The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³...

The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³ b. The foci of this ellipse are located at (c, 0), and (-c, 0), where c = (a² – b²)^1/2. The eccentricity, e, of this ellipse is given by e=c/a, while the length of the ellipse’s perimeter is

\int_0^((\pi )/(2)) 4a(1-e^(2)sin^(2)\theta )^((1)/(2))d\theta .

If 0 < e < 1, this integral cannot be integrated in terms of “well-known” functions. However, fnInt, may be used to approximate the integral.

The path of the earth lies in a plane, and follows an ellipse, with the sun at one of its foci. It takes one year for the earth to orbit the sun. The closest the earth comes to the sun is 91.5 million miles, and the furthest is 94.5 million miles.

1. For the earth and sun configuration, what are the values of a, b, c, and e?

2. How far does the earth travel in one orbit of the sun?

3. What is the average speed of the earth, around the sun, in miles per second? Why is this the average speed?

Expert Solution

genius_generous answered 2 years ago

Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If...

Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.

2- Gases A2 and B2 react according to the equation: A2 + B2 → AxBy ....

2- Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.

What is Corr[A1, A2] where A1 equals B1 minus B2, and A2 equals B2 minus B3and...

What is Corr[A1, A2] where A1 equals B1 minus B2, and A2 equals B2 minus B3and we are given that Bi ∼ Ber(p) for all i in {1,2}?

Suppose a , b , c ∈ Z . If a2 + b2 = c2 ,...

Suppose a , b , c ∈ Z . If a2 + b2 = c2 , then a or b is even. a) Proof by Contraposition b) Proof by Contradiction

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this...

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this exercise is to find the two points on this ellipse that are closest to and furthest away from the xy-plane. Thus, we want to optimize F(x,y,z)= z, subject to the two constraints G(x,y,z)= x+y+z= 24 and H(x,y,z)= x2+y2-z2= 0.

Common tangent equation of y2 = 16x parabola and x2/36 - y2/20 = 1 hyperbola you...

Common tangent equation of y2 = 16x parabola and x2/36 - y2/20 = 1 hyperbola you find.

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1. Let ? be the amount of labor, ? the amount of capital, and ? be the amount of other materials used. Let the profit function be defined by ?=?−(??+??+??) where the costs of labor, capital, and other materials are, respectively, ?, ?, and ?. Determine whether second order conditions for profit maximization hold, when the profit function is defined by ?=?−(30?+20?+10?) with ?=5?^0.3?^0.4?^0.2.

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

If the bond energy for A2, B2, and A-B is 300, 200 and 100 kJ/mole, respectively,...

If the bond energy for A2, B2, and A-B is 300, 200 and 100 kJ/mole, respectively, the change in energy for the following reaction A2+B2=2A-B should be (in kJ): 500 300 -300 400 -400 Based on Coulomb’s law, when the K+ and Cl- ions are placed 10 nm apart, their interaction energy should be (in J): -2.31x10-19 -2.31x10-20 2.31x10-20 2.31x10-19 -2.31x10-18 Using the energy equation for the H atom, determine its energy when its principal quantum number n=∞ (in J):...

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2, · ·...

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2, · · · f(an+1) = bn+1 where a1, a2, · · · an+1 are n + 1 distinct values. We will define a new polynomial g(x) = b1(x − a2)(x − a3)· · ·(x − an+1) / (a1 − a2)(a1 − a3)· · ·(a1 − an+1) + b2(x − a1)(x − a3)(x − a4)· · ·(x − an+1) / (a2 − a1)(a2 − a3)(a2 − a4)·...

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