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2 years ago

11

8r= -64 what does the 8r stand for?

1 answer:

Marianna [84]2 years ago

8 0

Answer:

r=8

Step-by-step explanation:

The number we are looking for is represented by 'r' which is multiplied by 8

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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

2 years ago

PLEASE WHAT IS THE AREA OF THIS HELP ME PLEASE

BARSIC [14]

Answer:

it should be 14,580 m^2

(the ^2 means squared btw)

7 0

3 years ago

Can 2 liters fit into 1/2 of a gallon?

svetlana [45]

Yes. bc once the first two liter goes in it will prolly fill up half of the the 1/2 gallon it will foam down and the other one will fit also

4 0

3 years ago

Read 2 more answers

Can you answer this for me? asap

galben [10]

46+19+54= 119, so the answer is 119

8 0

3 years ago

Read 2 more answers

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total

ololo11 [35]

Answer:

Step-by-step explanation:

c + f = 16......c = 16 - f

340c + 910f = 9430

340(16 - f) + 910f = 9430

5440 - 340f + 910f = 9430

-340f + 910f = 9430 - 5440

570f = 3990

f = 3990/570

f = 7 <====== 7 first class tickets bought

c + f = 16

c + 7 = 16

c = 16 - 7

c = 9 <====== 9 coach tickets bought

3 0

3 years ago