Question

Algebra 2 Question

A. The surface area S of the greenhouse is given by S = πr^2+πrl. Substitute 600 for S and then write an expression for l in terms of r.

B. The volume V of the greenhouse is given by V = 1/2πr^2l. Write an equation that gives V as a polynomial function of r alone.

** l meaning length **

Answer 1

May I help?

Answer 2

Yes please

Answer 3

Of course.
That is with my pleasure!

Answer 4

For A:
The surface area S of the greenhouse is given by S = πr^2+πrl. Substitute 600 for S and then write an expression for l in terms of r.

I think it is a simple substitution operation.

Just replace S with 600 and solve for l, can you?

Answer 5

600 - πr^2 / πr = l

Answer 6

you mean this:
\[\Large 600=πr^2+ πrl\]
\[\Large 600-πr^2= πrl\]
\[\Large\frac{ 600-πr^2 }{ πr }= l\]
??

Answer 7

Yes

Answer 8

For A\[\Huge\color{red}\checkmark\]

Answer 9

Ok good! Now for B, this is where I struggle

Answer 10

Now: B...easy In Sha' Allah

B. The volume V of the greenhouse is given by V = 1/2πr^2l. Write an equation that gives V as a polynomial function of r alone.

please type in the volume form in terms of r only. Can you?

Answer 11

\[V = (1/2πr^2) 600-πr^2/πr\]

Answer 12

Can you use the parentheses, please?
It matters a lot!

Answer 13

\[V = (1/2πr^2) (600-πr^2/πr)\]

Answer 14

That makes sense! and it is away better!

Answer 15

Are there more steps/ can it be simplified anymore?

Answer 16

\[\Huge\color{DodgerBlue}{V=\frac{ 1 }{ 2 }\color{Brown }{\pi r}^2[\frac{ 600-\pi r^2}{ \color{Brown }{\pi r} }]}\]

Can you cancel something?

Answer 17

the πr right? Then what happens with the exponent?

Answer 18

\[V=\frac{ 1 }{ 2 }^2\left( 600-πr^2 \right)\]

Answer 19

\[V=\frac{ 1 }{ 4}(600-πr^2)\]

Answer 20

"the πr right? "

Yes, that is right!

Answer 21

\[\Huge\color{DodgerBlue}{V=\frac{ 1 }{ 2 }\color{Brown }{(\pi r)}*r[\frac{ 600-\pi r^2}{ \color{Brown }{\pi r} }]}\]

Does it make sense now?

Answer 22

Yes

Answer 23

so it would be \[V = \frac{ 1 }{ 2 }r(600-πr^2)\]

Answer 24

\[\Huge\color{Chocolate }\checkmark\]


Can you now "write an equation that gives V as a polynomial function of r alone"?
that means: mutiply \(\frac{1}{2}\) by the parentheses!

Answer 25

\[V=300r-1.57r^3\]

Answer 26

\[V = -1.57r^3 +300r\]

Answer 27

\[V = -π(\frac{ 1 }{ 2 })r^3+300r\]

Answer 28

\[\Huge\color{Orchid }{V = -(\frac{ \pi }{ 2 })r^3+300r}\]
\[\Huge\color{Orange }\checkmark\]

Answer 29

You are one of the best students I have ever met who quickly responds!
You are Awesome!

Answer 30

Thank you very much for your help. I really appreciate it!

Answer 31

I thank you that you gave me that chance to help you!
Honor is mine to be your helper!

Answer 32

If there are any more questions, pleasure is mine to help!

Answer 33

Let me know where you are back!