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wel
3 years ago
13

Order the following from least to greatest. 0.208, 0.0769, 0.546, 0.317, 0.00998​

Mathematics
1 answer:
OlgaM077 [116]3 years ago
5 0
0.00998, 0.0769, 0.546, 0.317, 0.208
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1 year ago
Find the following integral
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There's nothing preventing us from computing one integral at a time:

\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2

\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2

\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx

Expand the integrand completely:

x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x

Then

\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}

4 0
2 years ago
Use the figure below to find the distance across the river (IK)
Black_prince [1.1K]
<h2>JK = 18m</h2><h2>_______________</h2>

<u>Step-by-step explanation:</u>

ΔJLK = ΔNLM ( <em>v</em><em>e</em><em>r</em><em>t</em><em>i</em><em>c</em><em>a</em><em>l</em><em>l</em><em>y</em><em> </em><em>o</em><em>p</em><em>p</em><em>o</em><em>s</em><em>i</em><em>t</em><em>e</em><em> </em>Δ)

ΔJKL = ΔNML ( <em>e</em><em>a</em><em>c</em><em>h</em><em> </em><em>9</em><em>0</em><em>°</em><em> </em><em>)</em>

so,

triangle JKL = triangle NML (<em>b</em><em>y</em><em> </em><em>A</em><em>A</em><em> </em><em>s</em><em>i</em><em>m</em><em>i</em><em>l</em><em>a</em><em>r</em><em>i</em><em>t</em><em>y</em><em>)</em>

JK / KL = NM / ML

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JK = 42 × 21 ÷ 49

JK = 18m

<h2>_______________</h2><h2>FOLLOW ME</h2>
3 0
3 years ago
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