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4 years ago

8

The radius of a circular baking tray is 6 cm. Find its area correct to 2 decimal places. Use the π button on your calculator for

π in your calculations.

1 answer:

ELEN [110]4 years ago

5 0

Answer:

$A \approx 113.10cm^2$

Step-by-step explanation:

The circle is a flat surface or area limited or closed by a circumference. It is a two-dimensional figure and is formed by making a curve where it will always have the same distance to the center. Its area can be calculated using the following formula:

$A=\pi r^2\\\\Where:\\\\r=radius$

Therefore the area of the circular baking tray is:

$A=\pi (6)^2=\pi*36=36 \pi=113.0973355\approx 113.10 cm^2$

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4 years ago

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Rewrite the second factor in the numerator as

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$\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt$
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So let's just assume the integral is being taken over a domain on which $\tan t>0$ so that $|\tan t|=\tan t$ . This allows us to write

$=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt$
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We can show pretty easily that

$\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C$
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$\displaystyle\int\sec^3t\csc t\,\mathrm dt=\frac12\sec^2t+\ln|\tan t|+C$

which means the integral above becomes

$=3\sqrt3\sec^2t+6\sqrt3\ln|\tan t|-18\sec t+18\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|-6\ln|\csc t+\cot t|+C$
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Back-substituting to get this in terms of $x$ is a bit of a nightmare, but you'll find that, since $t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}$ , we get

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Read 2 more answers