3 years ago

What fraction of the rectangle is shaded? write the answer as a rational expression in simplified form.

1 answer:

3 0

Area of rectangle = x(x+2) = x^2 +2x

area of triangle = x*2/2 = x

so the shaded fraction of the rectangle will be x(x+2)/(x+2)=x

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BlackZzzverrR [31]

Answer:

x=81 or 1/3

Step-by-step explanation:

$x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3$

3 0

3 years ago

Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=2.

astraxan [27]

$\bf \textit{area of a circle}=A=\pi r^2
\\\\\\
\cfrac{dA}{dt}=\pi \cdot 2r^1\cdot \cfrac{dr}{dt}\implies \cfrac{dA}{dt}=\pi \cdot 2r\cdot \cfrac{dr}{dt}\quad 
\begin{cases}
r=2\\
\frac{dr}{dt}=3
\end{cases}
\\\\\\
\cfrac{dA}{dt}=\pi \cdot 2(2)(3)$