mathematics question?

Question

(a)Find for the following function:

(i)y = 4(2x3 – 3x)5
(ii)y =
(iii)y = 5(3x – 1)5(7 – 2x2)6(8 + x3)9
[7 marks]

(b) Find g’(4) given that f(4) = 3, f ’(4) = 4 and g(x) = f(x)
[3 marks]

(c) Suppose that the function f is differentiable everywhere and F(x) = x f(x). Express F(2007)(x) in terms of x and the derivatives of f.
[Note: F(2007)(x) means “the 2007th derivatives of F with respect to x]
[4 marks]

(d) A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 a metre, while the remaining two sides will use standard fencing selling for $2 a metre. What are the dimensions of the rectangular plot of the greatest area that can be fenced in at the cost of $6000?
[5 marks]

(e) Find the area bounded by the x-axis and the curve y = x3 – x and the lines x =1, x = 2.
[4 marks]

(f) Suppose that p, q and t are positive. Which of the following two expressions is larger

(a) If 9 140 = + , and 0 < A < B, find the value of B when A is minimum.
[4 marks]

(b) x : y = 5 : 6, and (x – 6) : (y – 6) = 4 : 5. Find the values of x and y.
[4 marks]

(c) Two shops are having sale. Shop A will give their member 20% discount on any item and shop B will give 10% discount on any item and for their member, another 10% discount will be given on the top of the discount price. If you want to buy something during the sale, and you are the member of these two shops, which shops will you go? Support your answer with the calculation.
[4 marks]

(d) At a certain hamburger stand, the owner sold soft drinks out of two 16-gallon barrels. At the end of the first day, she wished to increase her profit, so she filled the soft-drink barrels with water, thus diluting the drink served. She repeated the procedure at the end of the second and the third days. At the end of the fourth day, she had 10 gallons remaining in the barrels, but they contained only 1 pint of pure drink. How much pure soft drink was served in the four days?
[4 marks]

(e) Alan, Ben and Calvin went to a casino. At the beginning of the night, the amount of money each had was in the ratios 7:6:5. At the end of the night, the ratio was 6:5:4. One of the players won $1200. What were the assets of each player at the beginning of the night?
[8 marks]

(f) Harry and his wife Ginny have a vegetable garden and a fruit orchard. Working together they can collect the harvest from the garden in 3 hours, whereas Ginny, working alone, require 12 hours. Furthermore, together they can harvest the orchard in 2 hours, whereas Harry, alone, takes 10 hours. It would seem that to harvest both the garden and the orchard, they should first spend 3 hours in garden and then 2 hours in the orchard, a total of 5 hours in all. However, Harry is much more skillful at picking vegetables and Ginny is better at picking fruit, so that they can save time by having Harry work in the garden and Ginny work in the orchard until one of them finishes. That person would help the other. How much time can they save in this manner?
[6 marks]

Answer 1

do we have to solve thse questions? i dont have any thing to write about.
(i)y = 4(2x3 – 3x)5
(ii)y =
(iii)y = 5(3x – 1)5(7 – 2x2)6(8 + x3)9
[7 marks]

(b)Find g’(4) given that f(4) = 3, f ’(4) = 4 and g(x) = f(x)
[3 marks]

(c)Suppose that the function f is differentiable everywhere and F(x) = x f(x). Express F(2007)(x) in terms of x and the derivatives of f.
[Note: F(2007)(x) means “the 2007th derivatives of F with respect to x]
[4 marks]

(d)A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 a metre, while the remaining two sides will use standard fencing selling for $2 a metre. What are the dimensions of the rectangular plot of the greatest area that can be fenced in at the cost of $6000?
[5 marks]

(e)Find the area bounded by the x-axis and the curve y = x3 – x and the lines x =1, x = 2.
[4 marks]

(f)Suppose that p, q and t are positive. Which of the following two expressions is larger

(a)If 9 140 = + , and 0 < A < B, find the value of B when A is minimum.
[4 marks]

(b)x : y = 5 : 6, and (x – 6) : (y – 6) = 4 : 5. Find the values of x and y.
[4 marks]

(c)Two shops are having sale. Shop A will give their member 20% discount on any item and shop B will give 10% discount on any item and for their member, another 10% discount will be given on the top of the discount price. If you want to buy something during the sale, and you are the member of these two shops, which shops will you go? Support your answer with the calculation.
[4 marks]

(d)At a certain hamburger stand, the owner sold soft drinks out of two 16-gallon barrels. At the end of the first day, she wished to increase her profit, so she filled the soft-drink barrels with water, thus diluting the drink served. She repeated the procedure at the end of the second and the third days. At the end of the fourth day, she had 10 gallons remaining in the barrels, but they contained only 1 pint of pure drink. How much pure soft drink was served in the four days?
[4 marks]

(e)Alan, Ben and Calvin went to a casino. At the beginning of the night, the amount of money each had was in the ratios 7:6:5. At the end of the night, the ratio was 6:5:4. One of the players won $1200. What were the assets of each player at the beginning of the night?
[8 marks]

(f)Harry and his wife Ginny have a vegetable garden and a fruit orchard. Working together they can collect the harvest from the garden in 3 hours, whereas Ginny, working alone, require 12 hours. Furthermore, together they can harvest the orchard in 2 hours, whereas Harry, alone, takes 10 hours. It would seem that to harvest both the garden and the orchard, they should first spend 3 hours in garden and then 2 hours in the orchard, a total of 5 hours in all. However, Harry is much more skillful at picking vegetables and Ginny is better at picking fruit, so that they can save time by having Harry work in the garden and Ginny work in the orchard until one of them finishes. That person would help the other. How much time can they save in this manner?

Answer 2

You ask too much and do not express your questions well.