Answer:
x = -7
Step-by-step explanation:
5(x-2)=3x+4(x+1)
First, multiply the 5 with the x and the 5 with the -2. You are using the distributive property.
5x -10 = 3x + 4 (x+1)
Then multiply the 4 with the x and the 4 with the 1 on the other side. Again, you are using the distributive property.
5x-10=3x+4x+4
Next, combine like terms. So you're going to combine the 3x and the 4x on the right side.
5x-10=7x+4
Then, subtract 5x from both sides. Also, subtract the 4 from both sides. You do this in order to get all of the x's on one side of the equation.
-14 = 2x
Finally, divide 2 from both sides. You do this because right now, the equation says 2 times x, and you need to get the x alone.
-7 = x
You are finished
Given:
Three numbers in an AP, all positive.
Sum is 21.
Sum of squares is 155.
Common difference is positive.
We do not know what x and y stand for. Will just solve for the three numbers in the AP.
Let m=middle number, then since sum=21, m=21/3=7
Let d=common difference.
Sum of squares
(7-d)^2+7^2+(7+d)^2=155
Expand left-hand side
3*7^2-2d^2=155
d^2=(155-147)/2=4
d=+2 or -2
=+2 (common difference is positive)
Therefore the three numbers of the AP are
{7-2,7,7+2}, or
{5,7,9}
Answer:
Step-by-step explanation:
The growth of the population can be modeled by the following differential equation:
Where r is the growth rate, P is the population, and t is the time measures in months.
I am going to solve the above differential equation with the separation of variables method.
Integrating both sides:
Where P(0) is the initial condition
We need to isolate P in this equation, so we do this
So
The problem states that P(0)=3000, so:
The problem wants us to find the value of r:
It states that the population doubles in size from 3000 to 6000 in a 6- month period, meaning that P(6) = 6000. So
To isolate 6r, we apply ln to both sides.
r = 0.1155
The particular solution to the differential equation with the initial condition P(0)=3000 is:
Answer:
......................
7(x+3)
Step-by-step explanation:
....
Answer:
107,778
Step-by-step explanation:
