Answers created by Teddy

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• What is the derivative of #Tan^-1 (y/x)#?
  
• What is the Cartesian form of #(0,pi)#?
  
• How do you find the extreme values of the function and where they occur?
  
• How do you evaluate #sec^-1(sec((9pi)/10))#?
  
• Prove that #a^2-1# is divisible by #8# for all odd integers #a# (induction)?
  
• How to find the cube roots of #sqrt(2) + isqrt(2)# ? Exhibit them as vertices of certain regular polygon, and identify the principal root
  
• If #A= <-8 ,3 ,-4 ># and #B= <-3 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
  
• What is the polynomial function #f# of least degree that has rational coefficients, a leading coefficient of 2, and the zeros -4, 0, 2, 4?
  
• What is the net area between #f(x)=ln(x^3-x+2)/x^2# in #x in[1,2] # and the x-axis?
  
• In an Isoceles #triangle# #ABC#,bisector #CD# of the #angle# #C# is equal to the base #BC#.Then the angle between #CDA# is ?
  
• What is #\lim _ { x \rightarrow 0} x \ln x#?
  
• Describe what is meant by a negative relationship between two variables with an example ?
  
• How do you expand the logarithmic expression #ln (x/3y)#?
  
• What is jump discontinuity in math?
  
• What is the primary objective of sampling from a population?
  
• What is meant by the determinant of a matrix?
  
• How do you convert 5i to polar form?
  
• Can someone help me with this contingency table??
  
• Triangle ABC is a right triangle. The shortest side is 7 m long and the longest side is 10 m long. What is the approximate length of the third side?
  
• What is the remainder when #(2x^3 – 8x^2 + 6x – 6) ÷ (x – 4)#?
  
• Two days before an election, city officials projected that 67% of all registered voters would vote. Two days after the election, after reviewing the actual voting turnout, they announced that 81% of registered voters had actually voted. Which of these percentages is a parameter, and which is a statistic?
  
• I flip a coin 10 times and I get 8 heads. what the propability of the 11th flip to be tails?
  
• How do you differentiate # f(x)=sqrt((7-2x^3)# using the chain rule.?
  
• How can you take second derivative of #(x^2+12)/(x-2)# ?
  
• A binary operation *,defined on the set of R of real numbers is given by x*y=x+y+2xy. Find the identity element? Show workings please
  
• How do you find the arc length of the curve #y=lnx# over the interval [1,2]?
  
• How do you find the slope of a tangent line to the graph of the function #sqrtx# at (4,2)?
  
• Find all x-values where x is discontinuous. For each discontinuity state which of the three conditions is not fulfilled. Can anyone help me with this?
  
• What is the derivative of tan(sin x)?
  
• Consider S={0,1,2} is the set of residue classes modulo 3 under addition then inverse of 2 is???
  
• How to show that #1/(2a) ln |(x - a)/(x + a)| + C# is equal to #1/(2a) ln |(x + a)/(x - a)| + K#?
  
• How do you write a polynomial equation for a graph that passes through point (2, -14) and has x-intercepts at (rad5,0), (-rad5,0), and bounces off x-axis at (6,0)?
  
• What is the formula for the sum of an arithmetic sequence?
  
• A circle has a chord that goes from #( pi)/2 # to #(13 pi) / 6 # radians on the circle. If the area of the circle is #5 pi #, what is the length of the chord?
  
• Find the measure of angle y. Round your answer to the nearest hundredth. (please type the numerical answer only) A right triangle is shown with one leg measuring 8 and the hypotenuse is labeled 13. An angle made with the leg measuring 8 and the...?
  
• How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_3 15#?
  
• How do you factor #5r ^ { 3} s + 30r ^ { 2} - 5r ^ { 2} s - 30r ^ { 3}#?
  
• Find the coordinates of the inflection points for f(x)=xe^x?
  
• Products from a certain machine are too large 15% of the time. What is the probability that in a run of 20 parts, 5 are too large?
  
• How do you write an expression for the nth term of the geometric sequence with a1=64, r=-1/2, and n=10? Find the indicated term.
  
• What is the derivative of #x^sin(x)#?
  
• Find dy/dx if y=e^2x sin2x ?
  
• The domain of f(x)=log(x) is?
  
• How do you differentiate #f(x)= sqrt (lnx^2-x)#?
  
• Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #24 #, how long are the other two sides?
  
• F(x)=\sqrt(x^(2)-5x+6), find the domain and range ?
  
• How do you write the partial fraction decomposition of the rational expression #(2x-3) / (x-1)^2#?
  
• How do you factor completely #p^4+2p^3+2p^2-2p-3#?
  
• For what value of #a# is the polynomial #x^3-ax^2-2x+5a-7# a multiple of #(x-a)#?
  
• What is the domain?
  
• How do you find all the solutions of the following equation in the interval [0, 2pi)? 48sin^2x = 48-24cosx
  
• How can you write -2=log9 1/81 in exponential form?
  
• How do you integrate #x^2/((x-3)^2(x+4))# using partial fractions?
  
• Integrate (1)/(sqrt(1-x^2)) from -1 to 1?
  
• What is the equation of a circle in general form if the center is 2,6 passes through the point 3,1? Thanks
  
• Integrate (logx)/(x(1+logx)(2+logx)) ?
  
• How do you differentiate #g(t)=t^3cost#?
  
• Someone help me with this please... The length of a rectangle is given by 2t^2 + 3t – 7 and the height is sq. root of 2t, where t is time in seconds and the dimensions are in feet. Find the rate of change of the area with respect to time? Thank you!
  
• What is the conjugate of the complex number -5 - 5i?
  
• What are the mean and standard deviation of a probability density function given by #Pr(X=k) = (4^ke^-4)/(k!) # for #k in {0,1,2... oo}#?
  
• Why does the change of base rule for logarithms work for any value of x?
  
• There are 14 NBA teams who do not make the playoffs. Of these teams, 3 of them will be randomly selected to make the 1st, 2nd, and 3rd pick. How many different ways can the 1st-3rd pick be arranged?
  
• What is the derivative lime of y=mx+b?
  
• Is the function #f(x)=x^4-6^-4+3x^2# even, odd or neither?
  
• A camera's flash mechanism fails on 14% of shots. If 20 shots are taken using the flash, what is the probability that the flash fails exactly twice?
  
• Which measure of central tendency (mean, median or mode) is most appropriate for income data and why? Give a clear explanation for your decision.
  
• How do you use the integral test to determine the convergence or divergence of #Sigma 1/n^(1/3)# from #[1,oo)#?
  
• Find the limit as x→ -∞ sech(x) ?
  
• What is Ramanujan summation?
  
• How do you solve #20^(n-2)+6.5=87#?
  
• How do you determine the quadrant in which #3.5# radians lies?
  
• How can we find tan inverse of a number without calculator,for eg. Tan inverse of -1 ?
  
• How do you factor sec^2(x)-sec(x)+sin^2(x)*sec^2(x)?
  
• Y=x^(2)-2x-5 y=x^(3)-2x^(2)-5x-9 can you write the steps to find the intersection?
  
• How are exponential functions related to geometric sequences?
  
• What is the discontinuity of the function #f(x) = |x-5|/(x-5)# ?
  
• The following quiz scores measured as a discrete variable are as follows: 2, 4, 2, 5, 6, 3, 4. Find the range and the interquartile range (IQR)?
  
• Are disjoint events always independent?
  
• What is #f(x) = int 2sinx-xcosx dx# if #f((7pi)/6) = 0 #?
  
• What is an example of when a limit does not exist?
  
• If #log_4 x =3#, then what is #x# equal to?
  
• How do you find vertical, horizontal and oblique asymptotes for #f(x)= (6x^4-x^3+6x+5)/(x^3+1)#?
  
• How do you convert #r = 2a cosθ# into a cartesian equation?