Answers edited by A. S. Adikesavan

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