11) the difference between the product of 4 and a number and the square of the number
1 answer:
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Answer:
Yes!
Step-by-step explanation:
We know that right triangles follow the Pythagorean Theorem, where
So we will put our side lengths into this formula, keeping in mind that c = the hypotenuse, which is the longest side. a and b are fairly arbitrary.
If this works, we know it's a right triangle.
1089 + 1936 = 3025
3025 = 3025
It worked! It's a right triangle!!
To check for continuity at the edges of each piece, you need to consider the limit as approaches the edges. For example,
has two pieces, and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have
By definition of , we have
, and the limits are
The limits match, so is continuous.
For the others: Each of the individual pieces of are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.