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3 years ago

Plssssssssssssssss help me

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

8 0

Square prism

because of the two squares on the side and it’s a prism not a pyramid because it just isn’t lol

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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

Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on X right so far. Select

dsp73

Answer:

A. 80-5x

Step-by-step explanation:

Let the number of rides be represented by = x

Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on x right so far.

The number of rides Thomas has been on so far= 5 × x = 5x

The expressions to show the number of tickets that Thomas has left is written as:

80 - 5x

Option A is the correct option.

3 0

3 years ago

Read 2 more answers

You have quarters and dimes that total $2.80. your friends says its possible that the number of quarters is 8 more than the numb

Sidana [21]

$\text{Let the number of dimes be x, then as per the friend the number of }\\
\text{quarters should be 8 more than dimes, so number of quarters}=x+8\\
\\
\text{we know that the value of 1 dime is }\$ 0.10 \text{ value of one quarter is }\$0.25\\
\\
\text{And since the total value of quarters and dimes is }\$2.80, \text{ so we have}\\
\\
0.10(x)+0.25(x+8)=2.80\\
\\
\Rightarrow 0.10x+0.25x+2=2.80\\
\\
\Rightarrow 0.35x=2.80-2\\
\\
\Rightarrow 0.35x=0.80$

$\Rightarrow x=\frac{0.80}{0.35}=2.29\\
\\
\text{so if we take 2 dimes then we'll have to take 10 quarters according to friend.}\\
\\
\text{So the statement of friend is }$ WRONG

6 0

3 years ago

A television regularly selling for $500 is marked down to $300.

Igoryamba

He saves $200 (the amount of change over the original amount $500

200/500 = 2/5 and 2/5 = 40% (divide 2 by 5 and get .4 which = 40%)

40% discount is the answer to your question

3 0

3 years ago

SOMEONE PLEASE HELP!<br>Set up an inequality showing that the radicand cannot be negative.

Stolb23 [73]

Answer:

3t-9 >= 0

Step-by-step explanation:

Original function f(t)= square root 3t-9

There cannot be a negative in the radicand therefore 3t-9 cannot equal a negative number.

6 0

3 years ago

Read 2 more answers