17 over 5 switched to a mixed number
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:
and
.
Step-by-step explanation:
Let I represent inches and F represent feet.
We have been given that on he scale drawing of a car, the length from bumper to bumper is 6 inches. The car's actual length, from bumper to bumper, is 16 feet.
We will use proportions to solve our given problem as:
Now, let us solve for .
Now, let us solve our equation for F.
Therefore, our required equations would be and
.