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3 years ago

13

I’ll give you brainiest if you answer correctly! I need help

1 answer:

Maurinko [17]3 years ago

7 0

Answer:

y= -3/11x + 13

Step-by-step explanation:

hope this helps ( my cousins helped me) :))

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Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

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

are actually the curves

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

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

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

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

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

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

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

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

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

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

7 0

3 years ago

Type the expression that results from the following series of steps:

Sever21 [200]

6-z

Z-6 would be wrong because the question said start with 6

3 0

2 years ago

The quotient of a number and -9 increased by 10 is 11.

andrezito [222]

So the division of a number and -9 or
x/-9

+10=11 or

(x/-9)+10=11
subtract 10 from both sides
x/-9=1
multiply both sides by -9
x=-9

3 0

3 years ago

Read 2 more answers

Please help due by tonight EXPLAIN because I don’t want it to be wrong it’s one question. If you don’t know, don’t answer.

Annette [7]

Answer: C

Step-by-step explanation:

6 0

3 years ago

Find the value of x. Then find the measure of each interior angle. Show work algebraically

OleMash [197]

Answer:

Step-by-step explanation:

W=180-144

W=36 degrees

The sum of angles in a triangle always sum to 180 degrees.

6x+1+7x+36=180

13x+37=180

13x=143

x=11

U=6x+1

U=6(11)+1=67 degrees

V=7x

V=7(11)=77 degrees so

x=11 degrees, U=67 degrees, V=77 degrees, and W=36 degrees.

3 0

3 years ago