An expression is shown below.
1 answer:
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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
Answer:
8
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial being divided by a factor in the form of
, then the remainder of the polynomial is given by
.
We have the polynomial:
And it is being divided by:
We can rewrite our factor as:
Therefore:
Then our remainder will be:
Evaluate:
So, our remainder will be 8.
Answer:
The proportion is
Step-by-step explanation:
We have to:
In June 20 of 500 wagons failed
On July 25 of 625 wagons failed
If we call x the number of wagons and and the number of wagons that had failures then we have to for June:
For July we have
The proportions are the same for both months
The proportion is
This means that of every 25 wagons, one has faults