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2 years ago

C is the midpoint of AD. B is the midpoint of AC. AC=13. What is the length of BD?

Mathematics

1 answer:

notka56 [123]2 years ago

5 0

Answer:

19.5

Step-by-step explanation:

If C is the midpoint of AD, and AC=13 then AD = 2 x 13 = 26

If B is the midpoint of AC, then AB = 13 ÷ 2 = 6.5

So BD = AD - AB = 26 - 6.5 = 19.5

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$\ln y=\dfrac12\ln x+x^2\ln e+12\ln(x^2+5)$

$\ln y=\dfrac12\ln x+x^2+12\ln(x^2+5)$

Now take the derivative of both sides with respect to $x$ :

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}$

$\dfrac{\mathrm dy}{\mathrm dx}=\left(\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}\right)y$

$\dfrac{\mathrm dy}{\mathrm dx}=\left(\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}\right)\sqrt x\,e^{x^2}(x^2+5)^{12}$

I'd stop there, but you could condense the right side a bit to get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x^4+21x^2+48x+5}{2x(x^2+5)}\sqrt x\,e^{x^2}(x^2+5)^{12}$

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Answer:

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