| Jumat, 27 November 2009 |
| My Assignment about problems of mathematics |
1. draw a contour curve z=k for values of k which given.
z= 1/2 (x^2+y^2 ) , k = 0,2,4,6,8.
2. showed that surface x^2+4y+z^2=0 and x^2+y^2+z^2-6z+7=0 each other touching in point (0, -1, 2), showing that they have same area in point (0, -1, 2)
3. calculate the area under 32 if given a normal distribution with µ = 40 and σ = 6.
4. calculate the value of x which the area under 45% with µ = 40 and σ = 6.
5. given a randow sample which have measure 24 which pulled by a normal population. calculate k if P (-2.069 < T < k)= 0.965.
SOLUTION:
1. 
2. F(x,y,z) x^2+y^2+z^2-6z+7=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 2y --> Fy (0,-1,2) = -2
<=> Fz (x,y,z) = 2z-6 --> Fz (0,-1,2) = -2
so, the surface area y+z-1=0
F(x,y,z) x^2+4y+z^2=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 4 --> Fy (0,-1,2) = 4
<=> Fz (x,y,z) = 2z --> Fz (0,-1,2) = 4
so, the surface area y+z-1=0
because the both of surface area is same, so the surface is proven that they have same area.
3. z = (x-µ)/σ = -4/3
P (X < 32) = P (Z < -4/3)
= 0.0918
so, the answer is 0.0918.
4. P(X < x) = 45% = 0,45
z which have value 0.45 is -0.13
z = (x-µ)/σ
(-0.13)(6) = x-40
x = 39.22
so, the value of x is 39.22
5. P (-2.069 < T < k)= 0.965
-2.069 = t(-0.025)
<=> 1 - k - 0.025 = 0.965
<=> k = 0.010
t(k)=t(0.010)= 2.500
so, the value of k is 2.500 |
posted by sOFFia aNisa H.A.C (08305141004) @ 22.03  |
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| 2 Comments: |
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Thank for the assignment. Please indicate who write the problems and who solve the problems.
Best Wishes.
Marsigit
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thanks for you comment sir..first, the problem which i wrote are the problems which I have never got the answer. that problem which I took away from some the duties have been given by my curator lecturer. then I deliver that problem to my handshake friend, because I believe that she can help me to get his solution. correct actually. she can finished the problem which I cannot get the answer, including concerning drawing the the graph. graph on the problem one is concerning depiction of curve in some dots k. if only in the form of sketch, of course the result of it do not nicely from program matlab. when I type it, I get some difficulty how to draw the the graph. blessing matlab, I can finish my duty, because matlab have in teaching in eye lesson computer application in last semester.
that is all Sir. thank you
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Thank for the assignment. Please indicate who write the problems and who solve the problems.
Best Wishes.
Marsigit