Posted by Julie on Sunday, February 10, 2013 at 9:54pm.
The formula for the area of a circle and the volume of a sphere an be though of as functions of the radii of the shapes.
(Anything you could answer would be so helpful) Thank you!!
a) Write a rule expressing the area of a circle as a function of its radius. What is the domain of this function? Sketch a graph.
b) does this function have an inverse? If so, write a rule for the inverse.
C) Explain why it makes sense that the radius of a circle should be a function of its area. In what contexts would this function be useful?
d) Does the function f(x)πx^2, where x is any real number, have an inverse? Compare your answer to that in part b. Explain any differences.
e) Now write a rule expressing the volume of a sphere as a function of its radius. What is the domain of this function? sketch a graph.
f) Does this function have an inverse function? If so, write a rule for the inverse function.
g) Explain why it makes sense that the radius of a sphere should be a function of its volume. In what contexts would this function be useful?
h) Does the function g(x)=4/3πx^3,where x is any real number, have an inverse? Compare your answer to that in part f. Explain any differences.
- Precalculus (Please Help!!??) - Steve, Monday, February 11, 2013 at 5:05am
(h) since x^3 is always increasing, there are no two values of x that give the same y. So, x^3 has an inverse
(b) not so for x^2, since there are two values of x for each y. If you restrict the radius to positive values, though, then x^2 has an inverse. Makes sense, since a negative radius makes no physical sense.
Answer this Question
Related Questions
math - The earth has a radius of 6,380 km. The formula for the volume of a ...
Precalculus - The sphereflake shown (not shown for question) is a ...
Physics - Sphere 1 has surface area A1 and volume V1, and sphere 2 has surface ...
8th grade math - circle A has a raduis that is twice the length og the raduis of...
Spheres, Locus (in space aka 3d) - 1) A "small circle" is a circle on ...
calculus - 3. The radius r of a sphere is increasing at a constant rate of 0.04 ...
surface area and volume - I really need some help, I don't fully understand...
Calculus - V=4/3 pi r ^3 is the formula for the volume of a sphere. Find dV for ...
Calculus (Parts A and B done, just help with C) - The radius, r, of a sphere is ...
math - Okay. So i'm doing this project for my geometry class about different...
For Further Reading
