Provide an appropriate response.Use Newton's method to approximate the root of x3 + 5x - 1 = 0 that lies between 0 and 1. Continue the approximation procedure until the difference of two successive approximations is less than 0.0001.

Fill in the blank(s) with the appropriate word(s).


0.19844

Mathematics

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Use a calculator with a  key to solve the problem.The function f(x) = 90e-0.2x + 10 models the percentage of information, f(x), that a particular person remembers x weeks after learning the information. a) Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b) Find the percentage of information that is remembered after 4 weeks. Round to the nearest thousandth of a percent.

A. a) 10%; b) 10.449% B. a) 50%; b) 210.299% C. a) 90%; b) 40.440% D. a) 100%; b) 50.440%

Mathematics

Solve the problem.Let f(x,y) = ln (x2 + y2). Which one of the following curves is a simple closed path in the domain of the function f?

A. The unit circle (x - 5)2 + y2 = 1
B. The ellipse  +   = 1
C. The rectangle with vertices at (-3, 2), (3, 2), (3, -2), and (-3, -2)
D. The unit circle x2 + y2 = 1

Mathematics

Graph the function.Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 4 - 4.

A.

B.

C.

D.

Mathematics

Translate into an equation, then solve.Bob is saving to buy a car. The total amount that he needs is $12,000. The amount that he has saved so far is $6000. How much more does Bob need?

A. 6000 - x = 12,000; Bob needs $6000 more. B. 6000 + x = 12,000; Bob needs $6002 more. C. 6000 - x = 12,000; Bob needs $6002 more. D. 6000 + x = 12,000; Bob needs $6000 more.

Mathematics