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Doss [256]
3 years ago
11

ILL MARK BRAINLIST , pls help n

Mathematics
1 answer:
bearhunter [10]3 years ago
5 0

Answer:

33

Step-by-step explanation:

{x}^{2}  - 5x  -  2 = 0 \\  \\ equating \: it \: with \\ a {x}^{2}  + bx + c = 0 \\ we \: find :  \\ a = 1 \\ b = -  5 \\ c =  - 2 \\  \\  {b}^{2}  - 4ac \\  =  {( - 5)}^{2}  - 4 \times 1( - 2) \\    = 25 + 8 \\   = 33 \\  \\ by \: quadratic \: formula \\  \\ x =  \frac{ - b \pm \sqrt{ {b}^{2} -4ac }   }{2a}  \\  \\ x =  \frac{ - ( - 5) \pm \sqrt{33}}{2 \times 1}  \\  \\ x =  \frac{ 5 \pm \sqrt{33}}{2}...(1)  \\  \\x =  \frac{ 5 \pm \sqrt{n}}{2}...(2)  (given)\\  \\ equating \: equations \: (1) \: and \: (2) \\  \\  \huge \red{ \boxed{n = 33}}

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PLZ HELP!!! Use limits to evaluate the integral.
Marrrta [24]

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]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

where 1\le i\le n. Each interval has length \Delta x_i=\frac{2-0}n=\frac2n.

At these sampling points, the function takes on values of

f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}

We approximate the integral with the Riemann sum:

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4

so that the sum reduces to

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

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

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

Just to check:

\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28

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Margarita [4]

Answer:

Step-by-step explanation:

The slope is the difference in y-coordinates of the 2 points divided by the corresponding difference in x-coordinates.

For example:

Find the slope of the line joining the points (3, 5) and (-2, 1)

The slope = (5 - 1) / (3 - (-2))

= 4/(3+2)

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NOTE:

You would get the same result if you reversed the values

- that is (1 - 5)/(-2 - 3

= -4/-5

= 4/5.

The important thing to remember is to use <em>corresponding </em>values in the calculation.

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3 years ago
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