We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))
Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>
Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>
<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>
Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2
<span>sqrt(y+9) = (2x + 2) / 2sqrt(2)
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>
y = ((2x+2)^2) / 8 - 9
Answer:
<h2>
The Slope Is <u>
12</u></h2>
Step-by-step explanation:
Below are the steps to follow to find the slope of any line.
First you need to pick two points. I chose (2,24) and (4,48). (It does not mater what points you chose.)
Now follow the equation
Slope (m) = ΔY/ΔX
ΔY = 48 – 24 = 24
ΔX = 4 – 2 = 2
24/2 = 12
Then no mater what points you chose, 12 should be your final answer
Answer:
the equilibrium expected growth rate is 6.65%
Step by step Explanation:
We were given stock sold per share of $32.50
Dividend per share =$1.25
Required Return rate = 10.5%
Then we can calculate Percentage of Dividend for share as;
dividend of br. 1.25 per share at the end of the year (D1=br.1.25)
= 1.25×100= 125
Let the dividend percentage = y
stock sold per share × y= 125
125= 32.50y
y = 125/32.50
y= 3.85
y= 3.85*100%
Then the Dividend percentage = 3.85%
Growth rate=(required rate of return -Dividend percentage)
= 10.5 - 3.85 = 6.65
Therefore, the equilibrium expected growth rate is 6.65%
Answer:
5/9
12
Step-by-step explanation:
La clase entera es 1.
1/3 estudian español.
1/9 estudian italiano.
1 - 1/3 - 1/9 estudian alemán.
1 - 1/3 - 1/9 = 9/9 - 3/9 - 1/9 = 5/9
<em>5/9 de los estudiantes estudian alemán.</em>
n = numero total de estudiantes en la clase.
5/9 n = 15
9/5 * 5/9 * n = 15 * 9/5
n = 27
Hay 27 estudiantes en la clase.
27 - 15 = 12
<em>12 estudiantes no estudian alemán.</em>
Answer:
1:8
Explanation:
1.5 (cleaner) to 12 (water)--> simplified is 1:8
