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3 years ago

7

The length, breadth and height of a room are 4 m, 3 m and 7 m respectively. Find the coast of white washing the walls of the roo

m and the ceiling at the rate of $6 per m².

1 answer:

scoray [572]3 years ago

3 0

Required area = lb + 2 × h ( l + b)
= 4 × 3 + 2 × 7 (4 + 3)
= 12 + 14 × 7 = 12 + 98 = 110 m²

Cost of white-washing at the rate of $6/m²
= $ 110 × 6 = $ 660

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Answer:

266 $\frac{2}{3}$

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2 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

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$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
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When $x=3$ , you're left with

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When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

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Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
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So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

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