Answer:
z = -12
Step-by-step explanation:
The given system of equations is:
xy/(x + y) = 1 ...........................(1)
xz/(x + z) = 2...........................(2)
yz/(y + z) = 3...........................(3)
From (1): x + y = xy
=> y = xy - x
y = x(y - 1)
x = y/(y - 1).......................................(4)
From (2): 2(x + z) = xz
=> 2x + 2z = xz
2x = xz - 2z
2x = z(x - 2)
z = 2x/(x - 2) ....................................(5)
From (3): 3(y + z) = yz
=> 3y + 3z = yz
3y = yz - 3z
3y = z(y - 3)
z = 3y/(y - 3)....................................(6)
Comparing (5) and (6)
2x/(x - 2) = 3y/(y - 3)
2x(y - 3) = 3y(x - 2)
2xy - 6x = 3xy - 6y
6(y - x) = xy .................................(7)
But from (1): xy = x + y
Using this in (7), we have
6(y - x) = x + y
6y - y - 6x - x = 0
5y - 7x = 0
5y = 7x
x = 5y/7................................................(8)
Using this in (4)
5y/7 = y/(y - 1)
1/(y - 1) = 5/7
(y - 1) = 7/5
y = 1 + 7/5
y = 12/5..........................................(9)
Using this in (8)
x = 5(12/5)/7 = 12/7 .......................(10)
Using (10) in (5)
z = 2x/(x - 2)
z = 2(12/7) ÷ (12/7 - 2)
= 24/7 ÷ -2/7
= 24/7 × (-7/2)
= -24/2 = -12
z = -12.
14. -6m²-2m+1
15. 14x-24
16.3b²
17.14p+7
do you need the steps?
Answer:
as in pic below
Step-by-step explanation:
Answer:
rate=55 percent
Step-by-step explanation:
SI=PRT
p=90
r=?
t=2
si=99
R=SI÷PT
R=99÷90×2
r=99÷180=0.55
r=0.55×100
R=55%
Answer:
x = 0 , π
Step-by-step explanation:
- Rewrite it by using the identity


- Add 4sin x to both the sides.


- Take sin x common from the expression in L.H.S.

Here , we can get two more equations to find x.
1) 
- Divide both the sides by sin x


- Substract 4 from both the sides.



2) 
- Divide both the sides by (sin x + 4)


over interval [0 , 2π).