pablo just moved from cairo to chicago and needs to buy a complete set of winter gear, the store has 2 kinds of parkas and 8 kin
1 answer:
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Answer: a=8 and b=1
Step-by-step explanation:
If x represents the paddling speed, and y represents the speed of the current.
Then Relative speed in upstream =x-y
Relative time in downstream=x-y
When she paddles upstream then distance covered by her=
⇒8=(x-y)2 or 2(x-y)=8
Thus we get, a=1
When she paddles downstream then distance covered by her=
⇒8=(x+y)1 or 1(x+y)=8
Thus we get b=1
Using the Factor Theorem, the polynomials are given as follows:
1.
2.
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
<h3>What is the Factor Theorem?</h3>The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
Item a:
The parameters are:
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
Item b:
The roots are:
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
Item 3:
The roots are:
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
More can be learned about the Factor Theorem at brainly.com/question/24380382
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