Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders:
since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is:
as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
Answer:

Step-by-step explanation:
Power is defined by work over time. In physics, work can be defined as the energy transferred over from an applied force over some distance. As a formula:
, where F = force applied and d = distance that force is applied over.
*It is worth noting that F must be parallel to the distance travelled. If it is perpendicular, no work is done, and if it is at an angle, find the parallel component and use that for F.
In this case, the force applied must counter the force of gravity on Martha, which is given by
, where m = Martha's mass and g = gravitational constant 9.8 m/s/s. Therefore,
. Since she raises her body 4.0 meters, the work done must be
.
Since power is equal to work over time and t = 2.3 seconds, we have:
(to two significant figures)
Answer:
A.8 B.(-1,4) C.(1,4)
Step-by-step explanation:
First, know that (3,2)=(x1,y1) and (-5,6)=(x2,y2)
A. The diameter is 8, given the diference between x1 and x2: 3-(-5)=8
B. The center point is given by (x1+x2)/2 and (y1+y2)/2
(x1+x2)/2 and (y1+y2)/2 = (3-5)/2 and (2+6)/2 = (-1,4)
C. The symmetric point of C about the x-axis is (1,4)
Answer:
Riley did better than Darby because One-half < Three-fifths.
Step-by-step explanation:
The statement that explains which girl did better would be that
Riley did better than Darby because One-half < Three-fifths.
There are a total of 60 minutes in an hour, If we multiply each of these fractions by 60 minutes it would give us the exact number of minutes that each girl took to finish the race.
Riley:
* 60 = 30 minutes
Darby:
* 60 = 36 minutes
Therefore, we can see that it took Riley 6 minutes less than Darby to finish the race meaning that she had the better result.