Pythagoras help needed please
1 answer:
Answer:
See explanation
Step-by-step explanation:
Find the diagonal of the square. The side of the square is 5 cm long. By the Pythagorean theorem,
If the square (being inside the circle) touches the circle, then the diagonal of the square is exactly the diameter of the circle. The diameter of the circle is twice the radius of the circle, so
Since the diagonal is shorter than the diameter, the square can fit into the circle without touching the circle.
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Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If , then
.
Let's simplify that.
Distribute with :
Combine the end like terms :
Use identity for
:
Combine like terms and
:
We are given .
So we have that .
The vertex happens at .
Compare to
to determine
.
Let's plug it in.
So the coordinate is 5.
Let's find the corresponding coordinate by evaluating our expression named
at
:
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is where the vertex is
.
Let's put into this form.
We are given .
We will need to complete the square.
I like to use the identity .
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of
which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.