If we consider the center of the habitat to be a point - then a circle with a radius of 1.5 km <u /><u />would satisfy the problem.
The path would go around the point (habitiat) and would always be 1.5 km from that point.
<span>let P(n)=4n² / n²+10000n
when n ----------> infinity, the main rule is as follow
lim </span><span>P(n)=4n² / n²+10000n = lim </span>P(n)=4n² / n²= lim 4= 4
n ----------> infinity <span> n ----------> infinity </span><span>n ----------> infinity
finally
</span>
<span>Lim->infinity 4n^2/n^2+10000n
= 4</span>
Answer:
7n²
Step-by-step explanation:
7/n² - 8/7n
Least common multiple will be the least common denominator
L.C.M = 7n²
Dividing the L.C.M by denominators and multiplying with numerators;
((7×7) - (n×8))/7n²
= (49 - 8n)/7n²
7n² is the least common denominator
First find all possible rational roots. To do this, find all the factors of the lowest order coefficient and the highest order coefficient. For #1, the highest order coefficient is 1 because the x^3 doesn't have a number in front of it. The lowest order coefficient is 30.
Here are all the factors:
Factors of 1 are: 1
Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Now divide each factor of 30 (positive and negative), and divide them by each factor of 1.
All possible rational roots are:
-1, 1, -2, 2, -3, 3, -5, 5, -5, 6, -10, 10, -15, 15, -30, 30
Now we perform synthetic division like you have started to do. Try dividing the polynomial by each possible root. If the result has a remainder, that possible root does NOT work. Try another possible root. If there is not a remainder, you have found one of the roots.
For example, when dividing x^3 - 4x^2 -11x + 30 by the possible root 2, we get x^2 - 2x - 15 without a remainder. That means 2 is a root. From here we can factor the result to (x-5)(x+3).
So the roots for #1 are x = -3, 2, and 5.
Let me know if you need help with the others :)
