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.
Based on the information given the original size of the bottle is 17.5 ounces.
Using this formula
Original size of the bottle
=New bottle size / Percentage increase
Where:
New bottle size=18.4 ounces
Percentage increase=(1+0.05)=1.05
Let plug in the formula
Original size of the bottle=18.4/(1+0.05)
Original size of the bottle=18.4/1.05
Original size of the bottle=17.5 ounces
Inconclusion the original size of the bottle is 17.5 ounces.
Learn more about original size of the bottle here:brainly.com/question/25001466
Answer:
The answer is A
Step-by-step explanation:
y=1.3(5) + 10 = 16.5 ---> True
y=1.3( 10) + 10 = 23 ----> True
y=1.3(15) + 10 = 29.5 ----> True
y=1.3(20) + 10 = 36 ----> True
0.77777777777777 and goes on forever since anything/9 is 0.(whatever that number is repeated)
D. 24x + 16y is your answer
