<h3>Given</h3>
- a rectangle x units wide and y units high divided into unit squares
<h3>Find</h3>
- The total perimeter of the unit squares, counting each line segment once
<h3>Solution</h3>
For each of the y rows of squares, there are x segments at the top, plus another x segments at the bottom. The total number of horizontal segments is then
... horizontal segment count = (y +1)x
Likewise, for each of the x columns of squares, there are y segments to the left, plus another y segments to the right of the entire area. Then the total number of vertical segments is
... vertical segment count = (x+1)y
The total segment count is ...
... total segments = horizontal segments + vertical segments
.. = (y+1)x +(x+1)y
... total segments = 2xy +x +y
_____
<u>Check</u>
We know a square (1×1) has 4 segments surrounding it.
... count = 2·1·1 +1 +1 = 4 . . . . (correct)
We know the 3×3 window in the problem statement has 24 segments.
... count = 2·3·3 +3 +3 = 18 +3 + 3 = 24 . . . . (correct)
We know a 1×3 row of panes will have 10 frame elements.
... count = 2·1·3 +1 +3 = 6 +1 +3 = 10
It looks like our formula works well.
Answer: x = {+-sqrt(3), +-2*sqrt(3)}.
Step-by-step explanation:
(x^2 - 8)^2 + (x^2 - 8) = 20
▪︎ Let (x^2 - 8) be y.
Then,
y^2 + y = 20
y^2 + y - 20 = 0
D = b^2 - 4ac = 1 + 20*4 = 81 = 9^2
y1 = (-b - sqrt(D))/(2a) = (-1 - 9)/2 = -10/2 = -5
y2 = (-b + sqrt(D))/(2a) = (-1 + 9)/2 = 8/2 = 4
1) x^2 - 8 = -5
x^2 = 8 - 5
x^2 = 3
x = +-sqrt(3)
2) x^2 - 8 = 4
x^2 = 8 + 4
x^2 = 12
x = +-sqrt(12)
x = +-2*sqrt(3)
Answer:
C 58
Step-by-step explanation:
I believe the slope you are looking for is 1,1 (don’t quote me though it been a while)
