For the initial value problem, compute the first two approximations u1 and u2 given by Euler's method using the given time step.y'(t) = -y, y(0) = -5; ?t = 0.5

A. u1 = -5; u2 = -2.5
B. u1 = -2.5; u2 = -1.25
C. u1 = -2.5; u2 = -2.5
D. u1 = 0; u2 = -2.25


Answer: B

Mathematics

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Show that the set has cardinal number ?0 by establishing a one-to-one correspondence between the natural numbers and the given set. Be sure to indicate the general correspondence.{0, 3, 6, 9, 12, ...}

A.

1,2,3,4,...,  n,...
0,3,6,9,...,  3n - 3, ...

B.
1,2,3,4,...,n,...
0,3,6,9,...,  3n, ...

C.
1,2,3,4,...,n,...
0,3,6,9,...,  3n - 1, ...

D.
1,2,3,4,...,n,...
?
0,3,6,9,...,  3n + 3, ...

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Solve the equation and express the solution in exact form using either ln or log as indicated.x = 16Express the answer using ln.

A.
B.
C.
D.

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Use factoring to find f(x) and g(x) so that h(x) = f(x)g(x).x2 + 3x - 108

A. f(x) = x - 12, g(x) = x + 1 B. f(x) = x - 12, g(x) = x - 9 C. f(x) = x + 12, g(x) = x - 9 D. f(x) = x - 12, g(x) = x + 9

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An arithmetic sequence is given. Find the common difference and write out the first four terms.{7n + 6}

A. d = 6; 7, 13, 20, 27 B. d = 7; 7, 13, 20, 27 C. d = 6; 13, 20, 27, 34 D. d = 7; 13, 20, 27, 34

Mathematics