For the following exercises, write the polynomial function that models the given situation. 79. A right circular cone has a radius of 3 x + 6 and aheight 3 units less. Express the volume of the coneas a polynomial function. The volume of a cone is V = 1 3 π r 2 h for radius r and height h .
For the following exercises, write the polynomial function that models the given situation. 79. A right circular cone has a radius of 3 x + 6 and aheight 3 units less. Express the volume of the coneas a polynomial function. The volume of a cone is V = 1 3 π r 2 h for radius r and height h .
For the following exercises, write the polynomial function that models the given situation. 79. A right circular cone has a radius of
3
x
+
6
and aheight 3 units less. Express the volume of the coneas a polynomial function. The volume of a cone is
V
=
1
3
π
r
2
h
for radius r and height h.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
The circumference of a sphere is a function of its volume, given by the formula:
C = (π)2/3(6V)1/3
Find the circumference when the volume is 36π.
A contractor is constructing the house shown in the figure. The cross section up to the roof is in the shape of a rectangle. The area of the rectangular floor of the house is 2500 square feet. Express the perimeter of the rectangular floor, P, as a function of the width of the rectangle, x.
Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis and the base on the x-axis.
The top curve of the cross-section is given by the function
Both and y are in cm. Assume that the bowl is solid.
Perimeter of the cross-section ===
y =
Surface area of the bowl =
√x²¹ (9 − x)
979
Use a calculator or a computer to evaluate the integrals.
1
- *(9+)
979
a. Find the perimeter of the entire cross-section (the grey region of the graph on the right). Round your answer to at least 3 significant figures and include the unit.
0≤x≤9.1
-9.1 <<0
b. Find the surface area of the bowl (top and bottom). Round your answer to at least 3 significant figures and include the unit.
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