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3 years ago

Please help me out..(:

Mathematics

1 answer:

Nitella [24]3 years ago

4 0

Let's call the left side of this tirangle y and downside z.

3² + 6² = y²

y² = 45

y² + z² = (3 + x)²

45 + z² = 9 + 6x + x²

x² + 6² = z²

45 + x² + 6² = 9 + 6x + x²

45 + x² + 36 = 9 + 6x + x²

45 + 36 - 9 = 6x

72 = 6x

x = 12

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A. Area of a circle is given by

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So to find the rate of the area:

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$\frac{dr}{dt}=\frac{726}{(t+11)^{3}}$

Then

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Multipying and simplifying:

$\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$

The rate at which the area is increasing is given by expression $A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$ .

B. At t = 5, rate is:

$A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}$

$A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}$

$A'(5)=\frac{2408693760\pi}{4294967296}$

$A'(5)=1.76268$

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

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