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3 years ago

Can somebody help me with these questions?

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

6 0

For 6, it's A. For 7, it's A, and for the last one, what's the question?

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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

The dimensions of a wading pool shaped like a rectangular prism are shown below. What is the volume of the pool?

sergey [27]

Answer:

i believe its b

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

In the image below, ABC ~ DEF What is the length of EF and the measure of D

Gwar [14]

If triangle ABC is congruent to triangle DEF, then EF = BC = 27
This is because BC and EF are the last two letters of ABC and DEF respectively. They match up and correspond, being congruent by CPCTC

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Similarly, if triangle ABC is congruent to triangle DEF, then angle D = angle A = 49 degrees

The letter D and the letter A are the first letters of DEF and ABC respectively. So they match up and are congruent by CPCTC

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

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So in short, the answer is choice B) 27; 49

7 0

4 years ago

What does 11 meters equal in centimeters

joja [24]

The answer is 1100 centimeters.

4 0

4 years ago

What is the value of a fraction when the numerator and denominator are the same? Please help.

vagabundo [1.1K]

The value would be always 1 because....
1) When the numerator and a denominator are the same they would be whole which is 1.
2) For example, 10/10 equals 1
3) Another example, 120/120 equals a whole which is 1 :)
4) Please give this a THANKS and the BRAINIEST ANSWER/CROWN!!!
5) HAVE A GREAT LOVELY DAY!!! :) :D

8 0

3 years ago

Read 2 more answers