I think the answer would be 4/5
The given equation of the ellipse is x^2
+ y^2 = 2 x + 2 y
At tangent line, the point is horizontal with the x-axis
therefore slope = dy / dx = 0
<span>So we have to take the 1st derivative of the equation
then equate dy / dx to zero.</span>
x^2 + y^2 = 2 x + 2 y
x^2 – 2 x = 2 y – y^2
(2x – 2) dx = (2 – 2y) dy
(2x – 2) / (2 – 2y) = 0
2x – 2 = 0
x = 1
To find for y, we go back to the original equation then substitute
the value of x.
x^2 + y^2 = 2 x + 2 y
1^2 + y^2 = 2 * 1 + 2 y
y^2 – 2y + 1 – 2 = 0
y^2 – 2y – 1 = 0
Finding the roots using the quadratic formula:
y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1
y = 1 ± 2.828
y = -1.828 , 3.828
<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828)
and (1, 3.828).</span>
Answer:
$3364.65
Step-by-step explanation:
The volume of the cone is given by the formula ...
V = (1/3)πr²h
Filling in the given numbers, we find the volume to be ...
V = (1/3)π(1.5 m)²(7 m) = 5.25π m³ ≈ 16.49336 m³
The cost of the rice will be the product of this volume and the price per cubic meter:
cost = (16.49336 m³)($204/m³) = $3364.65
The cost of the rice necessary to fill the volume is $3364.65.
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<em>Comment on pi</em>
If you use the value 3.14 for pi, the cost comes to $3362.94. A 3-digit value of pi only gives an answer good in its first 3 digits.
Answer:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
Step-by-step explanation:
27(1/3)^3
81^3
512
