Some questions (1 Viewer)

[Loz_metalhead]

The sum of the first four terms of a geometric sequence is 15 and the sum of an infinite number of terms if 16. Find the first term and the common ratio.


If dy/dx=2y and y=10 and x=0

express y as a function of x

 

[SoulSearcher]

dy/dx = 2y
.'. dx/dy = 1/2y
Therefore, integrating,
x = int. [1/2y]
= 1/2 int. [1/y]
= 1/2 ln y + c
y = 10 when x = 0
0 = 1/2 ln 10 + c
c = -1/2 ln 10
Therefore,
x = 1/2 ln y - 1/2 ln 10
2x = ln y - ln 10
2x = ln (y/10)
e^2x = y/10
y = 10e^2x

 

[sando]

the first one u just solve as a simulatenous equation.. i would do it but i its too hard typing up on the computer

 

[rickem]

dy/dx=2y S=intergral sign
When y=10, x=0
Find y=f(x)
dy/dx=2y
dx/dy=1/2y
x= 1/2 S (2/2y)
x= 1/2 S (1/y)
x= 1/2lny +C
0= 1/2ln10 +C
C= -1/2ln10
x=1/2lny-1/2ln10
2x=ln(y/10)
y/10=e^(2x)

Solution
y=10e^(2x)
seems right.