Answers edited by sente

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