real_name_x
New member
- Joined
- Aug 28, 2007
- Messages
- 5
IM stuck on these 5 questions. if anyone can help with any, i would be very greatfull. i really need help. ty.
#1. a) evaluate (1 + i)^2, where i = Squareroot(-1)
b) prove, by mathematical induction, that (1 + i)^(4n) = - 4^n, where n € N
c) hence or otherwise, find (1+ i)^32
#2. a farmer owns a triangular field ABC. The side [AC] is 104m, the side [AB] is 65m and the angle between these two sides is 60 degrees.
a) calculate the length of the third side of the field
b) find the area of the field in the form p *squareroot*(3), where p is an integer
(same prob) Let D be a point on [BC] such that [AD] bisects the 60 degree angle. The farmer divides the field into two parts by constructing a straight fence [AD] of length x meters.
c) (I) show that the area of the smaller part is given by (65x) / 4 and find an expression for the area of the larger part
(II) hence, find the value of x in the form q *squareroot* (3), where q is an integer
d) prove that BD / DC = 5 / 8
#3. the variables x,y,z satisfy the simultaneous equations....
x + 2y + z = k
2x + y + 4z = 6
x - 4y + 5z = 9
where k is a constant.
a) (I) show that these equations do NOT have a unique solution.
(II) find the value of k for which the equations are consistent (that is, they can be solved).
b) for this value of k, find the general solutions of these equations
#4. the ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is 6 / 13. If each term of this sequence is positive, and the product of the first terms and the third term is 32, find the sum of the first 100 terms of this sequence.
#5. solve the equation l e^(2x) - ( 1/ (x+2) ) l = 2
thank you again!!
#1. a) evaluate (1 + i)^2, where i = Squareroot(-1)
b) prove, by mathematical induction, that (1 + i)^(4n) = - 4^n, where n € N
c) hence or otherwise, find (1+ i)^32
#2. a farmer owns a triangular field ABC. The side [AC] is 104m, the side [AB] is 65m and the angle between these two sides is 60 degrees.
a) calculate the length of the third side of the field
b) find the area of the field in the form p *squareroot*(3), where p is an integer
(same prob) Let D be a point on [BC] such that [AD] bisects the 60 degree angle. The farmer divides the field into two parts by constructing a straight fence [AD] of length x meters.
c) (I) show that the area of the smaller part is given by (65x) / 4 and find an expression for the area of the larger part
(II) hence, find the value of x in the form q *squareroot* (3), where q is an integer
d) prove that BD / DC = 5 / 8
#3. the variables x,y,z satisfy the simultaneous equations....
x + 2y + z = k
2x + y + 4z = 6
x - 4y + 5z = 9
where k is a constant.
a) (I) show that these equations do NOT have a unique solution.
(II) find the value of k for which the equations are consistent (that is, they can be solved).
b) for this value of k, find the general solutions of these equations
#4. the ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is 6 / 13. If each term of this sequence is positive, and the product of the first terms and the third term is 32, find the sum of the first 100 terms of this sequence.
#5. solve the equation l e^(2x) - ( 1/ (x+2) ) l = 2
thank you again!!
