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Monica [59]
2 years ago
7

Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫

y%5E%7B2%7D%20%7D%20%7D" id="TexFormula1" title="\frac{1}{\sqrt{x^{2} +y^{2} } }" alt="\frac{1}{\sqrt{x^{2} +y^{2} } }" align="absmiddle" class="latex-formula">dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4\leq x^{2} +y^{2} \leq 9
Mathematics
1 answer:
xenn [34]2 years ago
5 0

It sounds like <em>R</em> is the region (in polar coordinates)

<em>R</em> = {(<em>r</em>, <em>θ</em>) : 2 ≤ <em>r</em> ≤ 3 and 0 ≤ <em>θ</em> ≤ <em>π</em>/2}

Then the integral is

\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}

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The top piece from a model of city hall is shown below.
alexandr402 [8]

Answer:

The area that she painted = 896 mm^2

Step-by-step explanation:

Given:

The given figure is a pyramid with square base.

Here we need to find the surface area of the figure that need to be painted.

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Read 2 more answers
Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?
Softa [21]

\boxed{ \mathfrak { question↷}}

Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}

\boxed{ \mathfrak { solution↷}}

Let Pip get be x and fiona get be x+35

Ratio = 6:1

\tt \frac{x + 35}{x }  = 6

\tt \: x + 35 = 6x

\tt \: 5x = 35

\tt \: x = 7

\boxed{ \sf \: Total  \: money = x + x + 35 = 14+ 35 = £49}

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A line parallel to one side of a triangle divides the other two sides proportionally true or false?
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Answer:

true

Step-by-step explanation:

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8 0
3 years ago
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