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Morgarella [4.7K]
3 years ago
9

Solve the system of equations. x + 3y = −12x + 2y = 6

Mathematics
1 answer:
UkoKoshka [18]3 years ago
7 0

Answer:

x=-3/19

y=39/19

Step-by-step explanation:

the equations can be written as the following system

x+3y=6\\-12x+2y=6

If the second equation is multiplied by 3/2 it will become -18x+3y=9

If that equation is then subtracted with the first you will obtain the following

-19x=3, it means x=-3/19

The other variable is obtained by substituting the new value for x in the first equationx+3y=6, thus we obtain that y=39/19

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3 determine the highest real root of f (x) = x3− 6x2 + 11x − 6.1: (a) graphically. (b) using the newton-raphson method (three it
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(a) See the first attachment for a graph. This graphing calculator displays roots to 3 decimal places. (The third attachment shows a different graphing calculator and 10 significant digits.)

(b) In the table of the first attachment, the column headed by g(x) gives iterations of Newton's Method. (For Newton's method, it is convenient to let the calculator's derivative function compute the derivative f'(x) of the function f(x). We have defined g(x) = x - f(x)/f'(x).) The result of the 3rd iteration is ...

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(c) The function h(x₁, x₂) computes iterations using the secant method. The results for three iterations of that method are shown below the table in the attachment. The result of the 3rd iteration is ...

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(d) The function h(x, x+0.01) computes the modified secant method as required by the problem statement. The result of the 3rd iteration is ...

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<em>Comment on these methods</em>

Newton's method can have convergence problems if the starting point is not sufficiently close to the root. A graphing calculator that gives a 3-digit approximation (or better) can help avoid this issue. For the calculator used here, the output of "g(x)" is computed even as the input is typed, so one can simply copy the function output to the input to get a 12-significant digit approximation of the root as fast as you can type it.

The "modified" secant method is a variation of the secant method that does not require two values of the function to start with. Instead, it uses a value of x that is "close" to the one given. For our purpose here, we can use the same h(x1, x2) for both methods, with a different x2 for the modified method.

We have defined h(x1, x2) = x1 - f(x1)(f(x1)-f(x2))/(x1 -x2).

6 0
2 years ago
What two numbers add together to equal 20 and multiply together to equal 36​
Alex

Answer:

Step-by-step explanation:

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your welcome

4 0
3 years ago
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Answer:

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Step-by-step explanation:

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