Question

check my ans please:

I am working on a differentiation question.
Can you please check if i have differentiated correctly below and solved for x

Answer 1

\[A=4x-2x^2-\frac{ \pi x^2 }{ 2 }\]
\[A'=4-4x-\pi x\]

Answer 2

correct!

Answer 3

now to set f'(x)=0
\[4-4x-\pi x=0\]
\[x=\frac{ 4 }{ 4+ \pi }\]

Answer 4

so then
\[2x=2*\frac{ 4 }{ 4+ \pi }\]
\[=\frac{ 8 }{ 4+\pi }\]

Answer 5

correct!

Answer 6

then i have
\[h=2-x-\frac{ \pi x }{ 2 }\]

Answer 7

no sorry, that is my h . i need to sub in x

Answer 8

then i have:
\[h=2-\frac{ 4 }{ 4+\pi }-\frac{ \pi }{ 2 }\frac{ 4 }{ 4+x }\]

Answer 9

\[h=2-\frac{ 4 }{ 4+\pi }-\frac{ 4 \pi }{ 8+2 \pi }\]

Answer 10

\[h=2-\frac{ 4 }{ 4+\pi }-\frac{ 2\pi }{ 4+\pi }\]

Answer 11

is \(A(x)\) the area of a triangle?

Answer 12

\[h=2-\frac{ 4-2\pi }{ 4+\pi }\]

Answer 13

my area equation and h equation is both correct

Answer 14

\[h=\frac{ 2(4+\pi) }{ (4+\pi) }-\frac{ 4-2\pi }{ 4+\pi }\]
\[h=\frac{ 8+2\pi }{ 4+\pi }-\frac{ 4-2\pi }{ 4+\pi }\]

Answer 15

\[h=\frac{ 4 }{ 4+\pi }\]

Answer 16

the answer reads (8/4+pi) and i got 4 .. .

Answer 17

from your drawing, I can write the area \(A(x)\) as below:
\[A\left( x \right) = 2hx + \frac{{\pi {x^2}}}{2}\]

Answer 18

this is the actual question

Answer 19

\(h(x)\) is correct!

Answer 20

maybe it is an error in the model answers?

Answer 21

also \(A(x)\) is correct!

Answer 22

maximum of \(A(x)\) is at:
\[x = \frac{4}{{4 + \pi }}\]
so, correct!

Answer 23

great thanks so much. i did about 4 pages of work trying to see where i went wrong..

Answer 24

by substitution into \(h(x)\), I get:
\[{x_0} = \frac{4}{{4 + \pi }},\quad h\left( {{x_0}} \right) = \frac{8}{{2\left( {4 + \pi } \right)}}\]

Answer 25

where am i going wrong

Answer 26

namely:
\[h\left( {{x_0}} \right) = \frac{8}{{2\left( {4 + \pi } \right)}} = \frac{4}{{4 + \pi }}\]

Answer 27

of, course the base is:
\[2{x_0} = \frac{8}{{4 + \pi }}\]

Answer 28

so maybe a printing error in the book?

Answer 29

I think it is possible

Answer 30

could you look over another question plz? its the wording of it i am not really sure of

Answer 31

ok!

Answer 32

last question

Answer 33

please wait, I'm working on it...

Answer 34

sure thanks..

Answer 35

could u also explain what part (c) is actually asking me to do please?

Answer 36

I start from point c)

the area of the rectangle is:
\[A\left( x \right) = 2x \cdot \left( {9 - {x^2}} \right)\]