For this case we have the following expression:

We have to:

Rewriting the expression and simplifying we have:

Answer:

Answer:
length of the longest pencil that can fit must be less than 13cm
Step-by-step explanation:
To get the longest pencil that fit the case, we will use the pythagoras theorem;
diameter = 10cm
radius = 10/2
radius = 5cm
Height = 12cm
Get the length of the longest side
l² = r²+h²
l² = 5²+12²
l² = 25 + 144
l² = 169
l = √169
l = 13cm
Hence the length of the longest pencil that can fit must be less than 13cm
Answer:
Compare the given equation of the circle (x - 1)² + (y -2)² = 2²
with standard form of circle: (x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle
and r is the radius of the circle.
Thus, The center of the circle is: (1, 2)
Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,
Substitute the value of y from equation of line in the equation of circle.
(x - 1)² + (2x + 2 - 2)² = 2²
⇒ (x - 1)² + (2x)² = 2²
⇒ x² + 1 - 2x + 4x² = 4
⇒ 5x² - 2x - 3 = 0
Applying Middle term splitting method
5x² - 5x + 3x - 3 = 0
⇒ 5x(x - 1) + 3(x - 1) = 0
⇒ (5x + 3)(x - 1) = 0
⇒ x =
and x = 1
Thus, we get coordinates:
and (1, 4)
7) 4/18 + 5/18 = 9/18 = 1/2
8) 3/18 + 4/18 + 5/18 = 12/18 = 4/5