Mathematics, 12.02.2020 03:25 kassidy49
Show that there is a root of the equation 5x3 β 10x2 + 3x β 2 = 0 between 1 and 2. SOLUTION Let f(x) = 5x3 β 10x2 + 3x β 2 = 0. We are looking for a solution of the given equation, that is, a number c between 1 and 2 such that f(c) = . Therefore we take a = , b = , and N = in the Intermediate Value Theorem. We have f(1) = 5 β 10 + 3 β 2 = β4 < 0 and f(2) = 40 β 40 + 6 β 2 = 4 > 0. Thus f(1) < 0 < f(2); that is N = 0 is a number between f(1) and f(2). Now f is continuous since it is a polynomial, so that the Intermediate Value Theorem says there is a number c between and such that f(c) = . In other words, the equation 5x3 β 10x2 + 3x β 2 = 0 has at least one root c in the open interval . In fact, we can locate a root more precisely by using the Intermediate Value Theorem again. Since f(1.7) = β1.235 < 0 and f(1.8) = 0.160 > 0 a root must lie between (smaller) and (larger). A calculator gives, by trial and error, f(1.78) = β0.145240 < 0 and f(1.79) = 0.005695 > 0. Do a root lies in the open interval .
Answers: 2
Mathematics, 21.06.2019 14:30
F(x)= 1/x-4, g(x)=4x+1/x a. use composition to prove whether or not the functions are inverses of each other. b. express the domain of the compositions using interval notation.
Answers: 2
Mathematics, 22.06.2019 05:00
Abigail made a quilt that has an area of 4800 square inches. the length of the quilt is 1 1/3 times the width of the quilt. what are the dimensions of the quilt
Answers: 1
Mathematics, 22.06.2019 05:30
When a number is decreased by 9.9% the result is 40. what is the original number to the nearest tenth? super urgent
Answers: 3
Show that there is a root of the equation 5x3 β 10x2 + 3x β 2 = 0 between 1 and 2. SOLUTION Let f(x)...
History, 21.11.2019 19:31
History, 21.11.2019 19:31
Mathematics, 21.11.2019 19:31
Arts, 21.11.2019 19:31
Mathematics, 21.11.2019 19:31
Computers and Technology, 21.11.2019 19:31
Computers and Technology, 21.11.2019 19:31