This is a work problem. It can be solved as follows:
Houston = 1/x
Dominique = (1/2x)
Together = 1/5
Then, we add Houston and Dominique:
1/x + 1/2x = 1/5
Solve for x,
x = 2/15
Therefore, it would take 15/2 hours for Houston to ice by himself, the last option.
Answer: $8,347.50 is the value of his account after five years.
Interest is $409.50 per year.
Total amount of interest paid is $2,047.50.
Answer:
Amanda found the equation 10x+5y=20 in the “linear equations” chapter of her math book.
Step-by-step explanation:
Amanda found the equation 10x+5y=20 in the “linear equations” chapter of her math book.
If (-1, -1) is an extremum of , then both partial derivatives vanish at this point.
Compute the gradients and evaluate them at the given point.
The first and third functions drop out.
The second function depends only on . Compute the second derivative and evaluate it at the critical point .
This indicates a minimum when . In fact, since this function is independent of , every point with this coordinate is a minimum. However,
for all , so (-1, 1) and all the other points are actually <em>global</em> minima.
For the fourth function, check the sign of the Hessian determinant at (-1, 1).
The second derivative with respect to is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.
The correct choice is the fourth function.