Questions asked by Ben Mai

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• How to I write half reactions and balance this oxidation-reduction reaction? #S_2O_(8(aq))^(2-) + Cr_((aq))^(3+) -> SO_(4(aq))^(2-) + Cr_2O_(7(aq))^(2-)#
  
• How could a strong acid have the same pH as a weak acid?
  
• The equation of line m is 8x-7y+10=0. a. For what value of k is the graph kx-7y+10=0 parallel to line m? b. What is k if the graphs of m and kx-7y+10=0 are perpendicular?
  
• Write an equation for a line that is parallel to the equation y= -9. The line must pass through the points (4, -11). How do I do this?
  
• How many grams of acetic acid would you use to make 10 L of a 0.1 M aqueous solution of acetic acid?
  
• A slice of pizza has 500 kcal. If the pizza is burned and its heat is used to warm a 50-L container of cold water, what would be the approximate increase in the temperature of the water? (Note: A liter of cold water weighs about 1 kg).
  
• What is the inverse of f(x) if f(x) = x ?
  
• Evaluate the inverse of f(5) where f(x) = 6 - x ?
  
• If f(x) = (x+1) / (x-2), find the inverse of f(x) ?
  
• If f(x) = 7-2x and g(x) = x+3 . A. What is g^-1 (x) ? B. What is f(g^-1(5)) ?
  
• If f(x) = 3x, g(x) = 2x - 5 and h(x) = f(g(x)) . What is the inverse of h(x) ?
  
• If #f(x) = sqrt(x - 5)#, for #x ≥ 5#, what is the inverse of #f(2)# ?
  
• Given that the inverse of h(a) = 3, what is the value of a ?
  
• What is the inverse of f(x) = -1/5x -1 ?
  
• Let f(x) = 2- x^2 and g(x) = x^2 -2. How do you solve f(x) = g(x) ?
  
• Solve 2x - 1 = (x + 1)÷(2x) by factorization?
  
• You are building a fence on a rectangular lot. Only three sides of the lot will be fenced. You have 15 meters of wood for the fence, what is the area of the largest lot you could build?
  
• A piece of wire 40 cm long is cut into two square pieces. If the side length of one of the squares is x cm, what is the side length of the other square?
  
• How do you factor the equation y = -2x^2 +3x +5 into the form y = (x-p)(x-q)?
  
• How can I simplify #(2n)/(4n^(1/2))#?
  
• How can I simplify #((f^-16)/(256g^4h^-4))^(-1/4)#?
  
• How do I simplify #((x^2)/(4y^-2))^(-1/2)#?
  
• How do you solve: 3^(2-x) = 4^(2x-5) using logs?
  
• How do you solve: 3^(x/3) = 5^(x+3) using logs?
  
• Let #f(x) = klog_2x# Given that #f^-1 (1) = 8# , what is the value of k?
  
• If 2#cos^2x# - #cosx# = 1 , what is the value of #x#?
  
• If 1 + #cosx# - 2#sin^2x# = 0 , what is the value of #x#?
  
• If 2#cos^2x# - 2#sin^2x# = 1 , what is the value of #x#?
  
• What is the equation of the tangent line of #f(x) = (x^3 - 3x + 1)(x + 2)# at the given point of (1, -3) ?
  
• At which point(s) does the graph of the function #f(x) = (x^2) / (x - 1)# have a horizontal tangent line?
  
• What is the second derivative of the function #f(x) = (x) / (x - 1)#?
  
• What is the derivative of #f(x) = x(sqrt( 1 - x^2))#?
  
• What is the derivative of #f(x) = ((x+5)/(x^2+2))^2#?
  
• What is the derivative of #f(x) = sin2x*cos2x#?
  
• How do you find the equation of the tangent line of the function #f(x) = sin(2x)# when given the point (#pi,0#)?
  
• What is the derivative of the function #y=sin(xy)#?
  
• At which points does the graph of the equation #25x^2+16y^2+200x-160y+400=0# have a vertical or horizontal tangent line?
  
• What is the derivative of #x^(2/3)+y^(2/3)=5# at the given point of #(8,1)#?
  
• What are the x-values on the graph of #y= 1/x# where the graph is parallel to the line #y= -4/9x+7#?
  
• Let #f# be the function given by #f(x) = 2x^4-4x^2+1#. What is an equation of the line tangent to the graph at #(-2,17)#?
  
• What is an equation of the line tangent to the graph of #y=cos(2x)# at #x=pi/4#?
  
• A square is inscribed in a circle. How fast is the area of the square changing when the area of the circle is increasing at the rate of 1 inch squared per minute?
  
• A collapsible spherical tank is being relieved of air at the rate of 2 cubic inches per minute. At what rate is the radius of the tank changing when the surface area is 12 square inches?
  
• For what value of #k# will #x+k/x# have a relative maximum at #x=2#?
  
• What is the slope of the tangent line to the equation #y=x^2(3x+1/x^3)# at #x=1/3#?
  
• The function #f(x) = tan(3^x)# has one zero in the interval #[0, 1.4]#. What is the derivative at this point?
  
• At how many points on the curve #y = 4x^5-3x^4+15x^2+6# will the line tangent to the curve pass through the origin?
  
• What is the value of #F'(x)# if #F(x) = int_0^sinxsqrt(t)dt# ?
  
• How do you integrate #int_1^eln(x)/xdx#?
  
• Does the series #sum_(n=1)^oo((2n)/(n!))# converge or diverge?
  
• Does the series #sum_(n=1)^oo(1+1/n)^(n^2)# converge or diverge?
  
• Does the series #sum_(n=1)^oo((2^(n-1)3^(n+1))/n^n)# converge or diverge?
  
• Does the series #sum_(n=1)^oo(-1)^nlnn/sqrtn# converge or diverge?
  
• How do I use Taylor expansions to show that #e^(itheta) = cos(theta) + isin(theta)#? Using this, what is the value of #e^(ipi) +1#?
  
• What is a Taylor expansion of #e^(-2x)# centered at #x=0#?