Questions asked by Kat

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• Prove that #(1-sin2x)/(1-cosx)=-cosx#?
  
• Prove that #(tanx-cotx)/(tanx+cotx)=1-2cos^2x#?
  
• Prove that sinxtanx+cosx=secx (where x is theta)?
  
• Determine the [OH-] of a solution that is 0.100 M in F-? Determine the pH of this solution?
  
• Lne^x=5 I know that x=5 but why?
  
• 1) Log(4)64=x 2) Log(3)243=2x+1 The numbers in parenthesis is the base. I know the first one I can just throw in the calculator, but that's now how we're supposed to solve these ones. What's the value of x?
  
• 1) Log(2)8^x= - 3 2) 5e^0.2x=7 The 2 in parenthesis is the base. What's the value of x?
  
• 2*10^2-x=5 What is x?
  
• 2cos^2x+sqrt(3)cosx=0 solution set: {pi/2, 3pi/2, 7pi/6, 5pi/6} I can't figure out how to get those solutions?
  
• 5sinx=5sqrt(3)cosx 0<x<2pi What are all possible solutions in radians?
  
• Tanx=(-2sqrt3/3)sinx 0<x<2pi What are all possible solutions?
  
• Solve an equilibrium problem (using an ICE table) to calculate the pH of of each solution: a solution that is 0.18M of HCHO2 in 0.14M of NaCHO2. What is the pH?
  
• 5sinx=5sqrt3cosx 0<x<2pi What are all possible solutions?
  
• 2sin^2x-9sinx+7=0 What's the solution set?
  
• Tanx=(2sqrt3/3)sinx What are all solutions?
  
• Without doing any calculations, determine the sign of ΔSsys and ΔSsurr for each of the chemical reaction. Predict under what temperatures (all, low, or high), if any, the reaction will be spontaneous? C3H8(g)+5O2(g)→3CO2(g)+4H2O(g) #ΔH_"rxn"^o =−2044kJ#
  
• Calcium phosphate will precipitate out of blood plasma when calcium concentration in blood is 9.2mg/dL, and Ksp for calcium diphosphate is 8.64x10^(-13), what minimum concentration of diphospate results in precipitation?
  
• All the oxides of nitrogen have positive values of dGof at 298K, but only one common oxide of nitrogen has a positive dSof. Identify that oxide of nitrogen without reference to thermodynamic data and explain.?
  
• A 100mL sample of 0.10 M NH3 has a Kb of 1.8*10^-5. What is the pH?
  
• A 1.50 L buffer solution is 0.250 M HF and 0.250 M NaF. What is the pH of the solution after the addition of 0.0500 moles of solid NaOH? Assume no volume change. Ka for HF is 3.5x10^-4
  
• Conics Question: Graph the equation x=-3y^2+12y+13 What are all applicable points? (vertex, focus, etc.)
  
• What's the equation of the circle? The end points of the diameter (4,8) and (8,-10)
  
• Graph the equation. #(3x^2)-(2y^2)-9x+4y-8=0# What are all applicable points (vertex, focus, center, etc)?
  
• Solve for x and y? xy-x^2= -20 x-2y=3
  
• Xy-x^2= -20 x-2y=3 What is x and y?
  
• (3x^2)-(2y^2)-9x+4y-8=0 Graph and find all applicable points (center, vertex, focus, asymptote)?
  
• A voltaic cell consists of a Zn/Zn2+ half-cell and a Ni/Ni2+ half-cell at 25 ∘C. The initial concentrations of Ni2+ and Zn2+ are 1.60 M and 0.130 M , respectively. What is [Ni2+] and [Zn2+] when the cell potential is 0.45V?
  
• The Ksp for BaCO3 is 5.1*10^-9. How many grams of BaCO2 will dissolve in 1000 ml of water?
  
• How does #(1-sqrt(2/2))/(sqrt(2/2))# simplify to #-sqrt2+1#?
  
• Solve the equation on the interval 0<x<2pi Cos^2x-sin^2x=1-sinx What is the whole solutions set?
  
• In which reaction does kp=kc? a) NO(g)+O2(g) <-->N2O3(g) b) N2(g)+O2(g) <-->2NO(g) c) CaCO3(s) <-->CaO(s)+CO2(g) d) N2(g)+H2O(g) <-->NO(g)+H2(g) e) None
  
• Consider s(t)=5sin(t) describes a block bouncing on a spring. Complete the table with average velocities. Make the conjecture about the value of the instantaneous velocity at t=pi/2?
  
• Simplify this division of square roots?
  
• How does this simpify?
  
• Evaluate? #lim/(xrarr0)##((2+h)^3-8)/h#
  
• Evaluate? #lim/(xrarr0)#(#1/(tsqrt(1+t))-1/t#)
  
• Give example of functions f and g such that #lim_(xrarrc)[f(x)*g(x)]# exists but either #lim_(xrarrc)f(x)# or #lim_(xrarrc)g(x)# does not?
  
• If #lim_(xrarr2)(f(x)-4)/(x-2)=C# for constant C. Find #lim_(xrarr2)#f(x). What theorems were used to come to conclusion?
  
• What is the limit? #lim_(x to -oo) (x+2)/(sqrt(9x^2+1)#
  
• What are the values for a & b that make f continuous? f(x)=#(x^2-4)/(x-2)# if #x<=2#; f(x)=#ax^2+bx+3# if 2<x<3; f(x)=2x-a+b if #x>=3#
  
• What is the limit? #lim_(theta->0)(tan(3theta^2)+sin^2 5theta)/(theta^2)# and #lim_(x->oo)(cos(pi/x))/(x-2)#
  
• What is the limit? #lim_(x->oo)cos(2tan^-1x)#
  
• What is a nonzero k that makes the function continuous at x=0? f(x) is #(tankx)/(x), x<0# and #3x+2k^2, x>=0#
  
• What is the limit? #lim_(xrarr2) (cos(pi/x))/(x-2)#
  
• What is it limit as #xrarr9#? #sqrtr/((r-9)^4)#
  
• Using the property of derivative differentiate? #root5(x^3)#
  
• What is #(d^2y)/(dy^2)#? #y^3+3x^4y-x^2=siny#
  
• A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
  
• What are the intervals which f increases and decreases, where f is concave up and down, and coordinates of inflection points? #x^4-5x^3+9x^2#
  
• g(x)=#int_sqrtx^xtan^(-1)tdt# Find? 1) g(#sqrt3#) 2) g'(#sqrt3#) 3) g"(#sqrt3#)