Answers edited by sente

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• Question #e07a4
  
• Among all pairs of numbers with a sum of 101, how do you find the pairs whose product is maximum?
  
• The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?
  
• How do you graph #g(x)= log_6 x#?
  
• What is #lim_(x->0) (x^3+12x^2-5x)/(5x)# ?
  
• Question #de166
  
• How do you simplify #(sina+tana)/(1+cosa)#?
  
• How do you show that if #a+b=0#, then the slope of #x/a+y/b+c=0# is #1#?
  
• What's the LCM of 6 and 8?
  
• Question #c5432
  
• How do you simplify #-2/(3-i)#?
  
• Is #sqrt(2)^(sqrt(2))# rational ? And #sqrt(2)^(sqrt(2)^sqrt(2))#?. And #sqrt(2)^(sqrt(2)^(sqrt(2)^cdots))#?
  
• How to write the first four terms of the Maclaurin series for the function f(x)=(x+1)e^(2x) given that ?
  
• What is the value of #1/n sum_{k=1}^n e^{k/n}# ?
  
• How do you find the number of terms in the following geometric series: 100 + 99 + 98.01 + ... + 36.97?
  
• How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?
  
• How do you simplify #((2n)!)/(n!)#?
  
• How do you integrate # 1/(1+e^x) # using partial fractions?
  
• Is there a systematic way to determine the number of numbers between 10 and, say, 50, divisible by their units digits?
  
• How do you show that integration of #x^m e^(ax)dx = (x^m e^(ax) )/a - m/a int x^(m-1) e^(ax) dx#?
  
• The movement of a certain glacier can be modelled by d(t) = 0.01t^2 + 0.5t, where d is the distance in metres, that a stake on the glacier has moved, relative to a fixed position, t days after the first measurement was made. Question?
  
• If the zeros of #x^5+4x+2# are #omega_1#, #omega_2#,.., #omega_5#, then what is #int 1/(x^5+4x+2) dx# ?
  
• What is 0.09 (repeating) as a fraction?
  
• How do you simplify # (2+2i)/(1+2i) # and write in a+bi form?
  
• What is 1 divided by 0.2?
  
• How do you express #sqrt(-4/5)# as a product of a real number and i?
  
• How do you find all solutions to #x^5+243=0#?
  
• If # n = 1/4#, what is the value of #(2n-5)/n#?
  
• How do you solve #log x + log (x-3) = 1#?
  
• How do you perform inversions for #y = x^2 and y = x^4?# Is #(dx)/(dy)# from the inverse #1/((dy)/(dx))?#
  
• Question #9c5a0
  
• How do I find the natural log of a fraction?
  
• Determine the interval whereby 6x^2 + 44x + 70 ≥ 0?
  
• Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?
  
• How do you solve #sin^2 x - cos^2 x=0# for x in the interval [0,2pi)?
  
• How do you convert #(3, -3sqrt3)# to polar form?
  
• How do you solve #120=100(1+(.032/12))^(12t)#?
  
• Question #5d611
  
• Write the equation of a function with domain and range given, how to do that?
  
• Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?
  
• Find the matrix #A# for the linear transformation #T# relative to the bases #B = {1,x,x^2}# and #B' = {1,x,x^2,x^3}# such that #T(vecx) = Avecx#?
  
• Solve for #x in RR# the equation #sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1# ?
  
• A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle?
  
• Question #9e52a
  
• In 1/6=1.6666..., repeating 6 is called repeatend ( or reptend ) . I learn from https://en.wikipedia.org/wiki/Repeating_decimal, the reptend in the decimal form of 1/97 is a 96-digit string. Find fraction(s) having longer reptend string(s)?
  
• Question #a71e9
  
• How do I graph the ellipse with the equation #x^2+4y^2-4x+8y-60=0#?
  
• Suppose there are m Martians & n Earthlings at a peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martians there is at least one Earthling?(see detail)
  
• How do you verify #(cosX+sinX)/(cscX+secX) = (cosX)(sinX)#?
  
• How do you solve #2/(x+3)-4/(x^2+2x-3)=1/(1-x)#?
  
• What is the Taylor series for #f(x)= cosx# centered on #x= pi/3#?
  
• What is #int_0^pi (lnx)^2 / x^(1/2)#?
  
• How do you simplify # (x^(1/3) + x^(-1/3))^2#?
  
• Question #6d8e6
  
• Is #sqrt33# an irrational number?
  
• ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
  
• Question #da791
  
• How do you find the number of terms in the following geometric sequence: -409.6, 102.4, -25.6,..., 0.025?
  
• 6 equal circular discs placed so that their centres lie on the circumference of a given circle with radius (r), and each disc touches its 2 neighbours. What is the radius of a 7th disc placed in the centre which will touch each of the each existing ones?
  
• Question #2b5bb
  
• What is #1/3# of #18#?
  
• What are the all the solutions between 0 and 2π for #sin2x-1=0#?
  
• How do you use the ratio test to test the convergence of the series #∑(2k)!/k^(2k) # from n=1 to infinity?
  
• How do you prove #sec^2 x - cot^2 ( pi/2-x) =1#?
  
• What are complex numbers?Thanx.
  
• Question #0f6bd
  
• Question #d2752
  
• How do you solve #tan^2 x=tan x#?
  
• Question #a43bd
  
• Question #db818
  
• How do you solve #tan^-1(2x)+tan^-1(x)= (3pi)/17#?
  
• A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?
  
• Question #98d02
  
• How do you simplify # cos (pi - theta)#?
  
• Suppose that #lim_(xrarrc) f(x) = 0# and there exists a constant #K# such that #∣g(x)∣ ≤ K " for all " x nec# in some open interval containing c. Show that# lim_(x→c) (f(x)g(x)) = 0#?
  
• What is the product of #2x^2+7x-10# and #x+5# in standard form?
  
• How do I perform matrix multiplication?
  
• Question #b5ab2
  
• How do you differentiate #p(y) = y^2sin^2(y)cos(y)# using the product rule?
  
• What is #(-7pi)/8 # radians in degrees?
  
• What is the frequency of #f(theta)= sin 3 t - cos 21 t #?
  
• Does #a_n=1/(n!) # converge?
  
• In the triangle embedded in the square what is the measure of angle, #theta#?
  
• How do you solve 2015 AP Calculus AB Question #1?
  
• What is the derivative of #f(x) = (lnx)^(x)#?
  
• What is the distance between #(0, 0, 8) # and #(9, 2, 0) #?
  
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