Answers created by Rui D.

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• How do you solve #x^4-sqrt(3)x^2+1= 0# ?
  
• An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(5 ,1 )# to #(3 ,2 )# and the triangle's area is #12 #, what are the possible coordinates of the triangle's third corner?
  
• The shorter leg of a 30-60-90 triangle is 4.3 feet long. What is the perimeter?
  
• A triangle has sides with lengths of 6, 4, and 3. What is the radius of the triangles inscribed circle?
  
• A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #7 # and the pyramid's height is #7 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?
  
• A line segment is bisected by a line with the equation # -7 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 4 )#, where is the other end?
  
• How do you find the determinant of #((2, 11, -3, 1), (1, 5, 7, -4), (6, 13, -5, 2), (4, 22, -6, 2))#?
  
• How do you find the determinant of #((3, 1, -2, 1), (1, 1, -3, 2), (2, 0, 2, 3), (3, 3, 1, -3)) # ?
  
• How do you find the determinant of #((-5, 6, 0, 0), ( 0, 1, -1, 2), (-3, 4, -5, 1), (1, 6, 0, 3))#?
  
• How do you find the determinant of #((5, 3, 1, 2), (0, 1, -1, 3), (2, 7, -4, 1), (3, 3, 5, -2))#?
  
• How do you find the determinant of #((2, 5, -3, -1), (3, 0, 1, -3), (-6, 0, -4, 9), ( 4, 10, -4, -1))#?
  
• How do you find the determinant of #((3, 4, 5, 2), (1, 0, 1, 0), (, 2, 3, 6, 3), (, 7, 2, 9, 4))#?
  
• How do you find the determinant of #((2, 0, -1, 3), (-1, 1, 0, 2), (0, 3, 2, 4), (4, 1, -1, 0))#?
  
• How do you find the determinant of #((44, 32, 18, 6), (-2, 10, 15, 5), (21, 12, -12, 4), (-8, -16, 4, 9))#?
  
• How do you find the determinant of #((5, 3, 2, 8), (0, 0, 4, 0), (2, 8, 3, 1), (0, 7, -4, 2))#?
  
• How do you find the determinant of #((2, 5, -3, -1), (3, 0, 1, -3), (-4, 5, -7, 8), (4, 10, -4, 1))#?
  
• How do you find the determinant of #((-7, 0, 0, 3), (-5, -5, 0, 0), (0, -5, 0, 0), (-9, -4, 5, 2))#?
  
• How do you find the determinant of #((5, 7, -1, 1, 0, 0), (2, 2, 1, 3, -1, 0), (-3, 4, -1, -2, 1, 2), (2, 9, -3, 0, 0, 0), (0, 1, 4, 0, 0, 0), (0, 0, 1, 0, 0, 0))#?
  
• Question #45dfa
  
• Representatives of every Allied nation except which country attended the peace conference in Paris?
  
• How do I solve 'log(base 10) 5' without using the calculator?
  
• How do you simplify the expression #(sqrt13+sqrt11)(sqrt13-sqrt11)#?
  
• Question #dc275
  
• Question #49d42
  
• How do you simplify #Cos(sin^-1 u + cos^-1 v)#?
  
• What is the logarithm of .0856?
  
• What is the arclength of #f(x)=2-3x # in the interval #[-2,1]#?
  
• What is the arclength of #f(x)=1/e^(3x)# on #x in [1,2]#?
  
• How do you calculate # log_32 64#?
  
• What is the equation of the perpendicular bisector of a chord of a circle?
  
• Question #97ac0
  
• Two circles have the following equations: #(x +6 )^2+(y -5 )^2= 64 # and #(x -9 )^2+(y +4 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
  
• Question #97ac0
  
• What is the arc length of #f(x)=((4x^5)/5) + (1/(48x^3)) - 1 # on #x in [1,2]#?
  
• What is the arc length of the curve given by #f(x)=x^(3/2)# in the interval #x in [0,3]#?
  
• What is the arclength of #f(x)=[4x^2–2ln(x)] /8# in the interval #[1,e^3]#?
  
• What is the arclength of #f(x)=sqrt(x+3)# on #x in [1,3]#?
  
• What is the arc length of #f(x) = ln(x^2) # on #x in [1,3] #?
  
• How do you find the determinant of #((7, 2, -8, 4, 6), (-3, -1, 4, -2, -3), (6, 2, 2, 4, 7), (1, 3, 7, 5, 1), (-2, 2, 3, 4, 7))#?
  
• How do you evaluate #arctan((arctan(9/7) - arctan(7/6)) / (arctan(5/3) - arctan(3/2)))#?
  
• What is the arc length of #f(x)= sqrt(x-1) # on #x in [1,2] #?
  
• Why was transportation on the Nile easy for trade and unification?
  
• A circle has a center that falls on the line #y = 8/9x +4 # and passes through # ( 4 ,1 )# and #(3 ,7 )#. What is the equation of the circle?
  
• What is the orthocenter of a triangle with corners at #(1 ,3 )#, #(5 ,7 )#, and (9 ,8 )#?
  
• What is #lim_(nrarroo)(-1)^(n-1)sin(pisqrt(n^2+0.5n+1))# ?
  
• What is the balance if $20,000 is invested at an annual rate of 7.8 percent for 5 years, compounded continuously. How long will it take for the original amount to double in size?
  
• How do you evaluate the integral of #int abssinx dx# from 0 to 3pi/2?
  
• What is #int_-oo^oo (e^x)/((e^(2x))+3) dx#?
  
• How do you find the volume of the solid generated by revolving the region bounded by the curves y = x^(1/2), y = 2, and x = 0 rotated about the x=-1?
  
• The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(4 ,5 )#, and #(8 ,4 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
  
• How do you integrate #int x / sqrt(-x^2+4x) dx# using trigonometric substitution?
  
• How do you integrate #int 3 * (csc(t))^2/cot(t) dt#?
  
• A parallelogram has sides with lengths of #14 # and #9 #. If the parallelogram's area is #63 #, what is the length of its longest diagonal?
  
• A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
  
• A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #14 #. If the volume of the solid is #2750 pi#, what is the area of the base of the cylinder?
  
• A triangle has corners at points A, B, and C. Side AB has a length of #35 #. The distance between the intersection of point A's angle bisector with side BC and point B is #14 #. If side AC has a length of #36 #, what is the length of side BC?
  
• What is the arc length of #f(x)= lnx # on #x in [1,3] #?
  
• What is #f(x) = int (x^2-2x)(e^x-sinx) dx# if #f(1 ) = 2 #?
  
• How do I evaluate cos(pi/10) without using a calculator?
  
• A factory produces bicycles at a rate of 80+0.5t^2-0.7t bicycles per week (t in weeks). How many bicycles were produced from day 15 to 28?
  
• How do you find the average rate of change of #f(x)=2x^2+2# from 4 to 6?
  
• What is the 8th term of the geometric sequence if #a_3 = 108# and #a_5 = 972#?
  
• How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 1 + 2i, 1- i?
  
• Question #028d7
  
• What is #int (2x^3-3x^2-4x-3 ) / (-6x^2+ 3 x -4 )dx#?
  
• How do you evaluate the integral of #int ( (2x^4 + 5x^3 + 17x^2 - 42x + 19) / (x^3 + 2x^2 + 5x - 26) ) dx#?
  
• How do you integrate #int (x^3 + 2x - 1) / (2x^2 - 3x - 2)# using partial fractions?
  
• How do you integrate #int (1-x^2)/((x-9)(x-5)(x+2))dx # using partial fractions?
  
• How do you write the expression #(sqrt(2) - i)^6# in the standard form a + bi?
  
• Question #a9735
  
• How do you solve #4r + 5s - 3t = 9#, #6r - 3s + 1t = 67#, #2r + 0s + 1t = 22#?
  
• How do you integrate #int x^2 e^(4-x) dx # using integration by parts?
  
• The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,1 )#, and #(3 ,2 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
  
• How do you find all the zeros of #P(x)=x^4+6x^2+9#?
  
• An ellipsoid has radii with lengths of #6 #, #7 #, and #12 #. A portion the size of a hemisphere with a radius of #8 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
  
• The population of Detroit, Michigan was 951,300 in 2000. Detroit has been experiencing a population decline of 1.4% per year since 2000. What is the projected population for 2005 in Detroit?
  
• What is #int (-x^3-2x-3 ) / (7x^4+ 5 x -1 )#?
  
• How do you find the determinant of #((5, 2, 0, 0, -2), (0, 1, 4, 3, 2), (0, 0, 2, 6, 3), (0, 0, 3, 4, 1), (0, 0, 0, 0, 2))#?
  
• How do you find the determinant of #((1, 1, 1, 1), (1, 3, 9, 27), (1, 5, 25, 125), (1, 7, 49, 343))#?
  
• How do you integrate #int x^3 / ((sqrt(16+x^2))^3) dx# using trigonometric substitution?
  
• How do you integrate #int e^x/sqrt(-e^(2x)-20e^x-96)dx# using trigonometric substitution?
  
• What is the area of the largest isosceles triangle that can be inscribed in a circle of radius 4?
  
• Question #9aee7
  
• Question #50f9b
  
• Cups A and B are cone shaped and have heights of #28 cm# and #15 cm# and openings with radii of #7 cm# and #3 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• Question #3c646
  
• How do you solve #-x + y + z = -1# and #-x + 5y - 15z = -13# and #3x - 2y - 7z = 0# using matrices?
  
• Cups A and B are cone shaped and have heights of #38 cm# and #25 cm# and openings with radii of #8 cm# and #13 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• What was the result of the Battle of El Alamein?
  
• How did Otto von Bismarck, the chancellor of Prussia, lead the drive for German unity?
  
• Points #(6 ,7 )# and #(7 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
  
• Question #6b9d0
  
• Triangle A has an area of #84 # and two sides of lengths #18 # and #15 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?
  
• A bookmark is like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of the bookmark?
  
• What are the equations of the planes that are parallel to the plane #x+2y-2z=1# and two units away from it?
  
• If #A = <8 ,1 ,-5 >#, #B = <6 ,5 ,-8 ># and #C=A-B#, what is the angle between A and C?
  
• How to construct triangle LMN , such that LN = 8 cm and ∠ LMN = 80 degrees and LM- MN= 3 cm?
  
• Why did the Napoleonic Wars represent a watershed in the history of warfare?
  
• Question #74eaa
  
• Question #5feb3
  
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