I solved this quadratic using the square root property. I did it 2 ways but I am not sure which one is correct.
2 answers:
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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}
_____
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.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
_____
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.
Answer:
Step-by-step explanation:
Given
x = hours spent on cardiovascular work
y = hours spent on weight training
From the first statement,
Each week: he spends at least 9 hours
This is represented as:
From the second statement,
Each week: he spends a max of 12 hours on weights
This is represented as:
From the third statement,
Each week: he spends a max of 6 hours on cardio works
This is represented as:
So, the inequalities are:
See attachment for the graph where the solution are also highlighted
From the attachment, the solutions are:
