Factor the polynomial function over the complex numbers. f(x)=x4+9x3+15x2+9x+14 Enter your answer in the box. f(x)=
1 answer:
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A quadrilateral is said to be a parallelogram
1.Opposite sides are equal and parallel.
2. Diagonal bisect each other.
3. Opposite angles are equal.
It is given that , a Parrallelogram is graphed on a coordinate plane so the two points are in the first quadrant and two points are in the third quadrant.
Suppose ABCD is a Parallelogram.Then AB=CD and AD=BC.
Given, Vertices A,B lies in first Quadrant and Vertices C and D lies in Third Quadrant.Then Vertices of Parallelogram ABCD are
A=( x, y) and B=( y, x)
Then, C= (- x,- y) and D= (- y,- x), Arranged in Alphabetical order, that is A,B and C and D.
Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
<h3>Riemann sum</h3>When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
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<em>Additional comment</em>
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
