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1 year ago

Find the slope of the line that passes through (5,12) and (9,7)

Mathematics

1 answer:

omeli [17]1 year ago

8 0

The slope will be the difference between the y-coordinates divided by the difference between the x-coordinates:

then the slope of the line is:

$m=\frac{12-7}{5-9}=\frac{5}{-4}=-\frac{5}{4}$

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3 years ago

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Find the area of the region between two concentric circular paths. If the radii of the circular paths are 210 m. and 490 m. resp

taurus [48]

Given :

The radii of the circular paths are 210 m. and 490 m.

To Find :

The area of the region between two concentric circular paths.

Solution :

Area of the outer circle :

$\: \qquad \dashrightarrow \sf{{ \pi \: \times {(490)}^{2} {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{7} \times \:490 \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times \cancel{490} \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ {22} \times 70 \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 754600 \: {m}^{2}}}$

⠀

Area of the inner circle :

$\: \qquad \dashrightarrow \sf{{ \pi \: \times {(210)}^{2} {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{7} \times \:210 \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times \cancel{210} \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ {22} \times 30 \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 138600 \: {m}^{2}}}$

⠀

Therefore,

Area of the region inside the circular paths :

$\: \qquad \dashrightarrow \sf{{ \ (754600 - 138600 ) \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 616000 \: {m}^{2}}}$

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Step-by-step explanation:

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