Cindy wants to predict how much energy she will use to heat her home based on how cold it is outside. The table below shows the
mean amount of gas per day (in cubic meters) that Cindy used each month and the average temperature that month (in degrees Celsius) for one heating season.
a.)
b.)
c.)
d.)
a.)
b.)
c.)
d.)
2 answers:
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Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = (
) =
( or 60° )
Answer:
Statement A is TRUE.
Given an x value of 15, y would be ;
= 2.72 * 15
= 40.8
Coordinates would therefore be (15, 40.8)
Statement B is FALSE.
The coordinates of Y given are impossible given the coordinates of X. In this scenario, Y must always be greater than X as a result of the equation.
Statement C is TRUE.
The slope in the equation takes the form of the $2.72 price being charged per gallon of gasoline such that the total price of x gallons can be calculated by multiplying the number of gallons by $2.72
Statement D is FALSE.
If the price of gasoline were to decrease by $0.03, the slope would become 2.69 not 2.75. 2.75 would be the new slope if the price had increased by $0.03 instead of decreased.
