Answer: There are 360360 ways to appoint the members of the cabinet.
Step-by-step explanation:
Since we have given that
Number of eligible candidates = 15
Number of spots available = 5
We need to find the number of different ways the members can be appointed where rank matters
For this we will use "Permutations":
So, the required number of different ways in choosing the members for appointment is given by

Hence, there are 360360 ways to appoint the members of the cabinet.
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0

Let's find out the gradient (Slope " m ") of line q ;



Now, since we already know the gradient let's find of the equation of line by using its Slope and one of the points using point slope form of line :


Now, plug in the value of gradient ~

here we can clearly observe that, the Area under the curve can easily be represented as :

Since, all the values of y that lies in the shaded region is smaller than the actual value of y for the corresponding values of x in the equation of line q
An equation written in slope-intercept form is y=mx+b, where m is a constant equal to the slope. Parallel lines have the same slope. So a line parallel to y=-2x+3 is y=-2x+5. Perpendicular lines have slopes which are negative reciprocals of each other. So a line perpendicular to y=-2x+3 is y=1/2x+7. y=2x-1 is neither parallel of perpendicular to y=-2x+3.