Answer:
x = 7, y = 6
Step-by-step explanation:
solve for y for the first equation
2x + y = 20
-2x -2x , eliminate 2x
y = 20-2x
now that we have found y, substitute the y in for the second equation
-5y = -6x + 12
-5(20-2x) = -6x + 12, we just changed y into 20-2x. remember that we are multiplying all of 20 - 2x by -5
-100+10x = -6x + 12, we multiplied everything from the parathesis by -5
+100 + 100, eliminate -100
10x = -6x + 112
+6x +6x , eliminate 6x
16x = 112 , solve for x
x = 7
then y = 20 - 2x = 20 - 2*7 = 6
check:
2 * 7 + 6 = 20
20 = 20
-5 * 6 = -6 * 7 + 12
-30 = -42 + 12
-30 = -30
First, we need to solve the differential equation.

This a separable ODE. We can rewrite it like this:

Now we integrate both sides.

We get:

When we solve for y we get our solution:

To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:

When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
Answer:
x=4
Step-by-step explanation:
Let he first piece be x the second be 3x and the very last one be 7x + 2
Add all the pieces together and you ought to get the length of the rope which is 46 ft
So your equation would be
x + 3x + 7x + 2 = 46
11x = 44
x = 44 / 11
x = 4
so the 3 pieces are 4 , 12 and 30ft
Answer:
12 1/2 cups of flour
Step-by-step explanation:
2 1/2 cups for each batch
5 batches
2 1 /2 x 5 =
12 1 /2
Answer:
I guess this is the answer
Step-by-step explanation:
(x + y)²4x²y²
= [2xy(x + y)]²
= (2x²y²)²