Step-by-step explanation:
Parallelogram
Reflect y=-1 ;x changes sign
Consider a population of size N = 100 with the three individual mutants with relative growth rate rA = 2, rB = 1.01, and rC = 0.
1 answer:
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Answer:
Step-by-step explanation:
Prove: That the sum of the squares of 4 consecutive integers is an even integer.
An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.
Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;
= 25
= 36
= 49
= 64
The sum of the squares = 25 + 36 + 49 + 64
= 174
Also,
Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;
= 100
= 121
= 144
= 169
The sum of the squares = 100 + 121 + 144 + 169
= 534
Therefore, the sum of the squares of 4 consecutive integers is an even integer.
Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
