Answers edited by sente

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• Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?
  
• How do you show that if #a+b=0#, then the slope of #x/a+y/b+c=0# is #1#?
  
• How do you simplify #(sina+tana)/(1+cosa)#?
  
• How do you simplify # cos (pi - theta)#?
  
• How do you simplify #-2/(3-i)#?
  
• Question #9c5a0
  
• 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?
  
• Solve for #x in RR# the equation #sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1# ?
  
• What is 0.09 (repeating) as a fraction?
  
• How do you simplify #((2n)!)/(n!)#?
  
• What is #int_0^pi (lnx)^2 / x^(1/2)#?
  
• What is the value of #1/n sum_{k=1}^n e^{k/n}# ?
  
• How do I perform matrix multiplication?
  
• ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
  
• If # n = 1/4#, what is the value of #(2n-5)/n#?
  
• The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?
  
• Question #0f6bd
  
• How do I graph the ellipse with the equation #x^2+4y^2-4x+8y-60=0#?
  
• A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle?
  
• What is #1/3# of #18#?
  
• How do I find the natural log of a fraction?
  
• 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)
  
• What is the frequency of #f(theta)= sin 3 t - cos 21 t #?
  
• How do you solve #sin^2 x - cos^2 x=0# for x in the interval [0,2pi)?
  
• How to write the first four terms of the Maclaurin series for the function f(x)=(x+1)e^(2x) given that ?
  
• How do you solve #120=100(1+(.032/12))^(12t)#?
  
• What's the LCM of 6 and 8?
  
• What are the all the solutions between 0 and 2π for #sin2x-1=0#?
  
• What is the distance between #(0, 0, 8) # and #(9, 2, 0) #?
  
• How do you solve 2015 AP Calculus AB Question #1?
  
• How do you find the number of terms in the following geometric series: 100 + 99 + 98.01 + ... + 36.97?
  
• How do you find the number of terms in the following geometric sequence: -409.6, 102.4, -25.6,..., 0.025?
  
• How do you verify #(cosX+sinX)/(cscX+secX) = (cosX)(sinX)#?
  
• 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#?
  
• How do you perform inversions for #y = x^2 and y = x^4?# Is #(dx)/(dy)# from the inverse #1/((dy)/(dx))?#
  
• 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# ?
  
• Question #da791
  
• How do you graph #g(x)= log_6 x#?
  
• Question #5d611
  
• 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)?
  
• How do you solve #log x + log (x-3) = 1#?
  
• Among all pairs of numbers with a sum of 101, how do you find the pairs whose product is maximum?
  
• Question #d2752
  
• What is the product of #2x^2+7x-10# and #x+5# in standard form?
  
• How do you prove #sec^2 x - cot^2 ( pi/2-x) =1#?
  
• Does #a_n=1/(n!) # converge?
  
• How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?
  
• Question #9e52a
  
• Question #db818
  
• Question #2b5bb
  
• Question #a43bd
  
• Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?
  
• Question #98d02
  
• How do you convert #(3, -3sqrt3)# to polar form?
  
• What is #(-7pi)/8 # radians in degrees?
  
• 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?
  
• Is there a systematic way to determine the number of numbers between 10 and, say, 50, divisible by their units digits?
  
• Question #b5ab2
  
• Determine the interval whereby 6x^2 + 44x + 70 ≥ 0?
  
• How do you find all solutions to #x^5+243=0#?
  
• What is 1 divided by 0.2?
  
• Question #a71e9
  
• How do you solve #2/(x+3)-4/(x^2+2x-3)=1/(1-x)#?
  
• How do you differentiate #p(y) = y^2sin^2(y)cos(y)# using the product rule?
  
• What is the Taylor series for #f(x)= cosx# centered on #x= pi/3#?
  
• A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?
  
• Question #c5432
  
• Question #6d8e6
  
• What are complex numbers?Thanx.
  
• Is #sqrt(2)^(sqrt(2))# rational ? And #sqrt(2)^(sqrt(2)^sqrt(2))#?. And #sqrt(2)^(sqrt(2)^(sqrt(2)^cdots))#?
  
• How do you simplify # (x^(1/3) + x^(-1/3))^2#?
  
• Question #de166
  
• How do you integrate # 1/(1+e^x) # using partial fractions?
  
• Is #sqrt33# an irrational number?
  
• Write the equation of a function with domain and range given, how to do that?
  
• How do you simplify # (2+2i)/(1+2i) # and write in a+bi form?
  
• How do you solve #tan^2 x=tan x#?
  
• 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#?
  
• In the triangle embedded in the square what is the measure of angle, #theta#?
  
• How do you solve #tan^-1(2x)+tan^-1(x)= (3pi)/17#?
  
• 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 show that integration of #x^m e^(ax)dx = (x^m e^(ax) )/a - m/a int x^(m-1) e^(ax) dx#?
  
• How do you express #sqrt(-4/5)# as a product of a real number and i?
  
• What is #lim_(x->0) (x^3+12x^2-5x)/(5x)# ?
  
• Question #e07a4
  
• What is the derivative of #f(x) = (lnx)^(x)#?
  
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