1. Given: Area = 21.98, ℼ = 3.14, 2r = d or diameter, Area = ℼr²
Area = ℼr²
21.98 = (3.14)r²
21.98/(3.14) = (3.14)r²/(3.14)
7 = r²
√7 = √r²
r = √7
d = 2r
d = 2(√7)
d = 2√7
2. V = s³, s = (x + 4)
V = s³
V = (x + 4)³
Perfect Cube Formula:
(a + b)³ = a³ + 3a²b+3ab²+b³
(x + 4)³ = (x)³ + 3(x)²(4) + 3(x)(4)² + (4)³
(x + 4)³ = x³+12x²+48x+64
3. A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x – 2) has the zeroes x = –3 and x = 2, each occuring once (multiplicity of 1 for both factors).
Using this definition we find that zero 2 multiplicity 3 means:
(x - 2)³ = 0 because if x = 2, (2 - 2)³ = 0, (0)³ = 0, 0 = 0
And zero -1 means
(x + 1) = 0 because if x = -1, (-1 + 1) = 0, 0 = 0
so we have both factors to create a polynomic function:
P(x) = (x - 2)³(x + 1)
in this function if x = 2 or x = -1. The result will be 0
Answers & Comments
Answer:
1. d = 2√7
2. x³+12x²+48x+64
3. P(x) = (x - 2)³(x + 1)
Step-by-step explanation:
1. Given: Area = 21.98, ℼ = 3.14, 2r = d or diameter, Area = ℼr²
Area = ℼr²
21.98 = (3.14)r²
21.98/(3.14) = (3.14)r²/(3.14)
7 = r²
√7 = √r²
r = √7
d = 2r
d = 2(√7)
d = 2√7
2. V = s³, s = (x + 4)
V = s³
V = (x + 4)³
Perfect Cube Formula:
(a + b)³ = a³ + 3a²b+3ab²+b³
(x + 4)³ = (x)³ + 3(x)²(4) + 3(x)(4)² + (4)³
(x + 4)³ = x³+12x²+48x+64
3. A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x – 2) has the zeroes x = –3 and x = 2, each occuring once (multiplicity of 1 for both factors).
Using this definition we find that zero 2 multiplicity 3 means:
(x - 2)³ = 0 because if x = 2, (2 - 2)³ = 0, (0)³ = 0, 0 = 0
And zero -1 means
(x + 1) = 0 because if x = -1, (-1 + 1) = 0, 0 = 0
so we have both factors to create a polynomic function:
P(x) = (x - 2)³(x + 1)
in this function if x = 2 or x = -1. The result will be 0