Answered

Find the best solutions to your problems with the help of IDNLearn.com's experts. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

I need help please!!


assume that the height of your cylinder is 8 inches. consider a as a function of r, so we can write that as a(r)=2πr2+16πr. what is the domain of a(r)? in other words, for which values of r is a(r) defined? part b: continue to assume that the height of your cylinder is 8 inches. write the radius r as a function of a. this is the inverse function to a(r), i.e to turn a as a function of r into. r as a function of a.

I Need Help Please Assume That The Height Of Your Cylinder Is 8 Inches Consider A As A Function Of R So We Can Write That As Ar2πr216πr What Is The Domain Of Ar class=

Sagot :

Trancescientidn

Step-by-step explanation:

The domain of A(r) is [tex]r \geq 0.[/tex] The expression for A(r) is

[tex]A(r) = 2\pi r^2 + 16\pi r[/tex]

Let's write A(r) as simply A and divide the equation by [tex]2\pi[/tex] to get

[tex]r^2 + 8r = \dfrac{A}{2\pi}[/tex]

We can complete the square on the left hand side by adding 16 to both sides:

[tex]r^2 + 8x + 16 = \dfrac{A}{2\pi} + 16[/tex]

[tex]\Rightarrow (r + 4)^2 = \dfrac{A}{2\pi} + 16[/tex]

Taking the square root of the equation above and then solving for r, we get

[tex]r = -4 \pm \sqrt{\dfrac{A}{2\pi} + 16}[/tex]

Lhmarianateixeiraidn

In this exercise we have to use our knowledge about cylinders to calculate the function that best represents its value:

[tex]r=-4+\sqrt{\frac{A}{2\pi} +16}[/tex]

The area domain of A can be written as:

[tex]A(r)=2\pi r^2+16\pi r[/tex]

Let's write A(r) as simply A and divide the equation by [tex]2 \pi[/tex]to get:

[tex]r^2+8r=\frac{A}{2\pi}[/tex]

Now we can sum on both sides like:

[tex]r^2+8X+16=\frac{A}{2\pi}+16\\(r+4)^2=\frac{A}{2\pi}+16[/tex]

Taking the square root of the equation above and then solving for r, we get:

[tex]r=-4+\sqrt{\frac{A}{2\pi} +16}[/tex]

See more about cylinders at brainly.com/question/3692256

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.