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What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?


  1. Sketch the two vectors listed after the formula for r (t).
  2. Sketch, on the same plane, the curve C dterminated by r (t), and indicate the orientation for the given values of t.

    r (t)=t*i +4*cos (t)j +9*sin (t)k,

    r (0), r(Pi/4),  t>=0

How to convert an  algebraic equation to a parametrized one ?


How to sketch the curve of a circular cylinder , x^2+y^3^=a^2 with the parametric equations lying on it ?

x=a*cos't) , y=a*sin(t) , z=b*t , if t varies from 0 to 2*Pi, the point P starts at(a,0,0) and moves upward.

How to show that the parametric equations are indeed lying on the cylinder ?

How to plot the whole things ?


A concho-spiral is a curve C that has a parametrization :





where a, b, mu, are constants.

  1. Show that C lies on the cone a^2*z^2=b^2*(x^2+y^2).
  2. Sketch C for a = b = 4 and mu=-1.
  3. Find the length of C corresponding to the t-interval [0,infinity].

 1) find  the direction in which f(x,y) increases most rapidly at the point P(1,2), and find the maximum rate of increase
of f at P.

Interpret 1) using the graph of f.


Let f(x,y) = 2+x^2 +1/4*(y^2)

I need to make two graphs.  1st take the equation y= ln3x+3 and graph it and it's derivative.  Then find the equation of the tangent line and the normal line to the given function at x=e   Then I need to create a single graph containing the function, the tangent line, and it's normal line.  Any pointers or help would be greatly appreciated.  I can graph the equation and it's derivative ok but I don't know how to make a graph with multiple stuff on it.  Thanks

From some scientific experiments, the following set of data is available
(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).

We need to use least squares method to fit the curve to the data
y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)

Show your solution procedure in Maple and get the best fit for the coefficients. Finally
plot the data and the y curve together on the same graph to visualize the fitting. For the
data, use blue circles while for the y curve, use red solid line style. Use the leastsquares
command we learned in LinearAlgebra package.

What is the solution to the following system? Is the solution unique? Use
the reduced row echelon form to explain why.
x + 2y + 3z = 1,
4x + 5y + 6z = 1,
7x + 8y + 9z = 1

Find the eigenvalues and eigenvectors for

A =
2 0.37 0
0 1.1 −4.29
1.6 0 2.2

Can you estimate the largest eigenvalues (in absolute value) using Power method for this
problem? Try to explain why if you can

Find the quadratic polynomial which interpolates (2, 0),(6, 1),(8, 0). Solve this with Maple. Start the problem by setting f(x) = ax2 + bx + c for example, then the unknowns are a, b, c.



A flate metal plate lies on an xy plane such that the temperature T at (x,y) is given by T=10(x^2+y^2)^2 , where T is in degrees and x and y are in centimeters.

Find the instantaneous rate of change of T with respect to distance at (1,2) in the direction of

a) the x-axis

b) the y-axis

How to get the equations of circles A, B, C, such as circle A with center (1,1) is drawn in the first quadrant.

Circle B with radius 2 and circle C are placed so that each circle is tangent to the other 2 circles and the x-axis.

THe 3 circles are on the first quadrant.

1) do it with Maple

2) do it by hand

3) draw the figure



N := 8;

b := 2 ∗ P i;
data := [];
for n f rom 0 to N do
data := [op(data), [n ∗ b/N, sin(n ∗ b/N)]];

Since exact points are not needed, changed the loop (and reinitialize) to:

data := [];

for n from 0 to N do
data := [op(data), [evalf(n ∗ b/N), sin(evalf(n ∗ b/N))]];

Modify the second example so that it can be used to graph the sin function
over any interval from a to b. (You should suppress the output from the for-loop in your
example, so that you do not fill up the worksheet with an unwieldy amount of output.)

I have a question that says write a procedure that takes a random graph and three edges of that graph and returns true if those edges share a common vertex. So I was thinking of something along the lines of

proc55 := proc (G, {a, b}, {c, d})

if evalb({a, b} = {a, c} or {a, b} = {a, d} or {a, b} = {b, c} or {a, b} = {b, d}) then print(true)

else print(false)

end if;

end proc;


I guess my main question is how do I put edges in the parameters line? It will let me write proc (G, a, b, c, d) but not proc (G, {a, b}, {c, d}).

Is there just something I'm missing or am I approaching this in the wrong way?


For the following maps, determine whether they are linear transformations or not, and present an
appropriate proof.

(a) T : R^4 → M2,3 given by T(a, b, c, d) =  [a   a^2   a^3
                                                                   b    c       d ]
(b) T : M2,3 → M3,2 given by T(M) = M^T (transpose of M)
(c) T : P3 → P3 given by T(p(x)) = p(2) + 3x · p'(x), where p'(x) denotes the derivative of the polynomial p(x).


i know that the 2 rules for proving are T (u+v)= T(u) + T (v) and T (ku)= k T (u).....but how do i show it with the questions above, like do i just take any numbers , so confused

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