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3 years ago

14

PLEASE HELP!! I know I need to factor but I’m confused…

2 answers:

Veseljchak [2.6K]3 years ago

5 0

Answer:

x = 16

Step-by-step explanation:

Given a tangent and a secant from an external point to a circle, then

The product of the external part and the whole of the secant is equal to the square of the tangent, that is

9(9 + x) = 15²

9(9 + x) = 225 ( divide both sides by 9 )

9 + x = 25 ( subtract 9 from both sides )

x = 16

Alex787 [66]3 years ago

5 0

X=16 I believe(SORRY IF YOU GET UT WRONG)

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3 years ago

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where k is a positive constant.

The equation is equivalent to

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Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

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$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

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Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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3 years ago