April’s garden has 42 plants in each row. She has 2 rows of yellow corn and 20 rows of white corn.
1 answer:
Answer:
There are a total of 84 yellow corns and
840 white corns planted in the garden.
Step-by-step explanation:
Number of plants in each row = 42
Number of rows of yellow corn = 2
Number of rows of white corn = 20
To find the total number of yellow corns planted in the garden, we need to add the number of plants in each row 2 times.
i.e. 42 + 42 = 84
OR
we can say the following:
Total number of yellow corns planted in the garden = Number of rows of yellow corn Number of plants in each row
To find the total number of white corns planted in the garden, we need to add the number of plants in each row 20 times.
i.e. 42 + 42 + 42 + ....... + 20 times
OR
we can say the following:
Total number of white corns planted in the garden = Number of rows of white corn Number of plants in each row
Hence, there are a total of 84 yellow corns and 840 white corns planted in the garden.
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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
