Answer:
There is no point of the form (-1, y) on the curve where the tangent is horizontal
Step-by-step explanation:
Notice that when x = - 1. then dy/dx becomes:
dy/dx= (y+2) / (2y+1)
therefore, to request that the tangent is horizontal we ask for the y values that make dy/dx equal to ZERO:
0 = ( y + 2) / (2 y + 1)
And we obtain y = -2 as the answer.
But if we try the point (-1, -2) in the original equation, we find that it DOESN'T belong to the curve because it doesn't satisfy the equation as shown below:
(-1)^2 + (-2)^2 - (-1)*(-2) - 5 = 1 + 4 + 2 - 5 = 2 (instead of zero)
Then, we conclude that there is no horizontal tangent to the curve for x = -1.
The next term is double the previous term, so that the 
-th term is given recursively by
This rule tells us that
and so on, with the explicit rule
for 
.
If 512 is the 
-th term in the sequence, then
Answer:
The slope is: 
Step-by-step explanation:
The equation for slope is:
Point 1: -3=
, -2=
Point 2: 5=
, 4=
4-(-2)=6
5- (-3)=8
6/8=3/4
So he worked 30.5 hours, he just didn't write some of the hours down. To find the hours he didn't write down, you subtract 8+
+
from 30.5, which equals
