Answer: see attachment below
Step-by-step explanation:
Function is p(x)=(x-4)^5(x^2-16)(x^2-5x+4)(x^3-64)
first factor into (x-r1)(x-r2)... form
p(x)=(x-4)^5(x-4)(x+4)(x-4)(x-1)(x-4)(x^2+4x+16)
group the like ones
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
multiplicity is how many times the root repeats in the function
for a root r₁, the root r₁ multiplicity 1 would be (x-r₁)^1, multility 2 would be (x-r₁)^2
so
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
(x^2+4x+16) is not on the real plane, but the roots are -2+2i√3 and -2-2i√3, each multiplicity 1 (but don't count them because they aren't real
baseically
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
3(x-1)-8=4(1+x)+5
One solution was found :
x = -20
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*(x-1)-8-(4*(1+x)+5)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•(x-1))-8)-(4•(x+1)+5) = 0
Step 2 :
Equation at the end of step 2 :
(3 • (x - 1) - 8) - (4x + 9) = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
-x - 20 = -1 • (x + 20)
Equation at the end of step 4 :
-x - 20 = 0
Step 5 :
Solving a Single Variable Equation :
5.1 Solve : -x-20 = 0
Add 20 to both sides of the equation :
-x = 20
Multiply both sides of the equation by (-1) : x = -20
One solution was found :
x = -20
hope this is wht u wanted
Answer:
s = 
m
Step-by-step explanation:
Given s varies directly with m then the equation relating them is
s = km ← k is the constant of variation
To find k use the condition s = 9 when m = 30 , thus
9 = 30k ( divide both sides by 30 )
k = 
=
s = m ← equation of variation
Soh cah toa formula
n n n n n n
