What single decimal multiplier would you use to increase by 15% followed by a 17% decrease?
2 answers:
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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.
Answer:
Step-by-step explanation:
hg(x) means you multiply h(x) times g(x) and then we will set it equal to .
hg(x) = which simplifies to
. Now set that equal to
:
and get everything on the same side and factor:
. Factor by grouping:
and factor out what's common in each set of ( ):
which factors out to
. But
factors somoe to:
(x + 1)(x - 1)(x - 1) = 0 So the solutions for this are
x = -1, 1