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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 :

Trancescient

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]

lhmarianateixeira

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

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