Answer:
Step-by-step explanation:
<u>Equation of a Polynomial</u>
Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:
Where a is the leading coefficient.
We know the three roots of the polynomial -6, -3, and 1, thus:
Since the y-intercept of the polynomial is y=90 when x=0:
90=a(0+6)(0+3)(0-1)
90=a(6)(3)(-1)=-18a
Thus
a = 90/(-18) = -5
The polynomial is:
We must write it in standard form, so we have to multiply all of the factors as follows:
9×27+2×31-28= n
243+62-28=n
277=n
n=277
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Answer:
5
Step-by-step explanation:
First do substitution,
Which means |(4)-3|+4
Therefore 1+4=5
