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3 years ago

12

Use pictures or words to explain how to use the sum of 13 to show how to add in any order

1 answer:

schepotkina [342]3 years ago

6 0

3+3+4+3 im sure this is the answer just double chek

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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

Find the value of x that will make A||B<br> A-<br> 2x + 50<br> 5x - 80<br> B-<br> x = [?]

LenKa [72]

Answer:

15

Step-by-step explanation:

If A||B then the sum of given angles must be equal to 180°

2x + 5 + 5x - 80 = 180 add like terms

7x - 75 = 180 subtract 75 from both sides

7x = 105 divide both sides by 7

x = 15

8 0

3 years ago

Read 2 more answers

What is the quotient of 8887/4

Savatey [412]

Answer:

2221.75

Step-by-step explanation:

8887 ÷ 4 = 2221.75

4 0

2 years ago

Read 2 more answers

I donk know what to do

ohaa [14]

What’s the question?

7 0

3 years ago

The solution to the system equations

katovenus [111]

Let's solve this system of equations through substitution.

We have these two equations.

-7x-2y=14

6x+6y=18

Now let divide the second equation by 6.

6x+6y=18 ----> x+y=3

Next, let us move y to the right side of the equation.

x+y=3 -------> x=3-y (x equals 3-y)

Because we found out that what x is in terms of y, we can input that in for every instance of x in this equation below.

-7x-2y=14 becomes -7(3-y)-2y=14 (Why? Because x equals 3-y!)

We have a one variable equation now and can solve for y.

-7(3-y)-2y=14

-21+7y-2y=14

5y=35

y=7

Plug in 7 for y in any equation to find x.

x+y=3

x+7=3

x=-4

answer: x=-4, y=7

3 0

3 years ago