Hi,everyone. I have a advanced maths exercise I can't solve. The question is about constructing a sheep pen:
A farmer wishes to build a rectangular sheep pen with a 160m fence,using one side of the existing shed as the side. The shed is also rectangular of measurement 20m X 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 the part of the width of the sheep pen,find the length and width of the sheep pen with "maximum area".
***Please help me to solve the two questions. I would like you to check my answer for (a) ques: width of the sheep pen: 20m, its length 70m(only one width of sheep pen is subtracted since no fence will be constructed at the width of the shed) and the area is1400m square.
For ques,(b) chapter differentiation is related . Pls tell me clues and the answers so that I can discover. Thanks!
2006-11-02 02:16:13 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Yes, you're right Tsunamijo. the question is asked by Blaze. But isn't ques (b) is solved using differentiation using either x and y for the width and length of sheep pen. Then, do the 2nd differentiation to prove that the area is "maximum". Please help... Anyone solve ques. (b)
2006-11-02 02:35:26 · update #1
I would appretiate it a lot if anyone can help me to prove the max. area of SP in details.
2006-11-02 02:38:25 · update #2
let x be the amount of fence added to the length of the 20 foot shed. The width = 20+x and length = [160-2(20+x)]/2=60-x
So area = A = (20+x)(60-x)
Now find dA/dx and set it = 0 and solve for x
2006-11-02 02:34:17 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
For differentiating the term, you have to consider the standard formula to use. e.g. If you want to differentiate √(3x+1) , then it comes under the formula of √x. Then, consider which term is replacing 'x' in the formula. e.g. In √(3x+1), (3x+1) is replacing 'x'. Then, you have to use the formula for differentiation and multiply it by the derivative of term replacing 'x'. e.g. In √(3x+1), derivative = derivative according to formula * derivative of term replacing 'x'. =1/(2√(3x+1)) * derivative of (3x+1) =1/(2√(3x+1)) * 3 =3/(2√(3x+1))
2016-03-19 02:47:36 · answer #2 · answered by Anonymous · 0⤊ 0⤋
i've seen this question before. do a search under sheep pen on here and you'll find it
2006-11-02 02:20:17 · answer #3 · answered by tsunamijon 4 · 1⤊ 0⤋
i dont know
2006-11-02 02:24:38 · answer #4 · answered by curious me 1 · 0⤊ 0⤋