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.
is the number <em>L</em> such that

Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so <em>L</em> = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:

since 2*4 = 8, whose residue is 1 mod 7;

which we got for free by finding the inverse of 5 earlier. So

and so <em>R</em> = 2.
Then <em>L</em> - <em>R</em> = 1.
Answer:
slope is 2/3.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Comment
The square of the tangent = the external segment of the secant * the full length of the secant.
Formula
(x - 1)^2 = (x - 3)*(x - 3 + 5) Combine the right
Solution
(x - 1)^2 = (x - 3)*(x +2) Remove the brackets on both sides
x^2 - 2x + 1 = x^2 -3x + 2x - 6 Combine the right
x^2 - 2x + 1 = x^2 - x - 6 Subtract x^2 from both sides
-2x + 1 = - x - 6 Add 6 to both sides
-2x + 1 + 6 = -x - 6 + 6 Combine
-2x + 7 = - x Add 2x to both sides
-2x+2x + 7 = -x+2x Combine
7 = x
Answer
x = 7