For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 88. A right circular cylinder is to have a volume of40 cubic inches. It costs 4 cents/square inchto construct the top and bottom and 1 cents/square inch to construct the rest of the cylinder. Find theradius to yield minimum cost. Let x = radius.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 88. A right circular cylinder is to have a volume of40 cubic inches. It costs 4 cents/square inchto construct the top and bottom and 1 cents/square inch to construct the rest of the cylinder. Find theradius to yield minimum cost. Let x = radius.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 88. A right circular cylinder is to have a volume of40 cubic inches. It costs 4 cents/square inchto construct the top and bottom and 1 cents/square inch to construct the rest of the cylinder. Find theradius to yield minimum cost. Let x= radius.
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.
Assume a box has a square base and the length of a side of the base is equal to twice the height of the box.
a. If the height is 6 inches, what are the dimensions of the base?
The dimensions of the base are
inches X
inches =
square inches.
b. Write functions for the surface area and the volume that are dependent on the height, h.
S(h) = nh" square inches, where n =
and m =
%3D
V(h) =
ph° cubic inches where p =
and g =
%3D
c. If the volume has increased by a factor of 27, what has happened to the height?
The new height is
times the original height.
d. As the height increases, what will happen to the ratio of (surface area)/volume?
The ratio will
not chänge
e Textbook
Increase
decrease
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.
College Algebra with Modeling & Visualization (6th Edition)
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