Analytic Geometry and Conics
Determine the midpoint of the segment connecting P(1, 5) and Q(7, -3).
(4,1)
Find the 10th term of the arithmetic sequence 3, 7, 11, ...
39
Solve 3^(2x - 1) = 27 for x.
If cos(theta) = 3/5 and theta is in Quadrant IV, find sin(theta) and tan(theta).
Sin = -⅘ tan = -4/3
Find the inverse function of f(x) = 3x - 7.
(x+7)/3
Find the distance between points A(2, -1) and B(-3, 4).
5sqrt(2)
Find the sum of the first 12 terms of the arithmetic sequence 2, 5, 8, ...
222
Solve log base 2 of (x + 3) = 4 for x.
x=13
Express sin(2x) in terms of sin(x) and cos(x) and find sin(2π/3).
sin(2x)=2sin(x)cos(x) sin(2pi/3) = sqrt(3)/2
Determine if f(x) = x^3 - 6x + 2 is one-to-one.
Not one-one
Find the equation of the circle centered at (2, -3) with radius 5.
(x-2)^2+(y+3)^2=25
Determine the 6th term of the geometric sequence 4, 12, 36, ...
972
Simplify ln(e^(3x) * e^(-x)).
2x
Solve 2sin(x) - 1 = 0 for x in the interval 0 to 2π.
pi/6,5pi/6
Solve for x if f(x) = g(x) where f(x) = 2x^2 + 1 and g(x) = x + 5.
(1+sqrt(33))/4,(1-sqrt(33))/4
Determine the equation of a line passing through (1, 2) and perpendicular to y = 3x + 4.
y=-1/3x+7/3
Find the sum to infinity of the geometric series 8 + 4 + 2 + ...
16
If log(x) + log(x - 3) = 1, find x.
x=5
Verify the identity 1 + tan(x)^2 = sec(x)^2.
1 = (1-sin^2)/cos^2 = cos^2/cos^2 = 1
Determine the domain and range of f(x) = (2x - 3) / (x^2 - 4)
Domain: (-infty,-2)U(-2,2)U(2,infty)
Range: (-infty,infty)
Find the vertex, focus, and directrix of the equation y^2 - 4y - 8x + 16 = 0.
The Vertex is (1.5,2), the focus is (3.5,2), and directrix is x = -0.5
Find the sum to infinity of the geometric series 16 + 4 + 1 + ...
64/3
Solve e^(2x) - 5e^x + 6 = 0
ln(2),ln(3)
Simplify sin(x)^4 - cos(x)^4.
-cos(2x)
y = |x - 2| + 1, Identify any points of discontinuity
No Discontinuity