from the sun.
the closest mercury comes to the sun is about 46 million miles. the farthest mercury travels from the sun is about 70 million miles.

1. what is the distance between the perihelion and the aphelion?

2. what is the distance from the center of mercury’s elliptical orbit and the sun?

3. write the equation of the elliptical orbit of mercury, where the major axis runs horizontally. allow a and b to be measured in millions of miles. use the origin as the center of the ellipse.

4. what is the eccentricity of the ellipse? round your answer to the nearest thousandth.

5. what does the value of the eccentricity tell you about the relative shape of the ellipse?

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

the answer is c hope it

step-by-step explanation:

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step-by-step explanatio89

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w