Answer:
She used inductive reasoning. (False)
She used the law of detachment. (True)
Her conclusion is valid. (True)
The statements can be represented as "if p, then q and if q, then r." (False)
Her conclusion is true. (True)
Step-by-step explanation:
p = Two lines are perpendicular
q = They intersect at Right angles.
Given: A and B are perpendicular
Conclusion: A and B intersect at right angle.
According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.
Answer:
300 paper clips in one box
300 multiply to 10 box =3,000 paper clips
Both functions are the solution to the given Laplace solution.
Given Laplace's equation: 
- We must determine whether a given function is the solution to a given Laplace equation.
- If a function is a solution to a given Laplace's equation, it satisfies the solution.
(1) 
Differentiate with respect to x as follows:

Differentiate with respect to y as follows:

Supplement the values in the given Laplace equation.

The given function in this case is the solution to the given Laplace equation.
(2) 
Differentiate with respect to x as follows:

Differentiate with respect to y as follows:

Substitute the values to obtain:

The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
Know more about Laplace's equation here:
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The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)
Answer: x=9/4
Step-by-step explanation:
combine like terms then
4x+7=16
4x=9
x=9/4 or 2.25