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GummageFriend:
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I have:
2/pi  1/pi*(sum from n=1 to infinity)((4cos(2nx))/(n^21))
and I need:…
 updated 3 years ago
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GummageFriend:
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Give the definition of the norm of a matrix. Give a formula for the norm of an arbitrary invertible matrix A in terms of the eigenvalues of …
 updated 3 years ago
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GummageFriend:
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Give the definition of the norm of a matrix. Give a formula for the norm of an arbitrary invertible matrix A in terms of the eigenvalues of …
 updated 3 years ago
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GummageFriend:
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Give the definition of the norm of a matrix. Give a formula for the norm of an arbitrary invertible matrix A in terms of the eigenvalues of …
 updated 3 years ago
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GummageFriend:
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Suppose that X_1,...,X_n is a random sample of size n, from a normal distribution N(0,theta) with zero mean and variance theta.
State, justi…
 updated 3 years ago
 3 replies
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GummageFriend:
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F(x)= 0 for x<0, x for 0<x<1, 1 for x>=1.
Hence find the cumulative distribution function of the random variable Y =2lnX.
 updated 3 years ago
 22 replies
 2 Medals

GummageFriend:
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Find the Cumulative Density function of Y= 2ln(x)
 updated 3 years ago
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GummageFriend:
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Let f(x)= tan(x). What is the formula for the conditioning number of f. Let f(x)= tan(x). What is the formula for the conditioning number of…
 updated 3 years ago
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GummageFriend:
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For n = 1; 2; 3;... , let:
L(n) =INT(between 1&0) of (x^(n+1))/(2  x)dx.
By writing x^n = x^(n+1)(2  (2  x)), show that this sequence of …
 updated 3 years ago
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GummageFriend:
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For n = 1; 2; 3;... , let:
L(n) =INT(between 1&0) of (x^(n+1))/(2  x)dx.
By writing x^n = x^(n+1)(2  (2  x)), show that this sequence of …
 updated 3 years ago
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GummageFriend:
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Obtain the general solution of the following two CauchyEuler equations
(i) y''(x) +(1/x)y'(x) −(16/x^2)y(x) = 0,
(ii) x^2y''(x) + xy'(x) +…
 updated 4 months ago
 4 replies
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GummageFriend:
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Show that y1(x) = exp(x) is a solution of the diﬀerential equation
xy''=(x) − 2(x + 1)y'(x) + (x + 2)y(x) = 0 .
Hence ﬁnd another solution b…
 updated 3 years ago
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GummageFriend:
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Calculate an approximate value for 4^(3/4) using four steps of the secant method with the starting values x0 = 3 and x1 = 2.
 updated 3 years ago
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GummageFriend:
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Let F(x) = 1/sqrt(x+1). Sketch carefully the graph of y = F(x) for 0 <= x <= 2. Add the line y = x to your diagram, and indicate the locati…
 updated 3 years ago
 2 replies
 1 Medal

GummageFriend:
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Let F(x) = 1/sqrt(x+1). Sketch carefully the graph of y = F(x) for 0 <= x <= 2. Add the line y = x to your diagram, and indicate the locati…
 updated 3 years ago
 1 reply
 1 Medal

GummageFriend:
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Thanks.
 updated 3 years ago
 2 replies
 2 Medals

GummageFriend:
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This question deals with the upper half plane model of hyperbolic geometry. Points are
represented by complex numbers with positive imagina…
 updated 3 years ago
 2 replies
 1 Medal

GummageFriend:
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What is the symbol on the periodic table for hydrogen?
 updated 3 years ago
 7 replies
 2 Medals

GummageFriend:
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Suppose that a triangle ABC has sides a,b,c. Prove the cosine rule, that is: a^2= b^2 + c^2 2bc(cos(θ))
 updated 3 years ago
 9 replies
 1 Medal

GummageFriend:
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Suppose that the segement P Q is a diameter of the circle C = C(X, XP ) and Z ∈ C \ {P, Q}.
Show that in Euclidean Geometry ∠P ZQ is a righ…
 updated 3 years ago
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GummageFriend:
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Use the SAS Congruence Axiom to prove the ASA criterion
 updated 3 years ago
 6 replies
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GummageFriend:
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A bag of blood plasma at a temperature of −30◦C is taken from storage and placed in a water bath at 37◦C to thaw. After 10 minutes, a nurse…
 updated 3 years ago
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GummageFriend:
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Find the solution of
y˙ = (y + t)^2
that satisﬁes y(0) = 0. Hint: Use the substitution y(t) = z(t) − t to obtain a separable…
 updated 3 years ago
 5 replies
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GummageFriend:
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Let L be the hyperbolic line given by
{z ∈ H  z − 5 = 3} and let m be the hyperbolic line given by {z ∈ H  z − 7 =√5}.
(a) Find the p…
 updated 3 years ago
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GummageFriend:
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Explain what
is meant by a hyperbolic line (hline) in the upper half plane, H
 updated 3 years ago
 3 replies
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GummageFriend:
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If for the Matrix M, M(θ+ϕ) = MθMϕ holds, explain what this means geometrically, and draw a picture to help illustrate this.
 updated 3 years ago
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GummageFriend:
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If the line segment DE is a diameter of a circle with centre C, and F is any other point on
the circle, prove that (in Euclidean geometry) …
 updated 3 years ago
 2 replies
 2 Medals

GummageFriend:
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If the line segment DE is a diameter of a circle with centre C, and F is any other point on
the circle, prove that (in Euclidean geometry) …
 updated 3 years ago
 2 replies
 1 Medal

GummageFriend:
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The triangle ABC in the plane has vertices A(1, 0), B(3, 1), C(2, 2). The triangle PQR has vertices P(−1, 0), Q(−3, 1), R(−2, 2). Draw a ro…
 updated 3 years ago
 2 replies
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GummageFriend:
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HOw do you work out the parity of a permutation?
 updated 3 years ago
 8 replies
 1 Medal
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