Answers edited by A. S. Adikesavan

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• How fast does the earth orbit the sun?
  
• How do you find all solutions to #[sin (2x) + cos (2x)] ^2 = 1#?
  
• Question #24b9d
  
• How long is the precession of the equinoxes?
  
• What is the difference between a sidereal year and a tropical year? How is each calculated?
  
• Question #758c4
  
• What is the axis of symmetry and vertex for the graph #f(x) = x^2 - 4x#?
  
• What is the standard form of #y= (x - 8) (4x+1) #?
  
• How many light years away is the sun from pluto?
  
• How is the distance between stars and the earth calculated?
  
• How do you solve #log y = log (x-1) + 1#?
  
• An asteroid has a perihelion distance of 2.4 AU and an aphelion distance of 4.4 AU? How do you calculate its orbital semimajor axis, eccentricity and period?
  
• Suppose we want to construct an accurate scale model of the Solar System and we use an orange (diameter 10 cm) to represent the Sun. How far away would we have to put Pluto?
  
• What is the distance between earth and pluto in light years?
  
• How do you graph #r= 5 cos theta #?
  
• What does #sin(arc tan(2))+3cot(arctan(-1))# equal?
  
• Using Hubble's Law, how would you determine the distance to a galaxy which is moving away at a velocity of 3,500 km/s? (Assume H = 70km/s/Mpc)
  
• How far apart are Jupiter and Saturn? How is this distance calculated?
  
• How do you determine if the equation #y=90(5)^x# represents exponential growth or decay?
  
• Does the sun exert a greater force on the earth than that exerted on the sun by the earth?
  
• What is the size of the observable universe?
  
• Question #a2a6d
  
• Question #c9f34
  
• Question #94f10
  
• Question #2f37e
  
• What are the components of the vector between the origin and the polar coordinate #(5, (7pi)/8)#?
  
• How do you find the vertical, horizontal or slant asymptotes for #f(x) = 3(1/x)#?
  
• How many times more massive is the Sun than the Earth?
  
• What is a parsec and why is it necessary when a light year measures distance as well?
  
• How would you describe the position of earth in relation to the sun during the northern hemisphere's summer solstice?
  
• How do you find the vertex of #y=4x-x^2#?
  
• How do you graph #r(2 + cos theta) = 1#?
  
• How do you convert #y=x# to polar form?
  
• Is it significant when stars form in clusters? Why or why not?
  
• If you take millions of tons of metal off the earth in the form of satellites therefore reducing earth's specific mass, would this in turn affect the earth's orbit around the sun?
  
• What is Moho discontinuity?
  
• Why is stellar parallax important?
  
• Alpha Centauri, the nearest star, is just over 4 light years away. Traveling at a speed of 2000 miles per hour (the speed of a fast jet airplane), how long would it take to get there in years?
  
• How would you describe the graph of #y = 5 * 2^x#?
  
• During the winter and summer solstice, how far away is the sun from the earth?
  
• How fast is the Earth traveling through space?
  
• How do you use the binomial formula to find the coefficient of #u^(4)z^(15)# in the expansion of #(3u+z)^19#?
  
• Does the moon rotate on its axis like planet earth? Why or why not?
  
• How fast is the universe expanding in miles per hour?
  
• What is the distance between #(3 , (3 pi)/8 )# and #(9, pi )#?
  
• How do you solve the triangle given #A=60# degrees, #a=20((3)^(1/2)), b=40?#
  
• How do you express the Cartesian coordinates (0, - 3) as polar coordinates?
  
• What does #-sin(arccos(2))+tan(arccos(4))# equal?
  
• If you invest $8,000 at 12% interest, how much will you have in 7 years?
  
• What is the the vertex of #y = (x-3)(x+5) -x+12#?
  
• How do you find the domain & range for #y=Arccos x#?
  
• How do astronomers measure the distance to other stars? How accurate are their measurements?
  
• What day/night cycle would we have if earth was tilted like Uranus?
  
• How do you convert #y=x+x^2+2y^2 # into a polar equation?
  
• How far away is pluto from earth? Does this distance vary?
  
• How do you find the asymptotes for #f(x)=(2x)/(sqrt (9x^2-4))#?
  
• The distance between the perihelion and aphelion of the sun is 10A.U. What is its orbital period in term of years?
  
• How far is Jupiter from the Earth and the Sun?
  
• How far is Saturn from Earth?
  
• Why didn't the Apollo astronauts return with pictures of stars and galaxies taken from the Moon's surface? Are stars visible from the surface of the moon?
  
• What are some star constellations that can only be seen from the southern hemisphere?
  
• Are the planets in our solar system all on the same plane?
  
• Which planet completes its rotation in 59-60 Earth days?
  
• As orbits get more "out of round" in shape, does eccentricity increase or decrease?
  
• How do you graph and solve #|x – 4| + 7 = 4#?
  
• How do you use the binomial series to expand # (x-3)^5#?
  
• How do you use the important points to sketch the graph of #y=x^2+6x+5#?
  
• What does it mean if the the stellar parallax of a star is too small to be measured?
  
• What is the cosmological argument, the teleological argument and the ontological argument?
  
• What are the components of the vector between the origin and the polar coordinate #(2, (7pi)/4)#?
  
• Question #fcd99
  
• What is #lim_(nrarroo)(-1)^(n-1)sin(pisqrt(n^2+0.5n+1))# ?
  
• What is #(2p^-3)^5#?
  
• How important is the use of math in the subject of astronomy?
  
• Is #f(x) =sinx/x# concave or convex at #x=1#?
  
• What causes the angle of a parallax to increase?
  
• How do you find the exact value of #cos[2 arcsin (-3/5) - arctan (5/12)]#?
  
• At the poles, how fast does the earth spin?
  
• How do you measure the diameter of the sun?
  
• What is the distance between earth and Mars in km?
  
• Is the centripetal acceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?
  
• How do you convert # r = 1/(4 - costheta)# to rectangular form?
  
• How do you find the derivative of #sinh^(79x)#?
  
• What is the focus of the parabola #y^2+6y+8x+25 = 0#?
  
• What color is Venus?
  
• What are the inner and outer cores made of?
  
• Question #f647b
  
• An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, how do you find the first term of the series?
  
• How do you solve #e^(5-9 x)=990#?
  
• What is the full scale of the universe? Will it ever be known?
  
• If #A = <4 ,3 ,-7 >#, #B = <5 ,8 ,-4 ># and #C=A-B#, what is the angle between A and C?
  
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