Answers edited by Douglas K.

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• How do you write the partial fraction decomposition of the rational expression #(x^3 - 5x + 2) / (x^2 - 8x + 15)#?
  
• How do you find the limit of #sinx/(x+sinx)# as #x->0#?
  
• How do you find all the critical points to graph #x^2 - 9y^2 + 2x - 54y + 80 = 0# including vertices, foci and asympotes?
  
• How do you identity if the equation #2x^2+12x+18-y^2=3(2-y^2)+4y# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
  
• How do you solve the system of equations: \begin{array}{ l }{ 3x + 2y + 4z = 11} \\ { 2x - y + 3z = 4} \\ { 5x - 3y + 5z = - 1} \end{array}?
  
• The area of a rectangular piece of cardboard is 90 square centimeters, and the perimeter is 46 centimeters. How do you find the dimensions of the rectangle?
  
• How do you solve #x+2=e^(x) #?
  
• How do you find the exact values of #costheta# and #sintheta# when #tantheta=1#?
  
• How do you find an equation for the ellipse with vertices at (-6,4) and (10,4); focus at (8,4)?
  
• How do you differentiate #f(x)=(2x^2-6x+1)^-8#?
  
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3(1-costheta)#?
  
• How do you simplify #\frac{x-5y}{x+y}+\frac{x+7y}{x+y}#?
  
• How do you find the exact solutions to the system #y+x^2=3# and #x^2+4y^2=36#?
  
• What is the ellipse which has vertices at #v_1 = (5,10)# and #v_2=(-2,-10)#, passing by point #p_1=(-5,-4)#?
  
• How do you convert each parametric equation to rectangular form: x = t - 3, y = 2t + 4?
  
• How do you use partial fractions to find the integral #int (x^2-x+9)/(x^2+9)^2dx#?
  
• Why is it important to learn cardiopulmonary resuscitation?
  
• A triangle has corners at #(5 ,1 )#, #(2 ,4 )#, and #(7 ,2 )#. What is the area of the triangle's circumscribed circle?
  
• How do you convert the rectangular equation #5x+7y=12# into polar form?
  
• Use the Law of Sines to solve the triangle? 6.) A=60 degrees, a=9, c=10.
  
• How do you convert the following equation from standard to vertex form by completing the square: #y=3x^2+12x+5#?
  
• How do you find the vertex, focus and directrix of #4x-y^2-2y-33=0#?
  
• How do you find the coordinates of the center, foci, the length of the major and minor axis given #3x^2+y^2+18x-2y+4=0#?
  
• What is the Cartesian form of #r-theta = -2cos^3theta-cot^2theta #?
  
• How long does it take to get to Venus from Earth?
  
• Question #3bf5e
  
• How do you find the derivative of #y^3 = x^2 -1# at P(2,1)?
  
• How do you find #(d^2y)/(dx^2)# for #5=x^2-2y^2#?
  
• What type of atom is nickel?
  
• How do you convert # r=3theta - tan theta # to Cartesian form?
  
• How do you solve #2log_5(x-2)=log_5 36#?
  
• How do you identify the vertex, focus, directrix and the length of the latus rectum and graph #4(x-2)=(y+3)^2#?
  
• How do you find parametric equations for the line through the point (0,1,2) that is perpendicular to the line x =1 + t , y = 1 – t , z = 2t and intersects this line?
  
• What is the area of a regular octagon with a side length of 4.6 meters and a length from the center to a vertex of 6 meters?
  
• How do you find the equation of the circle given Radius 3 and Tangent to y-axis at (0,4)?
  
• Question #e9ae8
  
• Question #90cf3
  
• What is the net area between #f(x) = -xln(x^2-1) # and the x-axis over #x in [2, 4 ]#?
  
• How do you convert #r^2 = 9cos5(theta)# into cartesian form?
  
• A line segment is bisected by a line with the equation # 2 y + 3 x = 3 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
  
• How do you find #(d^2y)/(dx^2)# for #-4y^2+4=4x^2#?
  
• Given #csctheta^circ=sqrt3/2# and #sectheta^circ=sqrt3/3#, how do you find #sintheta#?
  
• A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 3, respectively. The angle between A and C is #(19pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?
  
• How do you find the unit vector which bisects the angle AOB given A and B are position vectors a=2i-2j-k and b=3i+4k?
  
• How do you find the coordinates of the center, foci, the length of the major and minor axis given #36x^2+81y^2=2916#?
  
• How do you find the missing side of each right triangle. Side c is the hypotenuse and Sides a and b are the legs, b=sqrt6 yd, c=4yd?
  
• How do you find the polar coordinates given #(-2, -2sqrt3)#?
  
• What is the arc length of #f(t)=(3t-4,t^3-2t) # over #t in [-1,2]#?
  
• How do you write an exponential function whose graph passes through (0,-0.3) and (5,-9.6)?
  
• How do you find the equation for a hyperbola centered at the origin with a horizontal transverse axis of lengths 8 units and a conjugate axis of lengths 6 units?
  
• How do you find the exact value of #sin(arcsin0.72)#?
  
• How do you write an equation for a hyperbola with vertices (1, 3) and (-5, 3), and foci (3, 3) and (-7, 3)?
  
• How do you find the second derivative of # ln(x^2+4)# ?
  
• Two corners of an isosceles triangle are at #(2 ,3 )# and #(1 ,4 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?
  
• How do you find the vector perpendicular to the plane containing (0,-2,2), (1,2,-3), and (4,0,-1)?
  
• What is the focus of the parabola #x + 5(y - 3)^2 = 6#?
  
• What is the period of #f(theta)= sin 7 t - cos 2 t #?
  
• How do you solve the system #y^2<x# and #x^2-4y^2<16# by graphing?
  
• How do you solve #log_2( 20x ( x - 11) )#?
  
• How do you solve the system #-3a-b-3c=-8#, #-5a+3b+6c=-4#, and #-6a-4b+c=-20#?
  
• How do you find the derivative of #y = arcsin(5x)#?
  
• How would you find the unit vector along the line joining point (2, 4, 4) to point (-3, 2, 2)?
  
• How do you find the slope of a tangent line to the graph of the function #f(x) = 5x^2 + x# at (-4, 76)?
  
• How do you integrate by substitution #int [x^2+1/(3x)^2]dx#?
  
• What is the slope of the tangent line of #r=(sin^2theta)/(-thetacos^2theta)# at #theta=(pi)/4#?
  
• What is the orthocenter of a triangle with corners at #(2 ,3 )#, #(5 ,1 )#, and (9 ,6 )#?
  
• How do you identity if the equation #2x^2+12x+18-y^2=3(2-y^2)+4y# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
  
• How do you find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (3,3) and C = (3, -2)?
  
• How do you find the particular solution to #ysqrt(1-x^2)y'-x(1+y^2)=0# that satisfies y(0)=sqrt3?
  
• What is the equation of the tangent line of #r=cos(2theta-pi/4)/sintheta - sin(theta-pi/8)# at #theta=(-3pi)/8#?
  
• How do you determine whether the pair (-2,-1) is a solution to #y> -sqrt(x+11)+1#?
  
• A triangle has corners A, B, and C located at #(5 ,2 )#, #(7 ,9 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
  
• How do you integrate #int (1-2x^2)/((x+1)(x-6)(x-7)) # using partial fractions?
  
• Which quadrant does (4, 0) lie?
  
• Question #b2680
  
• How do you find the inverse of #A=##((4, 4, 8), (3, 2, 6), (2, 1, 4))#?
  
• How do you simplify #(2-2i)*(-3+3i)#?
  
• Question #9cda7
  
• How do you graph #r = 4 / (2+sintheta)#?
  
• How do you multiply #((4, 0), (-1, 3), (2, -5))# with #((1),( -3))#?
  
• How do you write an equation of an ellipse in standard form given center at origin and passes through (√6, 2) and (-3, √2)?
  
• How do you solve these set of linear equations: #-2x + y - z = 2; - x - 3y + z = - 10; 3x + 6z = - 24#?
  
• How do you solve #-3x + 5y + z = 10#, #2x + 3y - z = 7#, and #-4x + 2y +3z = -1# using matrices?
  
• How do you solve #[(2x+y),(x-3y)]=[(5), (13)]#?
  
• How do you find the inverse of # f(x) = ln(4 - 7x) + ln(-7 - 5x)#?
  
• How do you simplify #Sin( cos^-1 (3/5))#?
  
• How do you rotate the axes to transform the equation #4x^2-sqrt3xy+y^2=5# into a new equation with no xy term and then find the angle of rotation?
  
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