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
Answer:
Start at postive 1 on the y axis put a dot there. From the dot go down 6 and go left 5.
Step-by-step explanation:
6/5=rise over run
1=y-axis
y=mx+b
m=slope
b=y-intersept
For
to be continuous at
, we need to have
Note that
means that
, but that
is *approaching* 5. We're told that for
, we have
We can write
and the limit would be
and so
is discontinuous.
<span>f(x)=5x+3/6x+7
This means that f(6/x) = [</span>5(6/x)+3] / [6(6/x)+7] = [ 30/x +3 ] / [36/x +7]
If we assume x≠0 , f(6/x) = [30 +3x]/ [36 + 7x]
g(x)=√<span> [ x^2-4x ]
</span>
g(x-4) = √ [ (x-4)^2-4(x-4) ] = √ [ x² -8x +16 -4x +16 ] = √ [ x^2-12x +32]
Answer:
900m
Step-by-step explanation:
All you have to do is find the difference between the two measurements
500 - (-400)
Then, two negatives create a positive:
500 + 400
= 900
