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Maurinko [17]
3 years ago
9

Fiona loves pizza. She ate of a pizza for dinner one night. She ordered another pizza the

Mathematics
1 answer:
kvv77 [185]3 years ago
4 0

\stackrel{1st~night}{\cfrac{5}{6}}+\stackrel{\textit{2nd night}}{\cfrac{1}{3} }\implies \cfrac{(1)5~~ +~~(2)1}{\underset{\textit{using this LCD}}{6}}\implies \cfrac{7}{6}\implies 1\frac{1}{6}

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Would it not be 20?

Step-by-step explanation:

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Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1
erik [133]

Answer:

\mathbf{(\overline x , \overline y ) = (\dfrac{5}{8},  \dfrac{5}{14})}

Step-by-step explanation:

Given that:

y =  x^{2/3} at y = 0 , x = 1

Then:

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Area = \begin {bmatrix} \dfrac{3}{5}x^{5/3} \end {bmatrix} ^1_0

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Then:

\overline x = \dfrac{1}{A} \int^b_a x (f(x) -g(x) ) \ dx

\overline x = \dfrac{5}{3} \int^1_0 x (x^{2/3} -0 ) \ dx

\overline x = \dfrac{5}{3} \int^1_0 x^{5/3} \ dx

\overline x = \dfrac{5}{3} \ [\dfrac{3}{8}x^{8/3}]^1_0

\overline x = \dfrac{5}{3} \times \dfrac{3}{8}

\overline x = \dfrac{5}{8}

Similarly;

\overline y = \dfrac{1}{A} \int^b_a \dfrac{1}{2} \begin{bmatrix} (f(x)^)2 - (g(x))^2 \end {bmatrix}  \ dx

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\overline y = \dfrac{5}{3} \int^1_0 \dfrac{1}{2} \begin{bmatrix} (x^{4/3} ) \end {bmatrix}  \ dx

\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{1}{2}  (x^{7/3} ) \times \dfrac{3}{7} \end {bmatrix} ^1_0

\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{3}{14}  (x^{7/3} ) \end {bmatrix} ^1_0

\overline y = (\dfrac{5}{3} \times \dfrac{3}{14} )

\overline y = \dfrac{5}{14}

Thus; \mathbf{(\overline x , \overline y ) = (\dfrac{5}{8},  \dfrac{5}{14})}

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38 is the correct answer
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