What are the roots of the quadratic equation 2x^2 - 5x - 3 = 0?
Mathematics
Question · Medium
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What is the value of log_10(1000) - log_10(10)?
Question · Easy
In an arithmetic progression, the first term is a_1 = 5 and the common difference is d = 3. What is the 15th term (a_15)?
What is the exact value of sin^2(60 degrees) + cos^2(60 degrees)?
What is the derivative of the function f(x) = 4x^3 - 5x^2 + 7x - 9 with respect to x?
Same battery. Which lets more through?
What is the slope of the straight line given by the equation 3x + 2y - 8 = 0?
What is the value of the definite integral ∫ from 1 to 3 of 2x dx?
What is the distance between the two points A(1, 2) and B(4, 6) in the Cartesian coordinate plane?
What is the solution for x in the equation 2^(x + 3) = 32?
Factor it
What is the value of the limit: lim_(x -> 2) ((x^2 - 4) / (x - 2))?
What is the sum of the interior angles of a convex polygon with 6 sides (a hexagon)?
If tan(theta) = 4/3 and theta is an acute angle in a right-angled triangle, what is the value of cos(theta)?
What is the area of a circle with a radius of 7 cm (using pi ≈ 22/7)?
What is the common ratio (r) of the geometric sequence 4, 12, 36, 108, ...?
What is the solution set of the linear inequality 3x - 7 > 8?
If a fair coin is tossed three times, what is the probability of obtaining exactly two heads?
What is the maximum value of the quadratic function f(x) = -x^2 + 6x - 5?
Question · Hard
Evaluate the expression sin(30 degrees) * cos(60 degrees) + cos(30 degrees) * sin(60 degrees).
A stone is dropped from the top of a tower and hits the ground after 4.0 seconds. Assuming g = 9.8 m/s^2 and neglecting air resistance, what is the height of the tower?
Physics
According to Newton's Second Law of Motion, what net force is required to accelerate a 1,200 kg vehicle at a rate of 2.5 m/s^2?
What is the kinetic energy of an object of mass 4 kg moving with a uniform velocity of 10 m/s?
What is the electric current flowing through an electric heater with a resistance of 44 ohms connected to a 220 V household power outlet?
What happens to the focal length of a concave spherical mirror when it is submerged completely under water?
What is the speed of sound in dry air at a temperature of 0 degrees Celsius?
What is the phenomenon where a moving sound source produces a higher perceived frequency as it approaches an observer and a lower frequency as it recedes?
Which of the following is the SI unit of electric capacitance?
According to the Photoelectric Effect equation (E = h*f = W_0 + KE_max), what happens when light with a frequency lower than the metal's threshold frequency (f < f_0) shines on the metal surface?
What is the equivalent resistance of two 6-ohm resistors connected in series, followed by a third 12-ohm resistor in parallel with that combination?
What is the pressure exerted by a force of 600 N applied perpendicularly over a flat rectangular surface of area 2.0 m^2?
Which of the following electromagnetic waves has the shortest wavelength and highest photon energy?
What is the amount of heat energy required to raise the temperature of 2.0 kg of liquid water (specific heat capacity c = 4,184 J/(kg·°C)) by 10 °C?
What is the law of physics stating that the induced electromotive force (EMF) in a closed circuit is directly proportional to the time rate of change of magnetic flux through the circuit?
What type of radioactive radiation consists of high-speed positively charged helium nuclei (^4_2He)?
An ideal transformer has 200 primary turns and 800 secondary turns. If the input primary AC voltage is 50 V, what is the output secondary voltage?
What is the total number of protons, neutrons, and electrons in a neutral Sodium-23 atom (^23_11Na)?
Chemistry
What is the molarity (M) of an aqueous solution prepared by dissolving 40.0 g of Sodium Hydroxide (NaOH, molar mass = 40.0 g/mol) in sufficient distilled water to make 2.0 liters of solution?
What type of chemical bond is formed when electrons are transferred completely from a metal atom to a non-metal atom, forming electrostatic attraction between oppositely charged ions?
What is the pH of a neutral aqueous solution at standard 25 degrees Celsius?
What is the general molecular formula for acyclic saturated hydrocarbons (alkanes)?
How many liters of volume does 1.0 mole of an ideal gas occupy at Standard Temperature and Pressure (STP: 0 °C and 1.0 atm)?
What is the catalyst used in the industrial Haber-Bosch process for synthesizing ammonia from nitrogen and hydrogen (N2 + 3 H2 -> 2 NH3)?
What is the oxidation state of Manganese in Potassium Permanganate (KMnO4)?
Which of the following organic compounds is an alcohol containing a hydroxyl (-OH) group?
What is the common chemical name of baking soda?
Across a period from left to right on the Periodic Table, what general trend is observed regarding atomic radius and electronegativity?
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