Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second. An olympian ran the 100-meter dash in 9.6 seconds. How mu
2 answers:
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Answer:
step 1: move the -4 to the right: x^2 -2x = 4
step 2: add 1 to each side: x^2 -2x + 1 = 4 + 1
step 3: factor the left side and simplify the right side: (x-1)^2 = 5
step 4: take the square root of each side: x - 1 = sqr root of 5
step 5: move the 1 to the other side: and
Answer:
x ≈ {0.653059729092, 3.75570086464}
Step-by-step explanation:
A graphing calculator can tell you the roots of ...
f(x) = ln(x) -1/(x -3)
are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.
In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.
Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.
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A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,
