Geometry
The term for a polygon where all angles have the same measure and all sides have the same length.
What is regular?
When a number is divisible by 3, this is always true about the sum of its digits. (The converse is also true.)
What is divisible by 3?
The term for a shape where for all points on this shape, the sum of the two distances to the focal point is constant. This shape has equation:
x2/a2 + y2/b2 = 1
What is an ellipse?
This value is equal to the slope of the tangent line to a curve.
The term for when two angles add up to 90 degrees.
What are complementary angles?
In the quadratic formula, when this value equals 0, the equation only has one solution.
What is the determinant, or b2 - 4ac
Each point on a parabola has the same distance to the focus of the parabola as to this fixed line.
What is directrix?
This system of coordinates has the form (r, theta), where r is the distance from the point to the origin, and theta is the angle from the positive x axis to the point.
What is polar coordinates?
The complement of angle A has a measure that is seven less degrees than half of the measure of the supplement of angle A. Find the measure of angle A.
What is 14 degrees?
The number of birds in Kim's aviary doubles every three months. If after nine months she has b birds, find the number of birds she will have after y years. (Write your answer as an expression in terms of b and y)
What is b(2(4y - 3))?
The number of real and complex solutions to the equation x3 = -8.
What is 3?
The slope of the tangent line to the graph of y = x2 + 20x + 22 at x = a is 50. Find a.
What is 15?
The length of the diagonal of a square with perimeter 200.
What is 50sqrt(2)?
A political polling firm is studying the voting patterns of husbands and wives. Suppose the probability that a married man votes is 0.45 while the probability that a married woman votes is 0.40. The probability that a married woman votes, given that her husband votes, is 0.60. Find the probability that both husband and wife vote.
What is 0.27?
Evaluate log49(343) + log49(7) - log2(512)
What is -7?
Approximate sqrt(2022) using a tangent-line approximation to the graph of y = sqrt(x) at (2024, 45).
What is 1349/30
A solid right circular cylinder is metal. It has radius 3 cm and height 12 cm. It is melted down with no loss of material, and the metal is poured into molds to make solid congruent spheres of radius 3 cm each. Find of the number of these spheres that can be made.
What is 3?
The function f is both an even and an odd function. Find f(2021).
What is 0?
Compute sin(pi/12) * cos(5pi/12)
What is (2 - sqrt(3))/2
Approximate the integral from 0 to 2 of x^2 + 3x dx, using a left handed Riemann sum with four equally sized subintervals.
What is 25/4