Which of the following functions is NOT a polynomial function?

Mathematics

1 answer:

Leni [432]2 years ago

7 0

Step-by-step explanation:

Option d is not a polynomial

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

Chart and assignment above, any actual help is appreciated!! Eighth grade math :)

Minchanka [31]

1. Car Mart sell 11 cars per day.
You can use the table by looking at day 2 and day 3. You can see underneath it, it shows how many cars is left after that particular day. So from day 2, you have 43 cars left and day 3, you got 32 cars left. From 43 car to 32 car is losing 11 car. So each day the Car Mart sell 11 car.

2. First we know that after 3 days, Winston have 32 cars left and after 5 day, it has 12 cars left.
Here’s the chart that I made for Winston:
Each day, Winston’s sell 10 cars. (Lose 10 cars per day)