Step-by-step explanation:
Claim:
it takes n - 1 number of breaks to break the bar into n separate squares for all integers n.
Basic case -> n = 1
The bar is already completely broken into pieces.
Case -> n ≥ 2
Assuming that assertion is true for all rectangular bars with fewer than n squares. Break the bar into two pieces of size k and n - k where 1 ≤ k < n
The bar with k squares requires k − 1 breaks and the bar with n − k squares
requires n − k − 1 breaks.
So the original bar requires 1 + (k−1) + (n−k−1) breaks.
simplifying yields,
1 + k − 1 + n − k − 1
1 - 1 + n - 1
n - 1
Therefore, we proved as we claimed that it takes n - 1 breaks to break the bar into n separate squares.
Answer:
<h3>
Any of them.</h3><h2>
a ∈ R</h2>
Step-by-step explanation:
-5x - 4y = 2a 4x - 5y = 2
-4y = 5x + 2a -5y = -4x + 2
y = (5x + 2a):(-4) y = (-4x + 2):(-5)
y = -⁵/₄x - ¹/₂a y = ⁴/₅x - ²/₅
m₁ = -⁵/₄, b₁ = -¹/₂a m₂=⁴/₅, b₂= -²/₅
-⁵/₄ ≠ ⁴/₅
Different slopes means that two lines have one point of intercept (no mater what the b's are). That means that the system of linear equations has exactly one solution for any value of a.
Answer:
After 10 years the ratio will be 10500: 500000
Answer:
Choice C: (x-2)^2 + (y-1)^2 = 25
