Answer:
10^5 = 100000
Step-by-step explanation:
✌️❤️✌️
....
Use the Chinese remainder theorem. Suppose we set
. Then clearly taken modulo 12, the second term vanishes, and incidentally
; taken modulo 13, the first term vanishes, but the second term leaves a remainder of 2. To counter this, we can multiply the second term by the inverse of 12 modulo 13, which is 12 since
.
So, we found that
, but the least positive solution is
, and in general we can have
for any integer
.
Now, since
, or
, we know that there are 32 possible integers
that satisfy the congruences.
Answer:
- 24 cm²
- 6400 -1600π ≈ 1373.45 square units
Step-by-step explanation:
1. You can look at this several ways.
It can be considered to be a stack of 1+2+3 = 6 squares that are 2 cm on a side, so have a total area of 6 × (2 cm)² = 24 cm².
You can lop off one of the squares sticking out and put it into the empty corner to form a 6 cm by 4 cm rectangle with an area of (6 cm)(4 cm) = 24 cm².
You can consider it to be a 6 cm square with 3 squares cut out of it that are 2 cm on a side: (6 cm)² -3(2 cm)² = (36 -12) cm² = 24 cm².
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2. The shaded area is the difference in areas of a square 80 units on a side and a circle of 40 units radius. If we let d represent the side dimension of the square, then the area formulas are ...
Square area = d²
Circle area = π(d/2)²
So the difference area is ...
shaded area = d² -(π/4)d² = d²(1 -π/4)
For d=80, the shaded area is ...
shaded area = 80²(1 -π/4) = 6400 -1600π ≈ 1373.45 square units
