The path of a prairie dog as it burrows underground is modeled by the equation
1 answer:
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Answer:
V = 1206.3
Step-by-step explanation:
This shape is made up of a cylinder on the bottom and a cone on the top. We'll find the volumes of these shapes separately and then add them together.
Volume of a cylinder = area (of the base) x height
Substitute in the formula for the area of a circle.
V(cylinder) = x h
Substitute in the values for the radius (8) and height (4)
V(cylinder) = x
x 4
Evaluate using a calculator
V(cylinder) = 804.2477
To the nearest tenth, V(cylinder) = 804.2
Volume of a cone = . This is the area of the circular part of the cone (
), multiplied by the height from the point to the base, all divided by 3.
Substitute in the values for the radius of the circle (8) and the height (6)
V(cone) = (On the top it's
x
x 6)
Evaluate using a calculator
V(cone) = 402.1239
To the nearest tenth, V(cone) = 402.1
Total volume = V(cylinder) + V(cone)
= 804.2 + 402.1
= 1206.3
Step-by-step explanation:
This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a
The formula for the foci of the vertical ellipse is
(h,k+c) and (h,k-c).
where c is
Our center (h,k) is (2, -5)
Here a^2 is 9, b^2 is 4.
So our foci is
and