What is the solution set for the quadratic equation x^2 - 7x + 12 = 0?
Mathematics
Question · Easy
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Short
If log_2(x) + log_2(x - 2) = 3, what is the valid real value of x?
Question · Medium
A Kankor item asks for the domain of the real-valued function f(x) = sqrt(16 - x^2). Which interval is correct?
What is the value of the limit: lim_(x -> 0) (sin(5x) / (2x))?
What is the derivative of f(x) = x^3 * e^(2x) with respect to x?
Question · Hard
What is the value of the definite integral ∫ from 0 to 2 of (3x^2 - 4x + 1) dx?
In a right triangle, if sin(theta) = 3/5 and theta is in the first quadrant, what is the value of tan(2*theta)?
What is the center and radius of the circle given by the equation x^2 + y^2 - 6x + 8y = 0?
In an arithmetic progression beginning 3, 7, 11, 15, ..., what is the sum of the first 25 terms?
What is the determinant of the 2x2 matrix A = [[4, -2], [3, 5]]?
If a vector u = 3i - 4j and vector v = 2i + 5j, what is their dot product u · v?
How many distinct permutations can be formed from the letters of the word 'KANKOR'?
What is the equation of the tangent line to the curve y = x^2 - 3x + 5 at the point (2, 3)?
What is the asymptote of the rational function f(x) = (3x^2 - 5) / (x^2 - 4)?
What is the solution to the system of linear equations: 2x + 3y = 13 and x - 2y = -4?
What is the sum of the infinite geometric series: 12 + 6 + 3 + 1.5 + ...?
What is the area of a triangle with vertices at (0, 0), (4, 0), and (2, 6) in the Cartesian plane?
Which of the following is the inverse function f^(-1)(x) of f(x) = (2x + 5) / (x - 3), for x != 3?
What is the period of the trigonometric function f(x) = 4 * cos(3x - pi/2)?
What is the critical point of the function f(x) = x^3 - 6x^2 + 9x + 2, and what is its nature at x = 1?
What is the radius of convergence of the geometric power series sum_(n=0)^infinity (3x)^n?
If two fair standard 6-sided dice are rolled simultaneously, what is the probability that the sum of the numbers is 8?
What is the eccentricity of the ellipse given by the equation (x^2 / 25) + (y^2 / 16) = 1?
What is the value of x that satisfies the exponential equation 3^(2x - 1) = 27?
Using the remainder theorem, what is the remainder when P(x) = 3x^3 - 4x^2 + 2x - 9 is divided by (x - 2)?
What is the exact value of cos(75 degrees)?
What is the distance between the two parallel lines 3x + 4y - 10 = 0 and 3x + 4y + 15 = 0?
What is the solution set for the inequality |2x - 5| <= 7?
If matrix B = [[2, 1], [0, 3]], what is B^2?
What is the value of the limit lim_(x -> infinity) ((4x^3 - 2x + 1) / (7x^3 + 5x^2 - 9))?
A car accelerates uniformly from rest to a speed of 20 m/s over a distance of 100 meters. What is the acceleration of the car?
Natural Sciences
A 5 kg block is pushed across a horizontal surface with a force of 30 N. If the coefficient of kinetic friction between the block and surface is 0.2 and g = 10 m/s^2, what is the net acceleration of the block?
Three resistors of 3 ohms, 6 ohms and 9 ohms are connected in parallel. What is the equivalent resistance of the combination, to two decimal places?
A ray of light in air (n_1 = 1.0) strikes a glass block (n_2 = 1.5) at an angle of incidence of 30 degrees. What is sin(theta_2) of the angle of refraction?
According to the first law of thermodynamics, if a system absorbs 500 J of heat from its surroundings and does 200 J of work on the surroundings, what is the change in internal energy (Delta U)?
What is the de Broglie wavelength of an electron with mass m = 9.1 * 10^(-31) kg moving at a velocity of 2.0 * 10^6 m/s, given Planck's constant h = 6.63 * 10^(-34) J·s?
A transformer has 500 turns on its primary coil and 100 turns on its secondary coil. If an alternating voltage of 220 V is applied to the primary, what is the output voltage on the secondary coil?
A pendulum has a length L on Earth where acceleration due to gravity is g. If the length of the pendulum is quadrupled (4L), what happens to its period of oscillation T?
What is the buoyant force acting on a completely submerged object of volume 0.02 m^3 in water (density rho = 1000 kg/m^3, g = 9.8 m/s^2)?
An ideal gas at temperature 300 K occupies a volume of 2.0 L at a pressure of 1.0 atm. If the pressure is increased to 3.0 atm while temperature remains constant, what is the new volume?
Two point charges of +3 microcoulombs and +4 microcoulombs are separated by a distance of 0.3 meters in vacuum. Given Coulomb's constant k = 9.0 * 10^9 N·m^2/C^2, what is the electrostatic repulsive force between them?
What type of radioactive decay occurs when a Carbon-14 nucleus (Z = 6) decays into a Nitrogen-14 nucleus (Z = 7)?
What is the ground-state electron configuration of a neutral Iron (Fe) atom with atomic number Z = 26?
What is the pH of a 0.001 M aqueous solution of strong hydrochloric acid (HCl)?
How many moles of carbon dioxide (CO2) are produced by the complete combustion of 2.0 moles of propane (C3H8) according to the balanced reaction: C3H8 + 5 O2 -> 3 CO2 + 4 H2O?
Which of the following elements has the highest electronegativity on the Pauling scale?
According to Le Chatelier's principle, what will happen to the equilibrium of the exothermic Haber process reaction: N2(g) + 3 H2(g) <=> 2 NH3(g) + Heat, if the temperature of the reaction vessel is increased?
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