Appearance
question:Determine the limit of #(x^3-8)/(x^2-4)# as x approaches 2 using L'Hopital's Rule.
answer:Applying L'Hopital's Rule by differentiating the numerator and denominator separately, we obtain: #lim_(x->2)(3x^2)/(2x)=lim_(x->2)(3/2)x=3#
question:Explain why electronegativity is considered a dimensionless property?
answer:Electronegativity is dimensionless because it represents a tendency, not a measurable quantity. It indicates the relative ability of atoms to attract electrons, but does not have any units of measurement.
question:Calculate the maximum allowable volume of ammonia leakage (in m^3) for a 2000 m^3 room at 120 kPa and 295 K, if the toxic level of ammonia is 0.60% by volume.
answer:STEP 1: Given values: * Pressure (P) = 120 kPa * Temperature (T) = 295 K * Molar mass of NH3 = 17 g/mol * Gas constant (R) = 8.314 J/(mol*K) = 0.489 kJ/(kg*K) STEP 2: Calculate the density of air: ``` ρ = P/(RT) = (120*10^3)/(0.489*10^3*295) = 0.83 kg/m^3 ``` STEP 3: Calculate the volume of ammonia for the mixture to be toxic: ``` Volume of ammonia = 0.60/100 * 2000 = 12 m^3 ``` Therefore, the maximum allowable volume of ammonia leakage for a 2000 m^3 room is 12 m^3.
question:What is the minimum GMAT score required to be admitted to a program that accepts only the top 3% of applicants, given that the GMAT is normally distributed with a mean of 545.6 and a standard deviation of 121.07?
answer:Given: Population mean: {eq}mu = 545.6 {/eq} Population standard deviation: {eq}sigma = 121.07 {/eq} {eq}P(X < x) = 0.03 P(dfrac{X - mu}{sigma} < dfrac{x- mu}{sigma}) = 0.03 P(Z < dfrac{x- 545.6}{121.07}) = 0.03 P(Z < z) = 0.03 {/eq} Excel function for the value of z: =NORMSINV(0.03) {eq}z = -1.88 dfrac{x - 545.6}{121.07} = -1.88 x = 545.6+1.88times 121.07 x = 773.21 {/eq} Therefore, the minimum GMAT score required to be admitted to the program is 773.21.