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damaskus [11]
3 years ago
12

4/9 = 13/q I'm supposed to solve it and round it to the nearest hundredth if necessary

Mathematics
1 answer:
Elodia [21]3 years ago
8 0

Answer:

5.78

Step-by-step explanation:

Multiply 13 to both sides to get q by itself

4/9*13=q

this gives you

5.77777778=q

but we need to round it to the nearest hundredth

so

5.78

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$e^{-(x^2+2y^2)/10^4}=k$

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The equation is equivalent to

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We sketch the level curves for K =1,2,3 and 4.

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

b). We have :

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

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ 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 $\frac{dr}{dt}=\lambda \triangledown C$

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

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$\ln y=2 \ln x$

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$\Rightarrow kx_0^2=y_0$

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

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

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