For the following exercises, determine the function described and then use it to answer the question. 59. The surface area, A , of a sphere in terms of its radius, r , is given by A ( r ) = 4 π r 2 . Express r as a function ofV , and find the radius of a sphere with a surface areaof 1000 square inches.
For the following exercises, determine the function described and then use it to answer the question. 59. The surface area, A , of a sphere in terms of its radius, r , is given by A ( r ) = 4 π r 2 . Express r as a function ofV , and find the radius of a sphere with a surface areaof 1000 square inches.
For the following exercises, determine the function described and then use it to answer the question.
59. The surface area, A, of a sphere in terms of its radius,r, is given by
A
(
r
)
=
4
π
r
2
.
Express r as a function ofV, and find the radius of a sphere with a surface areaof 1000 square inches.
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.
A carton of milk has spilled on a tile floor. The milk flow can be expressed with the function m(t) = 9t, where t represents time in minutes and m represents how far the milk is spreading. The flowing milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A(m) = πm2.
Part A: Find the area of the circle of spilled milk as a function of time, or A[m(t)]. Show your work.
Part B: How large is the area of spilled milk after 2 minutes? You may use 3.14 to approximate π in this problem.
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.
The circumference C of a circle is a function of its radius given by C(r)=2πr.
a. Express the radius of a circle as a function of its circumference. Call this function r(C).
Enter the exact answer.
Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).
r(C)=
b. Find r(28π) and interpret its meaning.
r(28π)=
A
The radius of a circle with a circumference of 28π is r(28π).
Or
B
The radius of a circle with a circumference of r(28π) is 28π.
Differential Equations and Linear Algebra (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY