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.
Answer:
144 and 18
Step-by-step explanation:
18 ×24=432÷3=144
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Given Information
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Adrian can run 3/4 mile in 1 morning.
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Find how long he needs to run 1 mile
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3/4 miles = 1 morning
[ Divide by 3/4 on both side ]
3/4 ÷ 3/4 miles = 1 ÷ 3/4
1 miles = 4/3 morning
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Find how long he needs to take to run 3 miles
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1 miles = 4/3 morning
[ multiply by 3 through ]
3 miles = 4/3 x 3
3 miles = 4 mornings
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Answer : 4 mornings
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