Answer:
Step-by-step explanation:
a. Create a direction field for the specified differential equation
b. By observing the direction field, comment on the behavior of the solutions as t becomes large.
The solutions seem to oscillate
All solutions appear to approach the function y0(t)=4
All solutions seem to converge to the function y0(t)=0
All solutions appear to have negative slopes eventually and thus decrease indefinitely
All solutions seem to have positive slopes eventually and therefore increase without limit
C
As t approaches infinity
All solutions seem to exhibit positive slopes eventually and thus decrease indefinitely
The solutions seem to gradually approach the function y0(t)=0
All solutions appear to eventually have negative slopes leading to decrease without bounds
All solutions seem to converge to the function y0(t)=4
The results are oscillatory
Robert covered a distance of 292 miles.
He took 4 hours to complete this journey.
Next, let's convert miles to feet.
1 mile equals 5280 feet.
Thus, 292 miles in feet equals 292 * 5280 = 1541760 feet.
Now, converting 4 hours into seconds.
1 hour translates to 3600 seconds.
Therefore, 4 hours equals 3600 * 4 = 14400 seconds.
The question asks for speed in feet per second.
Thus,
is 107.067 feet per second.
Answer:
16 years
Step-by-step explanation:
Let x represent the count of years. The suburb population increases at a rate of 5000 annually, which can be formulated as:
320000 + 5000x
The city population decreases at a rate of 14000 per year, represented as:
624000 - 14000x
The point in time when both the suburb and city populations will match can be derived from:
320000 + 5000x = 624000 - 14000x
14000x + 5000x = 624000 - 320000
19000x = 304000
x = 304000 / 19000
x = 16
In 16 years, the populations of both the suburb and the city will be equivalent
Answer:
(12, 3), (-2, -5), (1, 15)
Step-by-step explanation:
The line may intersect any point where the x-coordinate is positive and the y-coordinate exceeds -1. Such points include...
(12, 3), (1, 15)
The line can also cross any point where the x-coordinate is negative while the y-coordinate is lower than -1. That point is...
(-2, -5)
__
In the provided diagram, the lines colored green demonstrate a positive slope, while the red lines do not.
x/4.24 = 6.82/2.2
x = (4.24*6.82)/2.2
x = 1.36
Explanation:
Starting from x/4.24 = 6.82/2.2
, multiply both sides by 4.24 to obtain 4.24*6.82 = 2.2x
