A swimming pool is shaped like a right rectangular prism with length 20 feet, height 8 feet, and width 15 feet. If the pool's wa
2 answers:
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Answer:
Option D
Step-by-step explanation:
We are given the following equations -
It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -
First, I swapped the first and third rows.
Leading coefficient of row 2 canceled.
The start value of row 3 was canceled.
Matrix rows 2 and 3 were swapped.
Leading coefficient in row 3 was canceled.
And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -
The positioning of the zeros indicated that there was no solution!
<u><em>Hope that helps!</em></u>
Answer:
x = 4
Step-by-step explanation:
For an equation of this sort, my first step is to rewrite it so the solutions are the x-intercepts of the graph:
(x +5)^(3/2) -(x +1)^3 = 0
The graph is attached. The one real solution is x=4.
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The solution method for something like this is necessarily ad hoc. Here, it appears that progress can be made by raising both sides of the equation to the 2/3 power:
((x +5)^(3/2))^(2/3) = ((x -1)^3)^(2/3)
x +5 = (x -1)^2
Now, you have an ordinary quadratic that can be solved using any of the usual methods.
x^2 -2x +1 = x +5 . . . . swap sides, expand the square
x^2 -3x -4 = 0 . . . . . . put in standard form
(x -4)(x +1) = 0 . . . . . . factor
The solutions to this are ...
x = 4, x = -1 . . . . . . . values of x that make the factors zero
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To see if either of these solutions is extraneous, we can check them:
(4 +5)^(3/2) = (4 -1)^3 . . . . . substitute 4 for x
9^(3/2) = 3^3 . . . . . . . . . true
(-1 +5)^(3/2) = (-1 -1)^3 . . . . . substitute -1 for x
4^(3/2) = (-2)^3
8 = -8 . . . . . . . . . . . false; x = -1 is extraneous
The solution is x = 4.
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<em>Additional comment</em>
You can eliminate the x=-1 "solution" by considering the domains of the left- and right-side expressions. The 3/2 power is equivalent to the square root of the cube. That will generally only be defined for non-negative values (x ≥ -5). The cube on the right will only be positive for x > 1, so the practical domain of this equation is x ≥ 1.
