Answers edited by A. S. Adikesavan

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