hello can somebody help me?????

Question

A farmer wishes to build a rectangular sheep pen with a 160m fence,using one side of an existing shed as the side.the shed is also rectangular of measurement 20m*20m.
a)Find the measurement and the area of the sheep pen if one side of the existing shed is used as the width of the sheep pen.
b)By using the fence of the same length and using the width of the shed as part of the width of the sheep pen,find the length and width of the sheep pen with maximum area.
c)If two sheep pens of the same size are built adjacent to each other,Find 1: the length of the new sheep pen if one side of the shed is used as the width of the sheep pen..2:the length and width of the sheep pen,which is adjusted so that rhe enclose area is maxmum.
d)find the maximum enclose area if the same fence is used to construct three rectangular sheep pens

Answer 1

I'll help with the first two, and then I think you'll get the idea for the rest.

a) If exactly one side of the existing shed is used, that means that one of the four sides of the rectangle is 20 meters in length. It also means that the opposite side is also 20 meters. That leaves 140 meters of fencing to finish the other two sides. So, the dimensions of the sheep pen are 20 by 70, and the area is 1400 square meters.

b) This is trickier. You need an equation for the area, which is h*w.
Then, if "h" is the side that includes the shed, h+h+w+w - 20 = 160.
so we know that 2h+2w = 180, or h+w = 90, or h = 90-w
Now we want to maximize area, so write the area as:
h*w or f(w) = w*(90-w) = 90w-w^2 and simply take the derivative of this function and find the point where it is zero.

Answer 2

lol reminded me of a song ive not heard for years sung by Charlie Drake In the bad bad lands of Australia many years ago The Aborigine tribes were meeting, having a big pow-wow (chanting) (low voice): We've got a lot of trouble, Chief, on account of your son Mac! (midrange voice): My boy Mac, what's wrong with him? (high-pitched voice, young prince): My boomerang won't come back! (low voices): Your boomerang won't come back (prince): My boomerang won't come back My boomerang won't come back I've waved the thing all over the place Practiced till I was black in the face I'm a big disgrace t' the Aborigine race My boomerang won't back I want a kangaroo (yeah yeah) Make kangatoo stew (yea yeah) But I'm a big disgrace t' the Aborigine race My boomerang won't back They banished him from the tribes' lair & sent him on his way He had a hapless boomerang, so here he could not stay (shrieks of animals) (prince): This is nice, isn't it? Getting banished at my time in life. What a way to spend an evening. Sittin' on a rock in the middle of the desert with me boomerang in me hand. I should very likely get bushwhacked. (animal shriek) (prince): Get out of here, nasty bushwhackin' animal! Think I'll make a nice cup of tea. (boing boing boing) (prince): Good gracious! There goes a kangaroo! I must have practice with me boomerang. Hey, right behind the left elbow, then slowly back... (kangaroo): If you throw that thing at me, I'll jump right on your head! (laughs) (prince): Ain't it marvelous! In a land full of kangaroos I might not get that one! For 3 long months he sat there, or maybe it was 4 Then an old old man in a kangaroo skin came a-knockin' at his door (old man): I'm the local with doctor, son. They call me Joe Joseph Black. Now tell me, what's your trouble, boy? (prince): My boomerang won't come back! (old man): Your boomerang won't come back (prince): My boomerang won't come back My boomerang won't come back I've waved the thing all over the place Practiced till I was black in the face I'm a big disgrace t' the Aborigine race My boomerang won't back (old man): Don't worry, boy, I know the trick & to you I'm gonna show it If you want your boomerang to come back, well, first you've got to throw it! (prince): Oh yes, never thought of that. Daddy will be pleased. Must have a girl... (old man): Excuse me. Now then, slowly back...& throw! (sound of boomerang flying) (old man): Oh my God! Avit the flying doctah! He-he-he-he! (prince): Can you do farther eat? (old man): Don't talk to me about first taste boy; you owe me 14 chickens for teaching you to throw the boomerang; first things first. (prince): Yes, I know that, but I mean, I think, on this occasion, you know ...& fade