Answer:
The original side length of the square was 9 ft
Step-by-step explanation:
Consider that the square was initially of side length "x" (our unknown). Then the sides were all increased by 5 ft, and now the perimeter (addition of all four sides) of the square render 56 ft.
Let's write an equation that represents the addition of the four sides of this new rectangle, and set it equal to 56 ft. Then solve for the unknown "x":
Therefore, the original side of the square was 9 ft.
Answer:
A. x = 11/16
Step-by-step explanation:
For the purpose here, it is convenient to rearrange the equation to f(x) -g(x) = 0. We know the root will be in the interval [0, 1] because (f-g)(0) = -3 and (f-g)(1) = +3. At each iteration, we evaluate (f-g)(x) at the midpoint of the interval to see which of the interval end points can be moved and still bracket the root.
Using the bisection method starting with the interval [0, 1] we find f(1/2)-g(1/2) < 0, so we can move the interval limits to [1/2, 1].
For the next iteration, we find f(3/4) -g(3/4) > 0, so we can move the interval limits to [1/2, 3/4].
For the third iteration, we find f(5/8) -g(5/8) < 0, so we can move the interval limits to [5/8, 3/4].
Then the root is approximately the middle of that interval:
x ≈ (5/8 +3/4)/2 = 11/16
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This value of x is 0.6875. The root is closer to 0.639802004233. The bisection method takes about 3 iterations for each decimal place of accuracy. Other methods can nearly double the number of accurate decimal places on each iteration.
