Answers edited by Leland Adriano Alejandro

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• What is the equation of the tangent line of #f(x)= x^2-3x+(3x^3)/(x-7)# at # x=2#?
  
• A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #7 # and #8 # and the pyramid's height is #5 #. If one of the base's corners has an angle of #pi/4#, what is the pyramid's surface area?
  
• How do you factor #x^9 - x^6 - x^3 + 1#?
  
• How do you find the inverse of #y = 2^x# and is it a function?
  
• How do you find the area of the rectangle with vertices A(-3,0), B(-2,-1), C(1,2), D(0,3)?
  
• The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 4000 years?
  
• Question #e8044
  
• How do you differentiate #e^(-10x)#?
  
• How do you integrate #int 1/sqrt(-e^(2x)-20e^x-101)dx# using trigonometric substitution?
  
• What is the variance of {8, 19, 10, 0, 1, 0}?
  
• Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(2 ,-1 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
  
• What is the equation of the line normal to #f(x)=x^3-6x # at #x=2#?
  
• How do you graph # y=-1+tan2x#?
  
• How do you integrate #int (x+5)/((x+3)(x-7)(x-5)) # using partial fractions?
  
• How to solve the separable differential equation and find the particular solution satisfying the initial condition y(−4)=3 ?
  
• Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/12 #, what is the difference between the areas of the rhombuses?
  
• What is the slope of the line normal to the tangent line of #f(x) = secx+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?
  
• How do you identify the oblique asymptote of #f(x) = (2x^2+3x+8)/(x+3)#?
  
• A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #60 #, what is the length of its longest diagonal?
  
• A triangle has corners at #(6, 5 )#, ( 3, -6)#, and #(8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
  
• What is the cross product of #[3, 2, 5]# and #[-1, 2, 2] #?
  
• Circle A has a center at #(1 ,5 )# and an area of #24 pi#. Circle B has a center at #(8 ,4 )# and an area of #66 pi#. Do the circles overlap?
  
• How do you evaluate the definite integral #int((sqrtx + 1)/(4sqrtx))^2 dx # from #[3,9]#?
  
• What is the period of #f(theta) = tan ( ( 15 theta)/7 )- sec ( ( 5 theta)/ 6 ) #?
  
• How do you evaluate the definite integral #int t sqrt( t^2+1dt)# bounded by #[0,sqrt7]#?
  
• The volume inside a rectangular storage room is 2,025 cubic feet. The room is 9 feet high. What is the area of the floor?
  
• How do you differentiate #g(x) = (2x^2 + 4x - 3) ( 5x^3 + 2x + 2)# using the product rule?
  
• Question #3cbbc
  
• What is the variance of {15, 9, -3, 8, 0}?
  
• A circle has a center that falls on the line #y = 1/8x +4 # and passes through # ( 5 ,8 )# and #(5 ,6 )#. What is the equation of the circle?
  
• Two corners of an isosceles triangle are at #(6 ,4 )# and #(4 ,1 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?
  
• A triangle has corners at #(-6 ,3 )#, #(3 ,-2 )#, and #(5 ,4 )#. If the triangle is dilated by a factor of #5 # about point #(-2 ,6 ), how far will its centroid move?
  
• Question #a8660
  
• How do you integrate #int (4x^2+6x-2)/((x-1)(x+1)^2)# using partial fractions?
  
• What is the axis of symmetry and vertex for the graph #y = x^2 – 8x + 11#?
  
• If a projectile is shot at an angle of #(7pi)/12# and at a velocity of #2 m/s#, when will it reach its maximum height?
  
• Circle A has a center at #(5 ,4 )# and a radius of #4 #. Circle B has a center at #(6 ,-8 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
  
• Circle A has a center at #(5 ,8 )# and an area of #18 pi#. Circle B has a center at #(3 ,1 )# and an area of #27 pi#. Do the circles overlap?
  
• Triangle A has sides of lengths #1 3 ,1 4#, and #11 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?
  
• Half an avocado has about 160 calories. How many calories do a dozen avocados have?
  
• What are the mean and standard deviation of a binomial probability distribution with #n=210 # and #p=12/21 #?
  
• The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,1 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
  
• How do you implicitly differentiate # xy + 3x + 5x^2 = 4/y^3-xy+1#?
  
• How do you subtract and simplify #2##11/12# #- 3/16#?
  
• How do you graph #y = abs[x - 1] + 4#?
  
• How do you solve #7y^2-5y-8=0# using the quadratic formula?
  
• How do you divide # (7-9i)/(-2-9i) # in trigonometric form?
  
• How do you express #cos(pi/ 3 ) * sin( ( 3 pi) / 8 ) # without using products of trigonometric functions?
  
• A cheetah was chasing and antelope which is 700m away. How many minutes will it take the cheetah, which is running at a constant speed of 110km/h to reach the antelope that is running at a constant speed of 75km/h?
  
• Is #f(x)=(3x^3-2x^2-2x+5)/(x+2)# increasing or decreasing at #x=3#?
  
• How do you find the axis of symmetry, and the maximum or minimum value of the function #f(x)=x^2 -2x -15#?
  
• Circle A has a center at #(-9 ,-1 )# and a radius of #3 #. Circle B has a center at #(-8 ,3 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?
  
• How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?
  
• What is the variance of {51, 3, 9, 15, 3, -9, 20, -1, 5, 3, 2}?
  
• Circle A has a center at #(-1 ,-4 )# and a radius of #3 #. Circle B has a center at #(-1 ,1 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
  
• How do you find the vertex of #y = 4x^2 + 8x + 7#?
  
• Is #4x = -6y# a direct variation equation and if so, what is the constant of variation?
  
• A triangle has corners at #(4 , 5 )#, #(3 ,2 )#, and #(5 ,3 )#. What is the radius of the triangle's inscribed circle?
  
• What is the equation of the tangent line of #f(x)=cosx-e^xsinx # at #x=pi/3#?
  
• How do you decide whether the relation #x + y = 25# defines a function?
  
• How do you find the asymptotes for #y = (7x-5)/(2-5x)#?
  
• How do you graph # r = 4sin(theta)#?
  
• What is the area under the polar curve #f(theta) = theta-thetasin((7theta)/8 )-cos((5theta)/3+pi/3) # over #[pi/6,(3pi)/2]#?
  
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #9 #. What is the area of the triangle's incircle?
  
• Circle A has a center at #(2 ,8 )# and a radius of #4 #. Circle B has a center at #(-3 ,3 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?
  
• A road repair crew can usually fix 825 potholes each week. How many potholes can they fix in 6 weeks?
  
• A rectangular piece of fabric measures 38 by 36 inches. A triangular scarf with a height of 23 inches and a base of 30 inches is cut from the fabric. What is the area of the fabric left over?
  
• How do you find the exact value of #Arctan(1/2)#?
  
• How do you express #cos theta - cos^2 theta + sec theta # in terms of #sin theta #?
  
• How do you find the asymptotes for #y = x/(x-6)#?
  
• What is the equation of the line normal to # f(x)=cos(5x+pi/4)# at # x=pi/3#?