Questions asked by Jacq

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• How to integrate 1/(1+sinx)?
  
• Show that the function #y=1/(1+tanx)# is decreasing for all values of #x#?
  
• Trigonometric Functions Question (Area underneath a curve). Help please?
  
• Approximate Solutions of Equations Question?
  
• Trig and Integration help please?
  
• A goat grazes a rectangular paddock 10 metres by 20 metres. It is tethered to the fence at one corner of the paddock by an inextensible rope of length #x# metres, where #10<x<20#? (More in 'details' section).
  
• I received an email saying that one of my questions had been answered, but when I went to look at the question, it had no answer?
  
• Using Newton's method, a root of #x^3+3x+7=0# correct to one decimal place is: A. x=1.6 B. x=1.5 C. x=1.4 D. x=1.3 Help please?
  
• Would #Im(z)=4# be plotted on the x-axis or y-axis?
  
• Show that #(n+2)!+(n+1)!+n!##=n!(n+2)^2# ?
  
• Find #n# if #""^nP_3=20n#?
  
• Complex numbers question. Help please?
  
• From a pack of 9 cards numbered 1-9, three cards are drawn at random and laid on a table from left to right. What is the probability that the digits are drawn in descending order?
  
• Three Greeks, three Americans and three Italians are seated at random around a round table. What is the probability that the people in the three groups are seated together?
  
• Twelve students sit around a circular table. Let three of the students be #A#, #B# and #C#. Find the probability that #A# does not sit next to either #B# or #C#?
  
• The normal #(2ap, ap^2)# to the parabola #x^2=4ay# meets the curve again at #Q(2aq, aq^2)#?
  
• #P# is a point on the parabola #x=t#, #y=t^2/2#. #A(4,1)# is a fixed point. As #P# varies, find the minimum distance of #P# from #A# and prove that for this position of #P#, #AP# is normal to the parabola?
  
• Barbara and John and six other people go through a doorway one at a time. Find the number of ways in which the eight people can go through the doorway if John goes through the doorway after Barbara?
  
• Find the equation of the tangent to the curve #y=ln(3x-2) + 4# at the point where #x=1#?
  
• #y=x^2e^(-x)# has a maximum turning point at #A(2,4/e^2)#. The equation #x^2e^(-x)-2=0# has 3 real, distinct roots. What are the possible values of #k#?
  
• Find the Cartesian equation of the locus of #arg((z-4)/(z+4))=pi/4#?
  
• Prove #((1 + cos2 x + i sin2 x)/(1 + cos2 x - i sin2 x))^n=cos2nx+isin2nx#?
  
• Evaluate #lim_(x->0)(1-cosx)/x^2#?
  
• #d/dx(tan^(-1)2x)=2/(4x^2+1)#. Why is there a #2# in the numerator?
  
• Prove #(1+sinx+icosx)/(1+sinx-icosx)=sinx+icosx#?
  
• Let #z=a+ib#, where #a# and #b# are real. If #z/(z-i)# is real, show that #z# is imaginary or #0#. Help?