Answer:
r < 1/3
Step-by-step explanation:
21r<7
Divide each side by 21
21r/21<7/21
r < 1/3
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:
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Step-by-step explanation:
Answer:
The final position is 5 feet below the back of the truck
Step-by-step explanation:
* Lets explain how to solve the problem
- A crane lifts a pallet of concrete blocks 8 feet from the back of
a truck
- The crane lowers the pallet 13 feet after the truck drives away
- Assume that the zero level of the position of the ballet of concrete
blocks is the back of the truck
∵ The crane lifts the pallet of concrete blocks 8 feet from the back
of the truck
- That means it take the pallet from zero to 8
∴ The height of the pallet of concrete blocks is 8 feet over
the starting position
∵ The crane lowers the pallet of concrete blocks 13 feet
- That means the crane lower the pallet from the height 8 and
lift it down 13 feet, so we must to take out from the 8 feet the
13 feet to find the final position of the pallet of concrete blocks
∴ The pallet position is ⇒ 8 - 13 = -5
∴ The position of the pallet of concrete blocks is 5 feet below the
starting position which is the back of the truck
* The final position is 5 feet below the back of the truck