In Exercises 25-30, use the formula for finding the future value of an ordinary annuity, A = R 1 + r m n - 1 r m to solve for n. You are given A, R and r. Assume that payments are made monthly and that the interest rate is an annual rate. A = $ 12, 000 , R = 400 , r = 8 %
In Exercises 25-30, use the formula for finding the future value of an ordinary annuity, A = R 1 + r m n - 1 r m to solve for n. You are given A, R and r. Assume that payments are made monthly and that the interest rate is an annual rate. A = $ 12, 000 , R = 400 , r = 8 %
Solution Summary: The author explains that an annuity is a regular stream of equal payments, made at equal intervals. Its future value depends on interest rate, size, and number of payments.
Q1: consider the model problem
-(xu')' = x x = [0, L]
u'(0) = ho,
u' (L) = h₁
Where ho and h, are given parameter.
Find the variational form and finite element method.
Q2: Consider the variational problem with bilinear form
a(u,v) = (2u'v' + 3u'v + 4uv)dx
Prove that a() is V-elliptic. Where u(0) = u(1) = 0
Q3 Consider the general problem -Au = 0, in-,
n.Vu gn, on on
Prove that the linear form (v) = (gv)² (an) continuous.
Q4: consider a region R, 0 ≤ x ≤ 1,0 ≤ y ≤as shown in figure, that is decomposed
into four triangular sub regions, designated K1, K2, K3, K4. The vertices of these
regions are the nodes V1, V2, V3, V4, Vs. There is only one interior node, V1. The
coordinate of the node are given in matrix V. The triangles are defind by spe
the node indices of the three vertices of each triangle, Find
Vip
Vidk
1
2
Vizzdkz
k2
Vipy dks
A
3
K3
43 dk3
(+)
(370)
(3))
217
-3
K₂
Kj
2
31
L
Ki
Ки
0
-13
27.
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