Answer:
θ = π/3 and 5π/3
Step-by-step explanation:
x = r cos θ and y = r sin θ. Therefore:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)
In this case, r = 1 + cos θ and r' = -sin θ.
dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)
dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)
dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))
dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))
The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.
0 = 2 cos²θ + cos θ − 1
0 = (cos θ + 1) (2 cos θ − 1)
cos θ = -1 or 1/2
θ = π/3, π, 5π/3
0 = -sin θ (1 + 2 cos θ)
sin θ = 0 or cos θ = -1/2
θ = 0, 2π/3, π, 4π/3
Therefore, the answer is θ = π/3 and 5π/3.
Answer:
= 1/26
Step-by-step explanation:
Use Division Distributive Property:
(x/y)^a = x^a/y^a
(^, That means to the power of exponents.)
Then you Simplify 6^3 to 216
Then you will get 1 over 216.
Answer: 9 gallons
Step-by-step explanation:
How many gallons needed for small car: 375/32 = 11.7 or 12
How many gallons for large car: 375/18 = 20.8 or 21
21-12 = 9
The answer to your question is 3
