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,
the answer for 3y-4=6-2y is y=2
The final value, 5.3, is greater in the value of the answer.
Answer:
49,000 square cm
Step-by-step explanation:
To get the area of the dilated rectangle, we need the dilated dimensions
We simply multiply the scale factor by the dimensions
we have this as;
3.5 * 50 = 175 cm
and
3.5 * 80 = 280 cm
The area of the dilated rectangle is thus;
280 * 175 = 49,000 cm^2
Answer:
3/14
Step-by-step explanation:
We want to find the ratio of a to b, or a/b
9/17 = 3a/ (a+b)
Multiply each side by 17
17*9/17 =17* 3a/ (a+b)
9 = 51 a/ (a+b)
Multiply each side by (a+b)
9 (a+b) = 51a
Distribute the 9
9a +9b = 51a
Subtract 9a from each side
9a-9a +9b =51a-9a
9b = 42a
Divide each side by b
9b/b = 42a/b
9 = 42a/b
Divide each side by 42
9/42 = a/b
But we can simplify 9/42 because each is divisible by 3, so divide 9 and 42 by 3
3/14 = a/b