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3 years ago

13

A box of markers weighed 4 2/3 ounces.

1 answer:

Ahat [919]3 years ago

5 0

Answer:

i got none just me? i got 4

Step-by-step explanation:

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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

AB = [ 4 ]. Find A if B=(22]

Vladimir79 [104]

Answer:

A = 2/11

Step-by-step explanation:

22A= 4

(22A)/22 = 4/22

A = 4/22 = 2/11

7 0

3 years ago

HELP ME PLEASE LOVE THOU <3

12345 [234]

Answer:

$100\pi$

Step-by-step explanation:

Total Surface Area of cylinder = Lateral Surface Area + Area of both circle bases.

Lateral Surface Area = Circumference of Circle $\times$ Height

Lateral Surface Area = $(\pi \times2\times5) \times 5=50\pi$

Area of one circle base: $\pi (5)^{2} =25\pi$

Area of both circle bases: $25\pi \times2=50\pi$

Total Surface Area = $50\pi +50\pi =100\pi$

7 0

3 years ago

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I need to figure out how to find the top blank

dmitriy555 [2]

I think its 384 because if you multiply the two numbers underneath then you get 384 which is how they got all the other numbers

6 0

3 years ago

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6. Suppose that a password for a computer system must have at least 6, but no more than 9 characters, where each character in th

Verizon [17]

Answer:

How many of these passwords contain at least one occurrence of at least one of the five special characters?

6 0

2 years ago

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