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tigry1 [53]
3 years ago
12

Write 41 2/3% as a fraction in lowest form

Mathematics
1 answer:
Anika [276]3 years ago
5 0
13 2/3 is your anwser
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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
Angie and Kenny play online video games. Angie buys 1 software package and 2 months of game play, Kenny buys 2 software packages
Vikentia [17]
10 because 45x3=135 205-125=70 70 divided by 7 equals 10
5 0
2 years ago
PLEASE HELP asap it’s for a quiz if you know at least one answer please tell me
VARVARA [1.3K]
  1. 15
  2. about 94.25
  3. about 706.86

Lmk if you want to know how I got the answers

3 0
2 years ago
If a printer prints 28 copies in 1 minute how many would it print in 3 minutes and 45 seconds?
Wittaler [7]

3minutes 45 seconds = 3 45/60 = 3.75 minutes

28 copies/ 1 minute = x copies/3.75 minutes

using cross products

28 * 3.75 = 1 * x

105 = x

We can print 105 copies in 3 3/4 minutes

3 0
3 years ago
The condition of the car and its mileage are important variables to consider when making a decision to buy a used car.
zubka84 [21]

Answer:

True!

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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