Answers edited by Ratnaker Mehta

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• How do you express `f(theta)=sin^2(theta)+6cot^2(theta)-8cos^4theta` in terms of non-exponential trigonometric functions?
  
• What's the derivative of `f(x) = (arctan (x/2)) + ((5x-1)/(2(x^2) + 4))`?
  
• How do you find the slope given (0,5) and (-3, -4)?
  
• The mean of 3 numbers is 7. The mean of 4 other numbers is 8. The mean of 5 other numbers is 11. What is the mean of all 12 numbers?
  
• How do you evaluate `log_7 (-49)`?
  
• The sides of a triangle measure 6 inches 8 inches, and 10 inches. The triangle has one 90° angle. What type of triangle is it?
  
• How do you find the parametric equations of the line of intersection of the planes x+2z=0 and 2x-3y+4?
  
• Question #64850
  
• How do you find the 7th term of 2(sqrt{5}), 4(sqrt{5}), 6(sqrt{5}), ...?
  
• If sin A > 0 and tan A < 0, then A is in what quadrant?
  
• How do you find the first and second derivative of `(ln(x^2-1))/x^2`?
  
• How do you find the exact value of `csc ((5pi)/6)` using the half angle formula?
  
• How do you integrate `{x(sqrt(1+x^2)} dx` from 0 to 1?
  
• How do you use the sum and difference identity to evaluate `sin((7pi)/12)`?
  
• Segment `ST` has endpoints of `S(-2, 4)` and `T(-6, 0)`. What is the midpoint of segment `ST`?
  
• A line segment is bisected by a line with the equation `4 y - 3 x = 2`. If one end of the line segment is at `( 7 , 5 )`, where is the other end?
  
• How do you evaluate the definite integral `int (2t-1)^2` from `[0,1]`?
  
• How do you solve `(e-2)/2=(e+2)/3`?
  
• How do you find the derivative of `Y= (e^x-e^-x)/(e^x+e^-x)`?
  
• How do you solve the following equation `sin 2x - sin x = 0` in the interval [0, 2pi]?
  
• How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-5,9) and midpoint M(-8,-2)?
  
• How do you evaluate `sec^-1(sec((5pi)/6))`?
  
• How do you solve `sqrt(x+6)-5=x+1` and find any extraneous solutions?
  
• What is the limit of `(t^(1/3)-2)/(t-8)` as t approaches 8?
  
• How do you find the limit of `(1-sin(theta))/(1+cos(2theta))` as theta approaches pi/2?
  
• How do you solve `3|2y-5|=27` and find any extraneous solutions?
  
• How do you simplify `(3+9i)/(3i)`?
  
• How do you find the limit of `sec3xcos5x` as x approaches pi/2 from the left?
  
• How do you determine `(d^y)/(dx^2)` given `1-xy=x-y^2`?
  
• Bradley is extending his rectangular living room. The original dimensions are 6 feet by 11 feet. If he extended his room by `x+8` feet, what is the new area? How many square feet of area did he add?
  
• Can you construct a triangle that has side lengths 8 m, 10 m, and 19 m?
  
• How do you solve `1+ 6( 2x + 3) ^- 1+ 8( 2x + 3) ^- 2= 0`?
  
• How do you differentiate `sin^2(x/2)`?
  
• Question #e1c7e
  
• What are all the possible rational zeros for `f(x)=2x^3-4x+8` and how do you find all zeros?
  
• How do you find the second derivative of `ln(x/2)` ?
  
• How do you prove `[(sin 3x) / sin x ] – [(cos3x) / cos x)] = 2`?
  
• How do you evaluate the limit `(sqrt(x+1)-2)/(x^2-9)` as x approaches -3?
  
• Use the exponential growth model `P(t) = P_0e^(kt)`. The half-life of thorium-229 is 7,340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?
  
• What is the equation of the line that is normal to `f(x)=-e^x` at `x=-2`?
  
• What is the antiderivative of `x^3/(1+x^2)`?
  
• The length of a rectangular piece of carpet is 4 yards greater than the width. How do you express the area of the carpet as a function of the width?
  
• How do you find the x and y intercept of `4x + y = – 8`?
  
• Question #f9011
  
• There are 15 students. 5 of them are boys and 10 of them are girls. If 5 students are chosen, what is the probability that there are at least 2 boys?
  
• A circle has a center that falls on the line `y = 8/7x +2` and passes through `( 7 ,8 )` and `(3 ,9 )`. What is the equation of the circle?
  
• How do you find the value of `sin(theta/2)` given `tantheta=2` and `0<theta<pi/2`?
  
• How to find the distance from the point A(3,-5,5) to the line x = 2 + 3t , y= 1-2t, z= -1 + t ?
  
• How do you solve the equation on the interval [0,2pi) for `sin 3x = -sinx`?
  
• In a class of 300 students, 242 take math, 208 take science, and 183 take both math and science. How many students take neither math nor science?
  
• There were five people in group A, with a mean lQ of 100, and five in group B, with a mean IQ of 74. When Jack left group A for group B, both means increased, and the total of the two new means was 180. What Is Jack's IQ?
  
• How do you solve `5+(sqrt(x+2))=8+(sqrt(x-7))`?
  
• How do you simplify `(3sinx)/cos^2x*(cos^2x+cosxsinx)/(sin^2x-cos^2x)`?
  
• How do you find the domain and range of `f(x) = -x^2 + 2x + 1`?
  
• Question #58346
  
• Question #56a98
  
• Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. How do you find the numbers?
  
• How do you simplify `(8i)(7-3i)`?
  
• How do you integrate `(x^2-1)/(x^4-16)` using partial fractions?
  
• There are 3 red and 8 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probability of choosing 2 red balls and then 1 green ball?
  
• How do you find the equation of a circle whose center of this circle is on the line 2x-5y=9 and it is tangent to both the x and y axis?
  
• Question #9adaf
  
• How do you integrate `e^x*cos(x)`?
  
• How do you show `cos (arctan x) = [ 1 / ( sqrt(1 + x^2))]`?
  
• How do you determine algebraically the x coordinate of all points where the graphs of xy=10 and y= x+3 intersect?
  
• How do you implicitly differentiate `-1=(x+y)^2-xy-e^(3x+7y)`?
  
• How do you integrate `x/((x-1)(x^2+4)` using partial fractions?
  
• What is the equation of a circle with center `(2, -3)` and radius of `3`?
  
• How do you integrate `int x^3sqrt(x^2-1)` using substitution?
  
• Question #4f402
  
• What is the limit of `((1)+(3/x)+(5/x^2))^x` as x approaches infinity?
  
• Question #3e542
  
• How do you find the exact value of `arccos(sin(3*pi/2))`?
  
• How do you write the equation of a parabola in vertex form that has a focus at `(6,5)` and a directrix of `y=-1`?
  
• Let `a,b,c,m` and `n` be integers such that `m<n` and define the quadratic function `f(x) = ax^2+bx+c` where `x` is real. Then `f(x)` has a graph that contains the points `(m,0)` and `(n, 2016^2)`. How many values of `n-m` are possible?
  
• If `f(x)=1/(x+1)` how do you evaluate `(f(x+h)-f(x))/h`?
  
• A chord with a length of `3` runs from `pi/4` to `pi/3` radians on a circle. What is the area of the circle?
  
• Question #4d43b
  
• How do you find the domain and range of `f(x)=1/(x+3)`?
  
• Suppose an experiment begins with 5 bacteria, and the bacteria population triples every hour. What would be the population of the bacteria after 6 hours?
  
• How do you write the equation in point slope form given (8,7), (-2,-4)?
  
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