D 19 in2
find the area of a square, width times height
then find the area of the triangle, width times height divided by 2
There are no algebraic methods for finding solutions to a general mix of exponential and polynomial terms. A graphing calculator can be helpful.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
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In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.
Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.
The 5 people can seat in a row in 5! ways
But we need to exclude the ways <span>that ann and bob are seated next to each other which is = 4! * 2!
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So, the number of <span>ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other = 5! - 4! * 2! = 72
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<span>Another solution:
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<span>If ann seated in one of the ends, the number of ways = 3*2
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<span>If ann didn't seat in one of the ends , the number of ways = 2*3
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So, the total number of <span>ways that can <span>ann, bob be seated = 3*2 + 2*3 = 12
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The remaining persons can seat with a number of ways = 3! = 6
So, the total ways that the five persons can seat = 12*6 = 72