Answer:
Z = 0.198877274
Step-by-step explanation:
Hence, the value of Z = 0.198877274
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Answer:
3) Cubic polynomial with four terms.
4) Linear polynomial with two terms.
5) The zeros are: (1-sqrt(5))/2=-0.618, 1, and (1+sqrt(5))/2=1.618
The y-intercept is y=1
Please, see the attached graph.
6) The zeros are: -1.272, 1.272
The y-intercept is y=1
Please, see the attached graph.
7) Please, see the attached files.
8) Please, see the attached files.
9) Please, see the attached files.
10) Please, see the attached files.
Step-by-step explanation:
3) Degree is the maximun exponent that the variable "x" has, in this case 3, then this is a cubic polynomial, and it has four terms (6x^3, -7x^2, -10x, and -8).
4) Degree is the maximun exponent that the variable "x" has, in this case 1 (x=x^1), then this is a linear polynomial, and it has two terms (-10x, and 10).
5) f(x)=x^3-2x^2+1
Zeros:
f(x)=0→x^3-2x^2+1=0
Factoring:
x^3-2x^2+0x+1
! 1 -2 0 1
<u>1 !____1____-1_-1</u>
1 -1 -1 0
1x^2-1x -1 = x^2-x-1
x^3-2x^2+1=0→(x-1)(x^2-x-1)=0
The zeros are:
x-1=0→x-1+1=0+1→x1=1
x^2-x-1=0
ax^2+bx+c=0; a=1, b=-1, c=-1
x=(-b+-sqrt(b^2-4ac))/(2a)
x=(-(-1)+-sqrt((-1)^2-4(1)(-1))/(2(1))
x=(1+-sqrt(1+4))/2
x2=(1+-sqrt(5))/2=(1+2.236067978)/2=3.236067978/2=1.618033989=1.618
x=(1-sqrt(5))/2=(1-2.236067978)/2=-1.236067978/2=-0.618033989=-0.618
x3=(1+sqrt(5))/2
The zeros are: (1-sqrt(5))/2=-0.618, 1, and (1+sqrt(5))/2=1.618
The y-intercept is:
x=0→f(0)=(0)^3-2(0)^2+1→f(0)=0-2(0)+1→f(0)=0-0+1→f(0)=1
The y-intercept is y=1.
6) f(x)=-x^4+x^2+1
Zeros:
f(x)=0→-x^4+x^2+1=0
Factoring: Multiplyng both sides of the equation by -1:
(-1)(-x^4+x^2+1)=(-1)(0)
x^4-x^2-1=0
(x^2)^2-(x^2)-1=0
Changing x^2 by t:
t^2-t-1=0
at^2+bt+c=0; a=1, b=-1, c=-1
t=(-b+-sqrt(b^2-4ac))/(2a)
t=(-(-1)+-sqrt((-1)^2-4(1)(-1))/(2(1))
t=(1+-sqrt(1+4))/2
t1=(1+-sqrt(5))/2=(1+2.236067978)/2=3.236067978/2=1.618033989=1.618
t2=(1-sqrt(5))/2=(1-2.236067978)/2=-1.236067978/2=-0.618033989=-0.618
t^2-t+1=0→(t-1.618)(t-(-0.618))=0→(t-1.618)(t+0.618)=0
and t=x^2, then:
(x^2-1.618)(x^2+0.618)=0
Factoring the first parentheses using a^2-b^2=(a+b)(a-b), with:
a^2=x^2→sqrt(a^2)=sqrt(x^2)→a=x
b^2=1.618→sqrt(b^2)=sqrt(1.618)→b=1.272
(x^2-1.618)(x^2+0.618)=0→(x+1.272)(x-1.272)(x^2+0.618)=0
The zeros are:
x+1.272=0→x+1.272-1.272=0-1.272→x1=-1.272
x-1.272=0→x-1.272+1.272=0+1.272→x2=1.272
The zeros are: -1.272, and 1.272
The y-intercept is:
x=0→f(0)=-(0)^4+(0)^2+1→f(0)=-0+0+1→f(0)=1
The y-intercept is y=1.
Volume of a cone= 
When you calculate it, you will get 167.55
Then you will round that to 168.
So, the answer is D. 168 cubic cm
When you calculate it, you will get 167.55
Then you will round that to 168.
So, the answer is D. 168 cubic cm