Pgeometryevaluate
a. 6!
b. 8p5
c. 12c4

Part A

720



Work Shown:

6! = 6*5*4*3*2*1 = 720

The exclamation mark means factorial. You simply start with the given number 6 and count down til you get to 1. You multiply all of the numbers together.



Part B

6720



Work Shown:

Use the nPr formula to get...
nPr = (n!)/((n-r)!)
8P5 = (8!)/((8-5)!)
8P5 = (8!)/(3!)
8P5 = (8*7*6*5*4*3!)/(3!)
8P5 = 8*7*6*5*4
8P5 = 6720



Part C

495



Work Shown:

Use the nCr formula this time
n C r = (n!)/(r!(n-r)!)
12 C 4 = (12!)/(4!*(12-4)!)
12 C 4 = (12!)/(4!*8!)
12 C 4 = (12*11*10*9*8!)/(4!*8!)
12 C 4 = (12*11*10*9)/(4!)
12 C 4 = (12*11*10*9)/(4*3*2*1)
12 C 4 = (11880)/(24)
12 C 4 = 495

Discontinuity of function occurs when x = 4 or x = -4

zero of function is when x=0

Step-by-step explanation:

We are given:

f(x) = 4 - x/ x^2 - 16

Discontinuity of the function occur when the denominator is equal to zero.

So, we need to find the values of x that makes the denominator zero.

The denominator is x^2 - 16

x^2 - 16 =0

x^2 = 16

x = ± 4

So, if the value of x = 4 or value of x=-4 then the function will be discontinuous.

Zero of the function i.e f(x)=0

So, Putting the function equal to zero and finding the value of x

4(x) / x^2 - 16 = 0

4(x) = 0((x)^2 - 16)

4x = 0

x = 0

So, zero of function is when x=0