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3 years ago

5

The scale drawing for Lydia’s room is drawn so that 1 cm = 1 ft. If the scale drawing shows the area of her room to be 51 square

cm, what is the actual area of her room?

1 answer:

butalik [34]3 years ago

3 0

Should be 51 ft. sonve 1 cm = 1 ft

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Sauron [17]

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3 years ago

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

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Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

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Simplify the leading term as

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Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

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$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

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$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

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3 years ago

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2

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》2

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1 year ago