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- anonymous

2. Are the following statements always true, sometimes true, or never true? For statements that are always true or never true, explain how you know this. For statements that are sometimes true, draw an example showing the statement’s being true and an example showing the statement’s being untrue.
(a) A triangle with an obtuse angle has an acute angle.
(b) A triangle with a right angle has an obtuse angle.
(c) A triangle with an acute angle has an obtuse angle.
(d) A triangle with an acute angle has another acute angle.

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a has both the acute angles
b.no,as sum of three angles=180
c.may or may not be true.
d. may or may not be true.

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3. Ms. Jones keeps her pigs in a fenced pen that has the shape of a regular pentagon. The area of the pen is 50 ft2 and the apothem is 4 ft. Ms. Jones has decided that she wants to remake the pig living area to be in the shape of a rectangle instead. She wants to reuse the same amount of fence to make the new rectangular living space.
Ms. Jones wants to give the pigs as much living space as possible. What should the dimensions and the area of the rectangular space be in order to provide the most area with the given amount of fence? Ms. Jones plans to cut the fence only in half- and whole-foot units. Show your work and explain your reasoning.

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|dw:1433866398706:dw|

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|dw:1433880737409:dw|
let x and y be the sides of the rectangle
then 2(x+y)=24
x+y=24/2=12
y=12-x
area A=xy=x(12-x)=12x-x^2
\[\frac{ dA }{ dx }=12-4x\]
\[\frac{ dA }{ dx }=0,~gives~12-4x=0,x=3\]
\[\frac{ d^2A }{ dx^2 }=-4\]
at x=3,\[\frac{ d^2A }{ dx^2 }=-4<0\]
Hence A is maximum at x=3
y=12-3=9
area=9*3=27

- anonymous

correction 2.9*2=5.8
make corresponding changes

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2*5.8=29

- anonymous

2(x+y)=29
x+y=29/2
y=29/2- x
A=xy=x(29/2-x)
\[A=\frac{ 29 }{ 2 }x-x^2\]

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