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
The attached image is the graph.
<h3>Answer:</h3>
133 ft
<h3>Step-by-step explanation:</h3>
Given in the question,
length of the rectangle = 31 ft
width of the rectangle= 20 ft
diameter of semicircle = 20 ft
radius of semicircle = 20/2 ft = 10 ft
<h3>Formula to use:</h3>
perimeter of rectangle + perimeter of semicircle
perimeter of rectangle = 2(l+w)
perimeter of semicircle = 1/2(2πr)
<h3>Plug values in the formula above</h3>
2(31 + 20) + 3.14(10)
133.4 ft
≈ 133 ft
Answer:
Density = 5751.66 gram per litre
Step-by-step explanation:
It is given that the density of a certain material 6 pounds per pint.
The conversion from pint to liter is as follows :
1 pint = 0.473 litre
The conversion from pounds to kg is as follows :
1 pound = 453.59 kg
We need to express the density from pounds per pint to grams per liter.
1 pound per pint = 958.611 gram per litre
So,
6 pound per pint = 958.611 × 6 gram per litre
6 pound per pint = 5751.66 gram per litre
I would try b the rise\run is 2\2 so give it a go
