Convert this improper fraction into a mixed number. 13/6
1 answer:
You might be interested in
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
__
<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.
Point D is the midpoint of the outer circle that we aim to find the area of
The circle has a diameter of WZ and radii of WC and CZ
We know that YZ=YD=10 cm
Let DC be
and CY be 
The radius of the outer circle can be written as
or 
which we can equate to find the value of
Therefore, the radius of the circle is
And hence the area of the circle is
=324
The circle has a diameter of WZ and radii of WC and CZ
We know that YZ=YD=10 cm
Let DC be
The radius of the outer circle can be written as
Therefore, the radius of the circle is
And hence the area of the circle is