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Trava [24]
3 years ago
7

Si tengo 30 marcadores y vendo 22 cuantos marcadores me quedan ?

Mathematics
1 answer:
AfilCa [17]3 years ago
6 0

Te van a quedar 8.

Porque tienes 30 pero le quitas 22 son 8 marcadores que te quedan.



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the plane is going at a speed of 22,000 per minute, namely, dx/dt = 22,000

so. .if you look at the picture below... we can simply use tangent
keeping in mind that, as the plane moves up and up, the angle is "constant", is never changing, whilst "y" and "x" and even "r" are changing, but we're not using "r" in this case.... we know what dx/dt is, we know the angle is a constant, this matters because the derivative of a constant is just 0

so, we really just need to find dy/dt then, because whilst dx/dt is telling us how fast is moving horizontally, dy/dt is telling us how long it took to cover those 10,000 feet

thus  \bf tan(\theta)=\cfrac{y}{x}\implies tan(\theta)=yx^{-1}\implies tan(9^o)=yx^{-1}\\\\
-----------------------------\\\\
0=\left( \cfrac{dy}{dt}\cdot \cfrac{1}{x} \right)+\left( y\cdot -\cfrac{1}{x^2}\cdot \cfrac{dx}{dt} \right)\implies 0=\cfrac{\frac{dy}{dt}}{x}-\cfrac{y\frac{dx}{dt}}{x^2}
\\\\\\


\bf \\\\\\
\cfrac{y\frac{dx}{dt}}{x^2}=\cfrac{\frac{dy}{dt}}{x}\implies \cfrac{y\frac{dx}{dt}}{x}=\cfrac{dy}{dt}
\\\\\\
\textit{so, what's "x" when y = 10000?}
\\\\\\
tan(9^o)=\cfrac{10000}{x}\implies x=\cfrac{10000}{tan(9^o)}\implies x\approx 63175.5

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