Answer:
4
Step-by-step explanation:
4*4*4=16*4=64
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Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

where
. Each interval has length
.
At these sampling points, the function takes on values of

We approximate the integral with the Riemann sum:

Recall that

so that the sum reduces to

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

Just to check:

Answer:
<h2>
y = -4/9</h2>
Step-by-step explanation:
Given the system of equations y = 3/2 x − 6, y = −9/2 x + 21, since both expressions are functions of y, we will equate both of them to find the variable x;
3/2 x − 6 = −9/2 x + 21,
Cross multiplying;
3(2x+21) = -9(2x-6)
6x+63 = -18x+54
collecting the like terms;
6x+18x = 54-63
24x = -9
x = -9/24
x = -3/8
To get the value of y, we will substitute x = -3/8 into any of the given equation. Using the first equation;
y = 3/2x-6
y = 3/{2(-3/8)-6}
y = 3/{(-3/4-6)}
y = 3/{(-3-24)/4}
y = 3/(-27/4)
y = 3 * -4/27
y = -4/9
Hence, the value of y is -4/9
The nature of a graph, which has an even degree and a positive leading coefficient will be<u> up left, up right</u> position
<h3 /><h3>What is the nature of the graph of a quadratic equation?</h3>
The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.
Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.
The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.
Learn more about the graph of a quadratic equation here:
brainly.com/question/9643976
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