the assumption being that "x" is a plain variable whilst "y" is a function, that matters because the chain rule would be needed for a function, not so for a plain variable.

$4x^2+4x+xy=5\implies 8x+4+\stackrel{\textit{product rule}}{\left( 1\cdot y+x\cdot \cfrac{dy}{dx} \right)}=0 \\\\\\ x\cfrac{dy}{dx}=-8x-4-y\implies \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x}$

now, we know that y(5) = -23, which is another way of saying that when x = 5, y = -23, but we already knew that, we can get that by simply plugging it into the equation hmmm y'(5), well

$\left. \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x} \right|_{\stackrel{x=5~}{\textit{\tiny y=-23}}}\implies \cfrac{-8(5)-4-(-23)}{5}\implies \cfrac{-21}{5}$

8 0

3 years ago

A trapezoid has an area of 30m^2. if all of its side lengths are tripled, what will its new area be

Norma-Jean [14]

Answer:

270

Step-by-step explanation:

Because we do not know what the side lengths are, as long as they multiply to 30m^2, it's fine

For this question, let's just say the base is 5, and the height is 6. If we triple 5, we get 15, and if we triple 6, we get 18. 15*18=270

Now what if, the sides are not 5 and 6. Will the area still be the same? Let's find out.

10*3=30 so we can say for this answer, the base is 3, and the height is 10.

10 tripled is 30, and 3 tripled is 9. 30*9=270

So as we look at these 2 answers. we can conclude that the new area, no matter the side lengths, will be 270

Hope this helpes!

5 0

4 years ago