Answers created by Salvatore I.

• Back to user's profile
• Question #1a166
  
• What is the maximum value of #(3-cosx)/(1+cosx)# for #0< x < (2pi)#?
  
• How do you differentiate #H(x)=(x+x^-1)^3#?
  
• How do you find the exact value of #(sin2theta)/(1+cos2theta)=4# in the interval #0<=theta<2pi#?
  
• A cone has a height of #9 cm# and its base has a radius of #8 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?
  
• How do you calculate #tan ^-1 (-1/2)#?
  
• How do you determine all solutions for the equation #2sin^2theta=1-sintheta# in the domain #0^circ<=theta<360^circ#?
  
• How do you evaluate #arctan(2/5)#?
  
• How do you use the remainder theorem to find the remainder for each division #(x^3-x+6)div(x-2)#?
  
• How do you convert #r(2 + cos theta) = 1# into cartesian form?
  
• How do you find the derivative of #sin(x cos x)#?
  
• A line segment has endpoints at #(1 ,6 )# and #(5 ,2 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?
  
• Circle A has a radius of #1 # and a center at #(3 ,3 )#. Circle B has a radius of #3 # and a center at #(6 ,4 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
  
• How do you divide #(8g^3-6g^2+3g+5)/(2g+3)#?
  
• How do you use the angle sum or difference identity to find the exact value of #cos((7pi)/12)#?
  
• A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #4#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?
  
• Differential Calculus Word Problem?
  
• How do you find the value of #cot ((2pi)/3)# using the double angle or half angle identity?
  
• How do you find the volume of a solid that is enclosed by #y=3x^2# and y=2x+1 revolved about the x axis?
  
• How do you determine dy/dx given #x^(2/3)+y^(2/3)=a^(2/3)#?
  
• What is the slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(pi)/3#?
  
• A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?
  
• What is the derivative of #sec((x^2)+3x)#?
  
• How do you solve #7e^{x} = 9- e^{- x}#?
  
• Question #bcaa7
  
• How do you write the following in trigonometric form and perform the operation given #(3+4i)/(1-sqrt3i)#?
  
• How do you find the sum of the geometric series #1/16+1/4+1+...# to 7 terms?
  
• How do you find #f^{-1}(c)# if #f(x)= 5x + 8 x^{11}#; c = -13?
  
• How do you integrate #f(x)=3^xe^(-x+1)# using the product rule?
  
• Question #3e769
  
• How do you simplify the expression #cos(arctan(x/5)) #?
  
• How do you find the 4rd root of #81e^(60i)#?
  
• How do you convert #4sqrt3-4i# to polar form?
  
• How do you find all solutions to #x^4-i=0#?
  
• How do you graph the polar equation #r^2=9sin2theta#?
  
• If #A= <4, 3 ,-1 ># and #B= <9 ,7 ,6 >#, what is #A*B -||A|| ||B||#?
  
• How do you find the polar equation for #3x-2y=1#?
  
• How do you find the derivative of #g(t)=t^2 2^t#?
  
• The sum of two consecutive even integers is -102. What are the two integers?
  
• How do you solve #(x-4)/(x+3)>0#?
  
• How do you solve the quadratic with complex numbers given #8x^2-4x+5=0#?
  
• How do you simplify #n!(n+1)#?
  
• What is the center and radius of the circle with equation #x^2 + y^2 – 8x – 20y + 80 = 0#?
  
• How do you find the antiderivative of #f(x) = 1 / (5cos^2(5x))#?
  
• A triangle has sides A, B, and C. Sides A and B are of lengths #3# and #9#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?
  
• A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?
  
• How do you find the volume bounded by #y=e^x# and the lines y=0, x=1, x=2 revolved about the y-axis?
  
• A line segment has endpoints at #(7 ,8 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #-2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
  
• What is the vertex form of # y= (x-14)(3x+4)-x^2+2x#?
  
• How do you find the area between #y=x^2# and #y=8x#?
  
• What is the instantaneous velocity of an object moving in accordance to # f(t)= (sin2tcost,tant-sect ) # at # t=(13pi)/12 #?
  
• A circle has a center that falls on the line #y = 8/7x +2 # and passes through # ( 2 ,1 )# and #(3 ,6 )#. What is the equation of the circle?
  
• Twice the sum of 3 times a number and 60 is 155 greater than the opposite of the number. What is the number?
  
• Question #57267
  
• Without solving, how do you determine the number of solutions for the equation #sintheta=sqrt3/2# in #0<=theta<2pi#?
  
• How do you simplify the expression #(1+costheta)(csctheta-cottheta)#?
  
• How do you find the slope of a tangent line to the graph of the function #f(x)= -3x^2+2# at (3, -25)?
  
• An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is # 15 #, the cap's height is #8 #, and the cap's radius is #9 #. What is the object's volume?
  
• A circle's center is at #(7 ,4 )# and it passes through #(8 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?
  
• How do you find the exact solutions to the system #x^2+y^2=36# and #y=x+2#?
  
• Question #40e1d
  
• How do you find the Vertical, Horizontal, and Oblique Asymptote given #(8x-48)/(x^2-13x+42)#?
  
• A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 14, respectively. The angle between A and C is #(17pi)/24# and the angle between B and C is # (pi)24#. What is the area of the triangle?
  
• How do you compute the 9th derivative of: #arctan((x^3)/2)# at x=0 using a maclaurin series?
  
• What are the three consecutive odd integers with a sum of 117?
  
• What is the Cartesian form of #r = -sintheta+4csc^2theta #?
  
• Juan read for 5/6 of an hour. Larissa read for 10/12 of an hour. Who read for a longer period of time?
  
• How do you solve the system of equations #8x - 7y = - 5# and #- 4x + 3y = 1#?
  
• A line segment is bisected by a line with the equation # - 6 y + 2 x = 4 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
  
• How do you evaluate # e^( ( pi)/4 i) - e^( ( 5 pi)/4 i)# using trigonometric functions?
  
• How do you find the roots of #4x^3-12x^2-x+3=0#?
  
• How do you solve the system of equations #-5x + y = 18# and #5x + 5y = - 30#?
  
• Two corners of an isosceles triangle are at #(9 ,2 )# and #(4 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?
  
• How do you use the first and second derivatives to sketch # f(x) = (x+1)e^x#?
  
• What is the equation of the line tangent to # f(x)=x^2/e^x-x/e^(x^2) # at # x=0#?
  
• How do you find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle?
  
• How do you find parametric equations for the path of a particle that moves around the given circle #x^2 + (y – 2)^2 = 4# clockwise, starting at (2, 2)?
  
• What are the points of inflection, if any, of #f(x)=x^(1/3)e^(3x) #?
  
• The base of a triangular pyramid is a triangle with corners at #(2 ,5 )#, #(6 ,3 )#, and #(7 ,8 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?
  
• What is the net area between #f(x) = 1/sqrt(x^2+2x+1) # and the x-axis over #x in [2, 4 ]#?