Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, and then rode from the beach to
2 answers:
Answer:
Elia was riding of an hour from the house to the beach,
of an hour from the beach to the house and rode
kilometers from the house to the beach and
kilometers from the beach to the house.
Step-by-step explanation:
1. Let b be the number of hours it took Elia to ride from her house to the beach, and p the number of hours it took her to ride from the beach to the park. The total duration of the rides was 1 hour, so
b + p = 1
2. Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, she was riding for b hour, then she rode 18b kilometers from her house to the beach.
Elia rode from the beach to the park at a constant speed of 15 kilometers per hour, she was riding for p hours, then she rode 15p kilometers from the beach to the house.
The distances she rode in each direction are equal, so
18b = 15p
3. Solve the system of two equations:
From the first equation
Substitute it into the second equation
Elia was riding of an hour from the house to the beach,
of an hour from the beach to the house and rode
kilometers to the beach and
kilometers fro mthe beach to the house.
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Answer:
The function that could be the function described is;
Step-by-step explanation:
The given parameters of the cosine function are;
The period of the cosine function = 3
The maximum value of the cosine function = 20
The minimum value of the cosine function = 0
The general form of the cosine function is presented as follows;
y = A·cos(ω·x - ∅) + k
Where;
= The amplitude = Constant
The period, T = 2·π/ω
The phase shift, = ∅/ω
k = The vertical translation = Constant
Therefore, by comparison, we have;
T = 3 = 2·π/ω
∴ ω = 2·π/3
The range of value of the cosine of an angle are;
-1 ≤ cos(θ) ≤ 1
Therefore, when A = 10, cos(ω·x - ∅) = 1 (maximum value of cos(θ)) and k = 10, we have;
y = A × cos(ω·x - ∅) + k
y = 10 × 1 + 10 = 20 = The maximum value of the function
Similarly, when A = 10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, we get;
y = 10 × -1 + 10 = 0 = The minimum value of the function
Given that the function is a reflection of the parent function, we can have;
A = -10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, to get;
y = -10 × -1 + 10 = 20 = The maximum value of the function
Similarly, for cos(ω·x - ∅) = 1 we get;
y = -10 × 1 + 10 = 0 = The minimum value of the function
Therefore, the likely values of the function are therefore;
A = -10, k = 10
The function is therefore presented as follows;
y = -10 × cos(2·π/3·x) + 10