Answers edited by A. S. Adikesavan

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