Synthetic division yields
-3 | 1 5 4 -6
. | -3 -6 6
- - - - - - - - - - - - -
. | 1 2 -2 0
which translates to
with remainder 0. Now by the quadratic formula,
and so
The equation in the question is not the same as the one in the picture so here's the answers to both of them.
Q1 - 1/3 or 0.333333
Q2 - 1/108 or 0.009259
Answer:
0.53πrad
Explanations:
Given the radius of the circular track = 60metres
If she walks a total of 100 meters, the length of the arc of the circle = 100metres
To calculate the radian angle she rotates about the center of the track, we will use the formula for calculating the length of an arc
L = θ/360° × 2πr
100 = θ/360× 2π(60)
36000 = 120π × θ
36000 = 376.8θ
θ = 36000/376.8
θ = 95.5°
Since 180° = πrad
95.5° = x
x = 95.5π/180
x = 0.53π rad
Answer:
Step-by-step explanation:
Consider the revenue function given by 
. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
From the first equation, we get, 
.If we replace that in the second equation, we get
From where we get that 
. If we replace that in the first equation, we get
So, the critical point is 
. We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that
We have the following matrix,
![\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Bmatrix%7D%20-10%20%26%20-2%20%5C%5C%20-2%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D)
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is 
and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
