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True [87]
2 years ago
15

Plz help me!!!!!!!! Which expressions are equivalent? A. B. C. D.

Mathematics
1 answer:
likoan [24]2 years ago
6 0

Answer:

Option A

Step-by-step explanation:

The answer is Option A because - \frac{2}{3} j + \frac{1}{5}k can be writen as \frac{1}{5}k - \frac{2}{3}j.

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Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
SOVA2 [1]

y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

Over each subinterval, we approximate f(x) with the quadratic polynomial

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that the integral we want to find can be estimated as

\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

5 0
3 years ago
How do you solve this question
Wewaii [24]

<h2>Solution:.</h2>

Let the ceilings be <em>a</em><em> </em><em>&</em><em> </em><em>b</em>

and the distance from one corner of the ceiling to the opposite be <em>c</em>

<em>then </em><em>using</em><em> </em><em>Pythagoras</em><em> theorem</em>

c =  \sqrt{a {}^{2} +  b  {}^{2} } \\  c =    \sqrt{16 {}^{2} +  12  {}^{2} } \\ c =  \sqrt{256 + 144 }  \\ c =  \sqrt{400}  \\ c = 20

hence ,c .°. the distance from one corner of the ceiling to the opposite is<em> </em><em>2</em><em>0</em>

3 0
2 years ago
Please answer &lt;33 I would lava it :)
allsm [11]

Answer:

5 gallons

Step-by-step explanation:

3/4 + 6/8 + 20/8 + 1

6/8 + 6/8 + 20/8 + 8/8

40/8 = 5 gallons

3 0
3 years ago
What is the slope of the line that passes through (3,5) (7,3)
Tju [1.3M]

Answer:

5/3

Step-by-step explanation:

6 0
3 years ago
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18 seats in 2 rows = <br> seats in 1 row
myrzilka [38]

Answer:

9

Step-by-step explanation:

18:2

?:1

?=9

3 0
2 years ago
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