Homework problems

[cal quw wus69]

1.A spherical balloon with radius r inches has volume defined by the function below. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. (Give the answer in terms of ? and r.)

V(r)=4/3(pi)r(to the third)... Already tried V(r)=4/3(pi)(r+2)(to the third).. didnt work

2.Find the domain of the function. (If you need to use - or , enter -INFINITY or INFINITY.)

G(u)=square root of (u) + square root of(1-u)... already tried (1,-infinity)

sorry about the wierd functions but im new to this form and dont know how to write equations in it yet.. ahh Calculus is a bitch and if someone could help i would really appreciate it

 

[BigGlenntheHeavy]

\(\displaystyle 2) \ g(u) \ = \ \sqrt u+\sqrt{1-u}\)

\(\displaystyle Now. \ in \ real \ number \ land \ the \ \ square \ root \ of \ anything \ must \ be \ \ge \ 0.\)

\(\displaystyle Hence, \ u \ \ge \ 0 \ and \ 1-u \ \ge \ 0, \ \implies \ u \ \ge \ 0 \ and \ u \ \le \ 1, \ ergo\)

\(\displaystyle the \ domain \ of \ g(u) \ is \ [0,1], \ QED\)

\(\displaystyle Note: \ We \ have \ to \ take \ each \ term's \ intersection \ so \ the \ whole \ equation \ is \ satisfied,\)

\(\displaystyle or \ (-\infty,1] \ intersection \ [0,\infty)\)

 

[galactus]

1.A spherical balloon with radius r inches has volume defined by the function below. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. (Give the answer in terms of ? and r.)

The amount of air required to inflate the balloon from \(\displaystyle \frac{4}{3}{\pi}r^{3}\) to \(\displaystyle \frac{4}{3}{\pi}(r+2)^{3}\)

Would be the difference between the two volumes.

\(\displaystyle \underbrace{\frac{4}{3}{\pi}(r+2)^{3}}_{\text{final amount}}-\overbrace{\frac{4}{3}{\pi}r^{3}}^{\text{initial amount}}=\underbrace{\frac{8\pi(3r^{2}+6r+4)}{3}}_{\text{amount added}}\)

 

[cal quw wus69]

AHH makes sense now.. Much thanks to you both!