Karen wants to buy 5 pounds of baby carrots. The packages of carrots each weigh14 ounces. How many will she need to buy to reach
1 answer:
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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.
Answer:
Average rate of fall =
Step-by-step explanation:
Since they give you an expression for the position of the object as a function of time, one can derive the average velocity of the object during the first 3 seconds of the fall by estimating the position of the object at time 0, the position of the object at time 3 seconds, finding the displacement of the object (distance covered) in that interval of time (via a subtraction of these two quantities), and finally dividing this change by the elapsed time (3 seconds) thus using the concept that velocity is the quotient between distance covered over the elapsed time:
Average rate of fall = (h(3) - h(0))/ 3
Average rate of fall =