Establish the identity.ln  + ln  = 2 ln  

What will be an ideal response?


ln  + ln  = ln ( ?  ) = ln  = ln  = 2 ln 

Mathematics

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Use a CAS integration utility to evaluate the triple integral of the given function over the specified solid region. over the tetrahedron bounded by the coordinate planes and the plane 

A. 231
B.
C. 462
D. 308

Mathematics

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.f(x) = 3|x| 

A.

B.

C.

D.

Mathematics

Solve the problem.A stone is thrown into a pond. A circular ripple is spreading over the pond in such a way that the radius is increasing at the rate of 5.2 feet per second. Find a function, r(t), for the radius in terms of t. Find a function, A(r), for the area of the ripple in terms of r. 

A. (A ? r)(t) = 27.04?2t B. (A ? r)(t) = 5.2?t2 C. (A ? r)(t) = 27.04?t2 D. (A ? r)(t) = 10.4?t2

Mathematics

Use integration to find the area of the triangle with the given vertices.

(0, 0), (1, 7), (4, 2)

Mathematics