Answers edited by Leland Adriano Alejandro

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• 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?
  
• How do you solve `7y^2-5y-8=0` using the quadratic formula?
  
• 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?
  
• What is the variance of {15, 9, -3, 8, 0}?
  
• What are the mean and standard deviation of a binomial probability distribution with `n=210` and `p=12/21`?
  
• How do you evaluate the definite integral `int((sqrtx + 1)/(4sqrtx))^2 dx` from `[3,9]`?
  
• 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?
  
• How do you integrate `int (4x^2+6x-2)/((x-1)(x+1)^2)` using partial fractions?
  
• How do you express `cos theta - cos^2 theta + sec theta` in terms of `sin theta`?
  
• The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 4000 years?
  
• How do you differentiate `e^(-10x)`?
  
• 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?
  
• What is the equation of the line normal to `f(x)=x^3-6x` at `x=2`?
  
• 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?
  
• 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?
  
• How do you graph `r = 4sin(theta)`?
  
• How do you find the asymptotes for `y = x/(x-6)`?
  
• How do you find the exact value of `Arctan(1/2)`?
  
• What is the axis of symmetry and vertex for the graph `y = x^2 – 8x + 11`?
  
• How do you find the axis of symmetry, and the maximum or minimum value of the function `f(x)=x^2 -2x -15`?
  
• How to solve the separable differential equation and find the particular solution satisfying the initial condition y(−4)=3 ?
  
• 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?
  
• 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?
  
• How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?
  
• 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 integrate `int 1/sqrt(-e^(2x)-20e^x-101)dx` using trigonometric substitution?
  
• Half an avocado has about 160 calories. How many calories do a dozen avocados have?
  
• How do you integrate `int (x+5)/((x+3)(x-7)(x-5))` using partial fractions?
  
• 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?
  
• How do you differentiate `g(x) = (2x^2 + 4x - 3) ( 5x^3 + 2x + 2)` using the product rule?
  
• How do you graph `y=-1+tan2x`?
  
• What is the variance of {51, 3, 9, 15, 3, -9, 20, -1, 5, 3, 2}?
  
• What is the variance of {8, 19, 10, 0, 1, 0}?
  
• How do you find the inverse of `y = 2^x` and is it a function?
  
• Question #a8660
  
• How do you find the vertex of `y = 4x^2 + 8x + 7`?
  
• How do you graph `y = abs[x - 1] + 4`?
  
• How do you subtract and simplify `2``11/12` `- 3/16`?
  
• What is the equation of the line normal to `f(x)=cos(5x+pi/4)` at `x=pi/3`?
  
• 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?
  
• 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 find the asymptotes for `y = (7x-5)/(2-5x)`?
  
• How do you factor `x^9 - x^6 - x^3 + 1`?
  
• How do you find the area of the rectangle with vertices A(-3,0), B(-2,-1), C(1,2), D(0,3)?
  
• Is `4x = -6y` a direct variation equation and if so, what is the constant of variation?
  
• 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?
  
• How do you implicitly differentiate `xy + 3x + 5x^2 = 4/y^3-xy+1`?
  
• What is the cross product of `[3, 2, 5]` and `[-1, 2, 2]`?
  
• 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?
  
• 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?
  
• A triangle has corners at `(4 , 5 )`, `(3 ,2 )`, and `(5 ,3 )`. What is the radius of the triangle's inscribed circle?
  
• Question #e8044
  
• Question #3cbbc
  
• 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?
  
• What is the equation of the tangent line of `f(x)=cosx-e^xsinx` at `x=pi/3`?
  
• How do you divide `(7-9i)/(-2-9i)` in trigonometric form?
  
• How do you evaluate the definite integral `int t sqrt( t^2+1dt)` bounded by `[0,sqrt7]`?
  
• How do you decide whether the relation `x + y = 25` defines a function?
  
• A road repair crew can usually fix 825 potholes each week. How many potholes can they fix in 6 weeks?
  
• How do you express `cos(pi/ 3 ) * sin( ( 3 pi) / 8 )` without using products of trigonometric functions?
  
• 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?
  
• Is `f(x)=(3x^3-2x^2-2x+5)/(x+2)` increasing or decreasing at `x=3`?
  
• 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?
  
• What is the slope of the line normal to the tangent line of `f(x) = secx+sin(2x-(3pi)/8)` at `x= (11pi)/8`?
  
• 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 `(-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?
  
• What is the area under the polar curve `f(theta) = theta-thetasin((7theta)/8 )-cos((5theta)/3+pi/3)` over `[pi/6,(3pi)/2]`?
  
• What is the period of `f(theta) = tan ( ( 15 theta)/7 )- sec ( ( 5 theta)/ 6 )`?
  
• 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 identify the oblique asymptote of `f(x) = (2x^2+3x+8)/(x+3)`?
  
• What is the equation of the tangent line of `f(x)= x^2-3x+(3x^3)/(x-7)` at `x=2`?