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2 years ago

100 points find the length of PQ

SAT

1 answer:

Zarrin [17]2 years ago

6 0

Answer:

32 cm is the length of PQ ans

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The point (−2,4) lies on the curve in the xy-plane given by the equation f(x)g(y)=17−x−y, where f is a differentiable function o

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The value of $\frac{dy}{dx}$ is -3. $\blacksquare$

<h2>Procedure - Differentiability</h2><h3 /><h3>Chain rule and derivatives</h3><h3 />

We derive an expression for $\frac{dy}{dx}$ by means of chain rule and differentiation rule for a product of functions:

$\frac{d}{dx}[f(x)\cdot g(y)] = [f'(x)\cdot \frac{dx}{dx}]\cdot g(y) + f(x) \cdot [g'(y)\cdot \frac{dy}{dx} ]$

$\frac{d}{dx}[f(x)\cdot g(y)] = f'(x)\cdot g(y) +f(x)\cdot g'(y)\cdot \frac{dy}{dx}$ (1)

If we know that $f(x) \cdot g(y) = 17-x-y$ , $f(-2) = 3$ , $f'(-2) = 4$ , $g(4) = 5$ and $g'(4) = 2$ , then we have the following expression:

$-1-\frac{dy}{dx} = (4)\cdot (5) + (3)\cdot (2) \cdot \frac{dy}{dx}$

$-1-\frac{dy}{dx} = 20 + 6\cdot \frac{dy}{dx}$

$7\cdot \frac{dy}{dx} = -21$

$\frac{dy}{dx} = -3$

The value of $\frac{dy}{dx}$ is -3. $\blacksquare$

To learn more on differentiability, we kindly invite to check this verified question: brainly.com/question/24062595

<h3>Remark</h3>

The statement is incomplete and full of mistakes. Complete and corrected form is presented below:

The point (-2, 4) lies on the curve in the xy-plane given by the equation $f(x)\cdot g(y) = 17 - x\cdot y$ , where $f$ is a differentiable function of $x$ and $g$ is a differentiable function of $y$ . Selected values of $f$ , $f'$ , $g$ and $g'$ are given below: $f(-2) = 3$ , $f'(-2) = 4$ , $g(4) = 5$ , $g'(4) = 2$ .

What is the value of $\frac{dy}{dx}$ at the point $(-2, 4)$ ?

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2 years ago