Answers edited by sente

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